| CMSA QUANTUM MATTER AND QUANTUM FIELD THEORY SEMINAR |
Artan Sheshmani (CMSA) |
Higher rank flag sheaves and Vafa-Witten invariants |
We study moduli space of holomorphic triples $f: E_{1} \rightarrow E_{2}$, composed of (possibly rank $>1$) torsion-free sheaves $(E_{1}, E_{2})$ and a holomorphic map between them, over a smooth complex projective surface $S$. The triples are equipped with a Schmitt stability condition. We prove that when the Schmitt stability parameter becomes sufficiently large, the moduli space of triples benefits from having a perfect relative and absolute obstruction theory in some cases (depending on Chern character of $E_{1}$). We further generalize our construction to higher-length flags of higher rank sheaves by gluing triple moduli spaces, and extend earlier work, with Gholampur and Yau, where the obstruction theory of nested Hilbert schemes over the surface was studied. Here we extend the earlier results to the moduli space of flags $E_{1}\rightarrow E_{2}\rightarrow \cdots \rightarrow E_{n}$, where the maps are injective (by stability). There is a connection, by wall-crossing in the master space, developed by Mochizuki, between the theory of such higher rank flags, and the theory of Higgs pairs on the surface, which provides the means to relate the flag invariants to the local DT invariants of any threefold given by a line bundle over the surface, $X :={\rm Tot}(L \rightarrow S)$. The latter DT invariants, when L is the canonical bundle of S, contribute to Vafa-Witten invariants. Joint work with Shing-Tung Yau, arXiv:1911.00124" |
December 18, 2019, 12:00 pm - 1:00 pm at CMSA, 20 Garden St, G10 |
| HARVARD-MIT-MSR COMBINATORICS SEMINAR |
Dapeng Weng (MICHIGAN STATE UNIVERSITY) |
Cluster Duality of Grassmannian and a Cyclic Sieving Phenomenon of Plane Partitions |
Fix two positive integers $a$ and $b$. Scott showed that the homogeneous coordinate ring of the Grassmannian $Gr_{a, a+b}$ has the structure of a cluster algebra. This homogeneous coordinate ring can be decomposed into a direct sum of irreducible representations of $GL_{a+b}$ which correspond to non-negative integer multiples of the fundamental weight $w_a$. We introduce a periodic configuration space $Conf_{a+b,a}$ equipped with a natural potential function $W$ and prove that the tropicalization of $(Conf_{a+b,a},W)$ canonically parametrizes bases for the irreducible summands of the homogeneous coordinate ring of $Gr_{a,a+b}$, as predicted by the cluster duality conjecture of Fock and Goncharov. We identify the parametrizing set of each irreducible summand with a collection of plan partitions of size $a\times b$. As an application, we use this identification to show a cyclic sieving phenomenon of plane partitions under a certain sequence of toggling operations. This is joint work with Linhui Shen" |
December 13, 2019, 3:30 pm - 4:30 pm at Science Center 530 |
| CMSA CONDENSED MATTER/MATH SEMINAR |
Yuya Tanizaki (NCSU) |
Modifying instanton sums in QCD |
In the path integral formulation, we need to sum up all possible field configurations to define a QFT. If the configuration space is disconnected, we must specify how they should be summed by giving extra data to specify the QFT. In this talk, we try to restrict the possible number of instantons in SU(N) gauge theories, Yang-Mills theory and QCD, and we find out the vacuum structures of them. For consistency with locality, we have to introduce an extra topological degrees of freedom, and the theory acquires the 3-form symmetry. The existence of this 3-form symmetry leads to extra vacua, and moreover it turns out to give an interesting selection rule for the domain-wall excitation/vacuum decay." |
December 12, 2019, 11:50 am â" 1 :00 pm at CMSA, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Liang Xiao (BICMR) |
Slopes of modular forms and ghost conjecture of Bergdall and Pollack |
In classical theory, slopes of modular forms are p-adic valuations of the eigenvalues of the Up-operator. On the Galois side, they correspond to the p-adic valuations of eigenvalues of the crystalline Frobenius on the Kisin s crystabelian deformations space. I will report on a joint work in progress in which we seems to have proved a version of the ghost conjecture of Bergdall and Pollack. This has many consequences in the classical theory, such as some cases of Gouvea-Mazur conjecture, and some hope towards understanding irreducible components of eigencurves. On the Galois side, our theorem can be used to prove certain integrality statement on slopes of crystalline Frobenius on Kisin s deformation space, as conjectured by Breuil-Buzzard-Emerton. This is a joint work with Ruochuan Liu, Nha Truong, and Bin Zhao" |
December 11, 2019, 3:00 pm at Science Center 507 |
| HARVARD-MIT-MSR COMBINATORICS SEMINAR |
Ross Berkowitz (YALE UNIVERSITY ) |
A local limit theorem for cliques |
Let $X$ denote the number of cliques of size 7 in a uniformly random graph on $n$ vertices. What is the probability that $X$ is exactly equal to its mean? A central limit theorem estimating the behavior of $X$ on a large scale is a classic result, and in this talk we extend this to understanding the pointwise distribution of $X$. Additionally, we will examine some random variables where central limit theorems do not extend to nice local limit theorems" |
December 11, 2019, 4:15 pm - 5:15 pm at MIT 2-139 |
| CMSA QUANTUM MATTER AND QUANTUM FIELD THEORY SEMINAR |
Yuya Tanizaki (NCSU) |
Constraints on possible dynamics of QCD by symmetry and anomaly |
Low-energy dynamics of Quantum Chromodynamics (QCD) is an important subject for nuclear and hadron physics, but it is a strongly coupled system and difficult to solve. In this situation, symmetry and also anomaly give us an important guide to make a solid conclusion on possible behaviors of QCD. We find a new discrete anomaly in massless QCD, which says that the baryon number current is anomalously broken under the background gauge field for vector-like flavor symmetry and discrete axial symmetry. To match this anomaly in the chiral-symmetry broken phase, the existence of baryons as Skyrmions is mandatory, and Skyrmion current must show the same anomaly. This is satisfied in the ordinary scenario of chiral symmetry breaking, but not satisfied in an exotic scenario of chiral symmetry breaking proposed by Stern about two decades ago. Since the anomaly matching is applicable even with the sign problem, Stern phase is excluded even for the finite-density QCD at zero temperatures." |
December 11, 2019, 10:30 am - 12:00 pm at CMSA, 20 Garden St, G10 |
| CMSA SPACETIME SEMINAR |
Ramis Movassagh (MIT) |
Highly entangled quantum spin chains: Exactly solvable counter-examples to the area law |
In recent years, there has been a surge of activities in proposing exactly solvable quantum spin chains with surprising high amount of ground state entanglement--exponentially more than the critical systems that have $\log(n)$ von Neumann entropy. We discuss these models from first principles. For a spin chain of length $n$, we prove that the ground state entanglement entropy scales as $\sqrt(n)$ and in some cases even extensive (i.e., as $n$) despite the underlying Hamiltonian being: (1) Local (2) Having a unique ground state and (3) Translationally invariant in the bulk. These models have rich connections with combinatorics, random walks, Markov chains, and universality of Brownian excursions. Lastly, we develop techniques for proving the gap. As a consequence, the gap of Motzkin and Fredkin spin chains are proved to vanish as 1/n^c with c>2; this rules out the possibility of these models to be relativistic conformal field theories in the continuum limit. Time permitting we will discuss more recent developments in this direction and generic aspects of local spin chains" |
December 10, 2019, 2:30 pm at CMSA, 20 Garden St, G02 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Peter Love (TUFTS UNIVERSITY) |
Pictorial thinking in quantum contextuality |
Contextuality captures the ability of quantum systems to express correlations that are not accessible to physically reasonable classical hidden variable theories. Contextuality is a resource for quantum computing and an obstacle to efficient classical simulation of quantum computers. In this talk I will present a number of results concerning contextuality that use geometrical or graphical reasoning" |
December 10, 2019, 3:30 pm at Jefferson 356 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Jie-qiang Wu (MIT) |
Covariant phase space with boundaries |
The covariant phase space method of Iyer, Lee, Wald, and Zoupas gives an elegant way to understand the Hamiltonian dynamics of Lagrangian ïŹeld theories without breaking covariance. However, in the original literature, the authors didn t systematically treat the total derivatives and boundary terms. In this talk, I will introduce a systematic treatment of the covariant phase space formalism for ïŹeld theories with spatial boundaries. With this formalism, we can give an explicit algorithm for the Hamiltonian, only assuming that the configurations satisfy the equations of motion and boundary conditions. Our formalism also produce an extra boundary term in the Hamiltonian, which is non zero even in Einstein s general relativity with permissive gauge fixing at the boundary. To illustrate this covariant phase space formalism, we study an interesting example the Jackiw-Teitelboim gravity, where we can explicitly solve the phase space and symplectic form. Reference: arXiv:1906.08616" |
December 09, 2019, 12:00 pm - 1:00 pm at CMSA, 20 Garden St, G10 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Song Sun (BERKELEY) |
Singular Hermitian-Yang-Mills connections and reflexive sheaves |
The Donaldson-Uhlenbeck-Yau theorem relates the existence of Hermitian-Yang-Mills connections over a compact Kahler manifold with algebraic stability of a holomorphic vector bundle. This has been extended by Bando-Siu in 1994 to a class of singular Hermitian-Yang-Mills connections on reflexive sheaves. We study tangent cones of these singular connections in the geometric analytic sense, and show that they can be characterized in terms of certain algebro-geometric invariants of reflexive sheaves. In a sense, this can be viewed as a" |
December 06, 2019, 3:30 pm at Science Center 507 |
| HARVARD-MIT-MSR COMBINATORICS SEMINAR |
Nima Arkani-Hamed (HARVARD UNIVERSITY) |
The (Dual) Amplituhedron |
" |
December 06, 2019, 3:30 pm - 4:30 pm at Science Center 309 |
| CMSA SPECIAL SEMINAR |
Nick G. Jones (UNIVERSITY OF BRISTOL) |
Toeplitz determinants and correlations in topological quantum chains |
Topological phases protected by symmetry can occur in both gapped and critical systems. I will discuss recent work on such phases for non-interacting fermions in one dimension with spinless time-reversal symmetry. I will show how the phases are classified by a topological invariant and a central charge, explaining also the connection to edge modes. The bulk order parameters of these phases are correlators of fermionic string operators. I will explain how to derive exact asymptotics of these correlation functions using Toeplitz determinant theory, giving insight into the interplay between topology and criticality. This is largely based on the papers: Asymptotic correlations in gapped and critical topological phases of 1D quantum systems, N. G. Jones and R. Verresen, J. Stat. Phys. 175 (2019) Topology and edge modes in quantum critical chains, R. Verresen, N. G. Jones and F. Pollmann, Phys. Rev. Lett. 120 (2018" |
December 06, 2019, 1:00 pm - 2:00 pm at CMSA, 20 Garden St, G02 |
| CMSA CONDENSED MATTER/MATH SEMINAR |
Yizhi You (PRINCETON UNIVERSITY ) |
Emergent fractons and algebraic quantum liquid from plaquette melting transitions |
Paramagnetic spin systems with spontaneously broken spatial symmetries, such as valence bond solid (VBS) phases, can host topological defects carrying non-trivial quantum numbers, which enables the paradigm of deconfined quantum criticality. In this talk, I will show that the defects of the valence plaquette solid(VPS) order parameter, in addition to possessing non-trivial quantum numbers, have fracton mobility constraints in the VPS phase. The spinon inside a single vortex cannot move freely in any direction, while a dipolar pair of vortices with spinon pairs can only move perpendicular to its dipole moment. These mobility constraints, while they persist near QCP, can potentially inhibit the condensation of spinons and preclude a continuous transition from the VPS to the NĂ©el antiferromagnet. Instead, the VPS melting transition can be driven by the proliferation of spinon dipoles. In particular, we argue that a 2d VPS can melt into a stable gapless phase in the form of an algebraic bond liquid with algebraic correlations and long-range entanglement. Such a bond liquid phase yields a concrete example of the elusive 2d Bose metal with symmetry fractionalization" |
December 05, 2019, 11:50 am - 1:00 pm at CMSA, 20 Garden St, G10 |
| THURSDAY SEMINAR |
Peter Haine () |
Motivic Thom spectra and Ω^â MGL |
" |
December 05, 2019, 3:00 pm - 4:00 pm at Science Center 507 |
| GROSS-SIEBERT PROGRAM SEMINAR |
Daniel Pomerleano () |
A symplectic perspective on Intrinsic Mirror Symmetry |
I will explain some recent work relating symplectic cohomology to the intrinsic mirror constructions that have been discussed in the seminar (Gross-Hacking-Keel, Gross-Siebert, Keel-Yue-Yu,...). The talk will focus on the complex surface case in order to keep things relatively concrete. Towards the end of my talk, I will discuss some open questions" |
December 05, 2019, 4:00 pm at Science Center 232 |
| HARVARD-MIT-MSR COMBINATORICS SEMINAR |
Colin Defant (PRINCETON ) |
Valid Hook Configurations and Uniquely Sorted |
In his 1990 Ph.D. thesis, Julian West introduced the stack-sorting map, a function that sends permutations to permutations. I will describe a method for computing the number of preimages of an arbitrary permutation under this map. This method, which can be applied to answer many questions about the stack-sorting map, relies on new combinatorial objects called valid hook configurations. I will discuss a surprising connection between these objects and free probability theory. This connection will allow us to enumerate uniquely sorted permutations, which are permutations with exactly 1 preimage under the stack-sorting map.I will also briefly discuss some bijective enumerations of pattern-avoiding valid hook configurations and uniquely sorted permutations, including recent (separate) works of Hanna Mularczyk and Maya Sankar." |
December 04, 2019, 4:15 pm - 5:15 pm at MIT Room 2-139 |
| SNAPSHOTS OF MATH AT HARVARD |
Alex Cowan, Elana Kalashnikov, Dori Bejleri (HARVARD UNIVERSITY) |
Three stories from arithmetic statistics; Mirror symmetry for quiver flag varieties and their subvarieties; Compactifying moduli spaces |
" |
December 04, 2019, 2:00 pm - 3:00 pm at Science Center 507 |
| CMSA COLLOQUIUM |
Xiao-Gang Wen (MIT) |
Emergence of graviton-like excitations from a lattice model |
I will review some construction of lattice rotor model which give rise to emergent photons and graviton-like excitations. The appearance of vector-like charge and symmetric tensor field may be related to gapless fracton phases" |
December 04, 2019, 4:30 pm- 5:30 pm at CMSA, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Michele Fornea (IAS) |
On the arithmetic of elliptic curves over quintic fields |
Bhargava showed that 100% of quintic fields have non-solvable Galois closure. For this reason, the arithmetic of elliptic curves over such fields is beyond the reach of methods based on Heegner points. In this talk we will report on a joint work in progress with Zhaorong Jin about the p-adic variation of Hirzebruch-Zagier cycles. The aim is to establish new instances of the rank zero BSD-conjecture over quintic fields" |
December 04, 2019, 3:00 pm at Science Center 507 |
| *CANCELED* DIFFERENTIAL GEOMETRY SEMINAR |
Niky Kamran (MCGILL UNIVERSITY) |
*CANCELED* Non-uniqueness results for the Calderon inverse problem with local or disjoint data |
The anisotropic Calderon inverse problem consists in recovering the metric of a compact connected Riemannian manifold with boundary from the knowledge of the Dirichlet-to-Neumann map at fixed energy. A fundamental result due to Lee and Uhlmann states that there is uniqueness in the analytic case. We shall present counterexamples to uniqueness in cases when: 1) The metric smooth in the interior of the manifold, but only H" |
December 03, 2019, 4:15 pm - 5:15 pm at Science Center 507 - **CANCELED** |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Christopher King (NORTHEASTERN UNIVERSITY) |
Contractive bounds for quantum Markov semigroups |
Contractive bounds for semigroups on commutative algebras provide estimates for mixing times of classical Markov chains. Extensions of these bounds to matrix algebras offers the possibility to obtain similar bounds for the rate of convergence of quantum Markov semigroups. I will describe some progress in this direction based on non-commutative hypercontractive bounds and log Sobolev inequalities, and indicate some of the challenges which remain" |
December 03, 2019, 3:30 pm at Jefferson 356 |
| CMSA SPECIAL SEMINAR |
Yaoyu Zhang (IAS) |
A Fourier Analysis Perspective of Training Dynamics of Deep Neural Networks |
This talk focuses on a general phenomenon of Frequency-Principle that DNNs often fit target functions from low to high frequencies during the training. I will present empirical evidences on real datasets and deep networks of different settings as well as theoretical results about Frequency-Principle. Specifically, I will talk about a Linear Frequency-Principle dynamics derived from two-layer neural networks at the NTK regime, which quantifies the priority of different frequencies during the training and gives rise to an apriori generalization error bound based on the frequency composition of the target function" |
December 02, 2019, 3:00 pm - 4:00 pm at CMSA, 20 Garden St, G02 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
W. A. Zuniga-Galindo (CINVESTAV) |
Strings and Quantum Fields Over p-Adic Spacetimes |
I will discuss some recent results on the connections between local zeta functions with the regularization of p-adic Koba-Nielsen string amplitudes, and with the construction of quantum fields over p-adic spacetimes. The theory of local zeta functions was started in the 50s by Gelâfand and Weil. In the 70s Igusa developed a uniform theory of local zeta functions over local fields of characteristic zero. In the last years the theory has suffered a tremendous expansion due to the introduction of the motivic Igusa zeta functions by Denef and Loeser. By using the theory of local zeta functions is possible to establish (in rigorous way) the regularization of Koba-Nielsen amplitudes on R, C or Q_{p}. There is empirical evidence that in the limit p approaches to one, the p-adic strings are related with the ordinary ones. The theory of local zeta functions allows to define rigorously the limit p tends to one of p-adic Koba-Nielsen amplitudes. Since the 50s is known that the existence of fundamental solutions (Green functions) is consequence of the existence of meromorphic continuation for the Archimedean local zeta functions. This fact is also true in the p-adic case, for this reason the p-adic local zeta functions play a central role in the construction of quantum fields over p-adic spacetimes" |
December 02, 2019, 12:00 pm - 1:00 pm at CMSA, 20 Garden St, G02 |
| CMSA QUANTUM MATTER AND QUANTUM FIELD THEORY SEMINAR |
Meng Cheng (YALE UNIVERSITY ) |
Gapped boundary of symmetric topological phases and relative anomalies in (1+1)d CFTs |
Many (2+1)d topological phases admit gapped boundaries. In the presence of global symmetry, the classification of symmetric boundary conditions is further enriched. I will discuss recent work on classifying such boundary conditions for a doubled topological phase, and a general construction of such boundaries in symmetry-enriched string-net models using module categories. I will also describe how the results can be used to compute relative ât Hooft anomalies in (1+1)d CFTs algebraically" |
November 27, 2019, 10:30 am - 12:00 pm at CMSA, 20 Garden St, G10 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Or Hershkovits (STANFORD) |
Ancient solutions to the Mean Curvature Flow and applications |
In the last 35 years, geometric flows have proven to be a powerful tool in geometry and topology. The Mean Curvature Flow is, in many ways, the most natural flow for hypersurfaces in Euclidean space. In this talk, which will assume no prior knowledge, I will present recent progress in classifying ancient solutions to the mean curvature flow (including joints work with Kyeongsu Choi, Robert Haslhofer and Brian White). I will also explain how this classification assists in answering fundamental questions regarding the singularity formation of the flow, and describe what are the remaining challenges in converting the mean curvature flow into the powerful tool we hope it can become" |
November 26, 2019, 4:15 pm - 5:15 pm at Science Center 507 |
| CMSA SPACETIME SEMINAR |
Stephan Stieberger (IAS) |
Strings on the Celestial Sphere |
" |
November 26, 2019, 2:30 pm at CMSA, 20 Garden St, G10 |
| CMSA CONDENSED MATTER/MATH SEMINAR |
Yu-An Chen (CALTECH) |
Exact bosonization in higher dimensions and the duality between supercohomology fermionic SPT and higher-group bosonic SPT phases |
The first part of this talk will introduce generalized JordanâWigner transformation on arbitrary triangulation of any simply connected manifold in 2d, 3d and general dimensions. This gives a duality between all fermionic systems and a new class of lattice gauge theories. This map preserves the locality and has an explicit dependence on the second StiefelâWhitney class and a choice of spin structure on the manifold. In the Euclidean picture, this mapping is exactly equivalent to introducing topological terms (Chern-Simon term in 2d or the Steenrod square term in general) to the Euclidean action. We can increase the code distance of this mapping, such that this mapping can correct all 1-qubit and 2-qubits errors and is useful for the simulation of fermions on the quantum computer. The second part of my talk is about SPT phases. By the boson-fermion duality, we are able to show the equivalent between any supercohomology fermionic SPT and some higher-group bosonic SPT phases. Particularly in (3+1)D, we have constructed a unitary quantum circuit for any supercohomology fermionic SPT state with gapped boundary construction. This fermionic SPT state is derived by gauging higher-form symmetry in the higher-group bosonic SPT and ungauging the fermion parity. The bulk-boundary correspondence in (3+1)D fermion SPT phases will also be briefly discussed" |
November 25, 2019, 10:30 am - 11:30 am at CMSA, 20 Garden St, G10 |
| CMSA SPECIAL SEMINAR |
Philsang Yoo (YALE UNIVERSITY ) |
From Quantum Field Theory to Geometric Representation Theory |
Quantum Field Theory is a framework of fundamental physics, which in particular has played important roles in the modern development of various subjects in mathematics, including enumerative geometry, knot theory, and low-dimensional topology. On the other hand, Geometric Representation Theory is a subject in mathematics that studies a linear model of various types of symmetries using powerful techniques of algebraic geometry. In recent years, there has been much progress relating the two subjects, enriching the subject of Geometric Representation Theory. In this colloquium style talk, we will review some recent advancements on the topic. No prior knowledge of either Quantum Field Theory or Geometric Representation Theory will be assumed" |
November 25, 2019, 3:00 pm - 4:00 pm at CMSA, 20 Garden St, G10 |
| CMSA COLLOQUIUM |
Madhu Sudan (HARVARD UNIVERSITY) |
Communication Complexity of Randomness Manipulation |
The task of manipulating randomness has been a subject of intense investigation in the theory of computer science. The classical definition of this task consider a single processor massaging random samples from an unknown source and trying to convert it into a sequence of uniform independent bits. In this talk I will talk about a less studied setting where randomness is distributed among different players who would like to convert this randomness to others forms with relatively little communication. For instance players may be given access to a source of biased correlated bits, and their goal may be to get a common random bit out of this source. Even in the setting where the source is known this can lead to some interesting questions that have been explored since the 70s with striking constructions and some surprisingly hard questions. After giving some background, I will describe a recent work which explores the task of extracting common randomness from correlated sources with bounds on the number of rounds of interaction. Based on joint works with Mitali Bafna (Harvard), Badih Ghazi (Google) and Noah Golowich (Harvard)" |
November 25, 2019, 4:30 pm- 5:30 pm at CMSA, 20 Garden St, G10 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
David Svoboda (PERIMETER INSTITUTE) |
From para-Hermitian geometry to mirror symmetry |
In recent years, para-Hermitian geometry has been used to describe T-duality covariant spacetimes for string theory. In my talk, I will present applications of para-Hermitian geometry to 2D (2,2) SUSY sigma models and show that this geometry gives rise to a new, yet unexplored, notion of mirror symmetry" |
November 25, 2019, 12:00 pm - 1:00 pm at CMSA, 20 Garden St, G10 |
| CMSA GENERAL RELATIVITY SEMINAR |
Shahar Hadar (HARVARD UNIVERSITY) |
Universal signatures of a black holeâs photon ring |
The Event Horizon Telescope image of the supermassive black hole in the galaxy M87 is dominated by a bright, unresolved ring. General relativity predicts that embedded within this image lies a thin âphoton ring,â which is composed of an infinite sequence of self-similar subrings that are indexed by the number of photon orbits around the black hole. The subrings approach the edge of the black hole âshadow,â becoming exponentially narrower but weaker with increasing orbit number, with seemingly negligible contributions from high order subrings. In the talk, I will discuss the structure of the photon ring, starting with non-rotating black holes, and then proceeding to the complex patterns that emerge when rotation is taken into account. Subsequently I will argue that the subrings produce strong and universal signatures on long interferometric baselines. These signatures offer the possibility of precise measurements of black hole mass and spin, as well as tests of general relativity, using only a sparse interferometric array" |
November 22, 2019, 10:30 am - 11:30 am at Science Center 530 |
| CMSA SPACETIME SEMINAR |
Cristian Vergu (NIELS BOHR INSTITUTE) |
The Octagonal Alphabet |
" |
November 21, 2019, 2:30 pm at CMSA, 20 Garden St, G10 |
| GROSS-SIEBERT PROGRAM SEMINAR |
Tim Large () |
Introduction to Symplectic Cohomology |
My plan is to give a gentle discussion of symplectic cohomology, its algebraic structures, and its place in the HMS conjectures. I ll specialize to the (log) Calabi-Yau setting, and try see both the formal algebraic consequences of the CY hypothesis (basically, grading), as well as the consequences for the geometry at infinity (Pascaleff s basis for SH)" |
November 21, 2019, 4:00 pm at Science Center 232 |
| CMSA CONDENSED MATTER/MATH SEMINAR |
Natalie Paquette (CALTECH) |
Koszul duality in field theory & holography |
" |
November 21, 2019, 11:50 am â" 1 :00 pm at CMSA, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Yihang Zhu (COLUMBIA UNIVERSITY) |
Stabilization of the trace formula for abelian-type Shimura varieties |
In a recent joint work with Kisin and Shin, we compared the Grothendieck-Lefschetz trace formula for abelian-type Shimura varieties with the stable Arthur-Selberg trace formulas. In this talk I will sketch some key ideas in the proof." |
November 20, 2019, 3:00 pm at Science Center 507 |
| CMSA FLUID DYNAMICS SEMINAR |
Steven Chong (UNIVERSITY OF TWENTE, THE NETHERLANDS) |
Confined Rayleigh-BĂ©nard, rotating Rayleigh-BĂ©nard, double diffusive convection and quasi-static magnetoconvection: A unifying view on their scalar transport enhancement |
For Rayleigh-BĂ©nard under geometrical confinement, under rotation or the double diffusive convection with the second scalar component stabilizing the convective flow, they seem to be the three different canonical models in turbulent flow. However, previous research coincidentally reported the scalar transport enhancement in these systems. The results are counter-intuitive because the higher efficiency of scalar transport is bought about by the slower flow. In this talk, I will show you a fundamental and unified perspective on such the global transport behavior observed in the seemingly different systems. We further show that the same view can be applied to the quasi-static magnetoconvection, and indeed the regime with heat transport enhancement has been found. The beauty of physics is to understand the seemingly unrelated phenomena by a simplified concept. Here we provide a simplified and generic view, and this concept could be potentially extended to other situations where the turbulent flow is subjected to an additional stabilization" |
November 20, 2019, 3:35 pm at CMSA, 20 Garden St, G02 |
| CMSA QUANTUM MATTER AND QUANTUM FIELD THEORY SEMINAR |
Subir Sachdev (HARVARD UNIVERSITY) |
Models of optimal doping criticality in the cuprate superconductors |
There is now much experimental evidence for a significant change in the electronic structure of cuprate superconductors near a hole doping p=p_c optimal for superconductivity. Only for p > p_c do the electronic properties agree with the predictions of band theory. We argue that the data supports the existence of a quantum critical point (QCP) at p=p_c, and for p < p_c we have a novel state characterized by emergent gauge fields, possibly co-existing with conventional symmetry breaking orders. We present evidence that such a QCP is present in the Hubbard model with random, and all-to-all, hopping and exchange. We also discuss a SU(2) gauge theory for the QCP in model of fluctuating incommensurate spin density waves in the absence of disorder" |
November 20, 2019, 10:45 am - 12:15 pm at CMSA, 20 Garden St, G10 |
| CMSA FLUID DYNAMICS SEMINAR |
Haoran Liu (UNIVERSITY OF TWENTE, THE NETHERLANDS) |
Applications of Phase Field method: drop impact and multiphase turbulence |
Will a mosquito survive raindrop collisions? How the bubbles under a ship reduce the drag force? In nature and industry, flows with drops and bubbles exist everywhere. To understand these flows, one of the powerful tools is the direct numerical simulation (DNS). Among all the DNS methods, we choose the Phase Field (PF) method and develop some models based on it to simulate the complicated flows, such as flows with moving contact lines, fluid-structure interaction, ternary fluids and turbulence. In this talk, I will firstly introduce the advantages and disadvantages of PF method. Then, I will show its applications: drop impact on an object, compound droplet dynamics, water entry of an object and multiphase turbulence" |
November 20, 2019, 3:00 pm at CMSA, 20 Garden St, G10 |
| OPEN NEIGHBORHOOD SEMINAR |
Brooke Ullery (HARVARD UNIVERSITY) |
Polynomials vanishing on points in the plane |
We all know that any two points in the plane lie on a unique line. However, three points will lie on a line only if those points are in a very special position: collinear! More generally if Z is a set of k points, we can ask what the set of polynomials of degree d that vanish on all the points of Z looks like. The answer depends not only on the values of k and d, but also on the geometry of Z. This question, in some form, dates back to at least the 4th century. We will talk about several attempts to answer it throughout history and some surprising connections to modern algebraic geometry" |
November 20, 2019, 4:30 pm at Science Center 507 |
| HARVARD-MIT-MSR COMBINATORICS SEMINAR |
Sunita Chepuri (MINNESOTA) |
Plabic R-matrices |
Description: Postnikov s plabic graphs in a disk are used to parametrize totally nonnegative Grassmannians. One of the key features of this theory is that if a plabic graph is reduced, the face weights can be uniquely recovered from boundary measurements. On surfaces more complicated than a disk this property is lost. In this talk, we investigate a certain semi-local transformation of weights for plabic networks on a cylinder that preserves boundary measurements. We call this a plabic R-matrix. We explore the properties of the plabic R-matrix, including the symmetric group action it induces on plabic networks and its underlying cluster algebra structure" |
November 20, 2019, 4:15 pm - 5:15 pm at MIT 2-139 |
| LOGIC COLLOQUIUM |
George E. Smith (TUFTS UNIVERSITY) |
Theory-Mediated Measurement of Interlinked Constants Evidence of a Different Kind? |
In his landmark paper of 1900 in which he derived his law of blackbody radiation from Boltzmannâs theory of entropy, Planck invoked as evidence inferred values for a series of theoretically interlinked microphysical constants none of which had been measured with precision before. In doing so he initiated a kind of evidence that had never been successfully deployed before, yet quickly came to be central to modern microphysics. The talk will examine the distinctive logic underlying this kind of evidence and sketch the history of its becoming increasingly authoritative before ending with questions first about just what it is evidence for and finally about the extent to which the measurements achieving extraordinarily precise values of the constants can legitimately be said to have gained experimental access to specifics of the microphysical realm" |
November 20, 2019, 4:30 pm- 5:30 pm at Logic Center, Room 420, 2 Arrow Street |
| CMSA COLLOQUIUM |
Xi Yin (HARVARD UNIVERSITY) |
An Introduction to the Non-Perturbative Bootstrap |
I will discuss non-perturbative definitions of quantum field theories, some properties of correlation functions of local operators, and give a brief overview of some results and open questions concerning the conformal bootstrap" |
November 20, 2019, 4:30 pm- 5:30 pm at CMSA, 20 Garden St, G10 |
| INFORMAL GEOMETRY AND DYNAMICS SEMINAR |
Dawei Chen (BOSTON COLLEGE) |
Volumes and intersection theory on moduli spaces of differentials |
Computing volumes of moduli spaces has significance in many fields. For instance, the celebrated Witten s conjecture regarding intersection numbers on moduli spaces of Riemann surfaces has a fascinating connection to the Weil-Petersson volumes, which motivated Mirzakhani to give a proof via Teichmueller theory, hyperbolic geometry, and symplectic geometry. In this talk I will introduce an analogue of Witten s intersection numbers on moduli spaces of holomorphic differentials to compute the Masur-Veech volumes induced by the flat metric of the differentials. This is joint work with Moeller, Sauvaget, and Zagier (arXiv:1901.01785)" |
November 20, 2019, 4:30 pm at Science Center 530 |
| JOINT CMSA AND DEPARTMENT OF MATHEMATICS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Vishesh Jain (MIT) |
A combinatorial approach to the quantitative invertibility of random matrices |
Let $s_n(M_n)$ denote the smallest singular value of an $n\times n$ random matrix $M_n$. We will discuss a novel combinatorial approach (in particular, not using either inverse Littlewood--Offord theory or net arguments) for obtaining upper bounds on the probability that $s_n(M_n)$ is smaller than $\eta \geq 0$ for quite general random matrix models. Such estimates are a fundamental part of the non-asymptotic theory of random matrices and have applications to the strong circular law, numerical linear algebra etc. In several cases of interest, our approach provides stronger bounds than those obtained by Tao and Vu using inverse Littlewood--Offord theory." |
November 20, 2019, 3:15 pm - 4:15 pm at CMSA, 20 Garden St, G02 |
| DIFFERENTIAL GEOMETRY SEMINAR |
John Loftin (RUTGERS UNIVERSITY) |
Limits of Hitchin Representations for Rank-2 Lie Groups |
It is well known that on a closed oriented surface S of genus at least 2, Teichmuller space can be viewed a component of the representation variety of the fundamental group of S into PSL(2,R). Hitchin used Higgs bundles to formulate a generalization of this component for higher rank split real Lie groups such as PSL(n,R). In the rank 2 cases PSL(3,R), PSp(4,R), and G_2, there is additional interesting structure: 1) Labourie showed that one may reformulate Hitchin s construction, which involves a fixed background conformal structure on S, invariantly under the action of the mapping class group, and 2) Baraglia showed that Hitchin s equations, which in general produce a metric on a vector bundle, reduce in this case to coupled equations which are amenable to study by the maximum principle. We present this theory in terms of limits of representations for which the conformal structure on S degenerates to a nodal curve, and we discuss new joint work in progress with Qiongling Li and Andrea Tamburelli in the case of PSp(4,R) representations" |
November 19, 2019, 4:15 pm at Science Center 507 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Dan Cristofaro-Gardiner (SANTA CRUZ) |
Refined asymptotics for the ECH spectrum |
In previous work, Hutchings, Ramos and I studied the embedded contact homology (ECH) spectrum for any closed three-manifold with a contact form, and proved a volume identity showing that the leading order asymptotics recover the contact volume. I will explain recent joint work with Savale that sharpens this asymptotic formula by better understanding the subleading term. I will then discuss some conjectures about what an optimal bound on the subleading asymptotics might be: for example, for certain generic domains in \mathbb{R}^4, Hutchings has conjectured that the subleading asymptotics recover a contact Ruelle invariant. Future schedule is found here: https://scholar.harvard.edu/gerig/semina" |
November 15, 2019, 3:30 pm at Science Center 507 |
| HARVARD-MIT-MSR COMBINATORICS SEMINAR |
Jacob Bourjaily (PENN STATE UNIVERSITY) |
Stratifying On-Shell (Cluster) Varieties |
There exists a deep and powerful correspondence between physically important objects encoded by two-colored graphs called on-shell diagrams and specific (cluster variety) subspaces of the Grassmannian Gr(k,n) defined by the graphs boundary measurements. When these diagrams are planar, the corresponding on-shell varieties are positroids, but much less is known about those associated with non-planar diagrams. In this talk, I reviewâin broad termsâthe relevance of these objects to physics, and describe several ways to define their connection to Grassmannian geometry. I explain what is known about non-planar diagrams, including the brute-force classification of on-shell varieties of G(3,6). More details of these results can be found in [arXiv:1608.00006], [arXiv:1412.8475], and [arXiv:1212.5605]" |
November 15, 2019, 3:30 pm - 4:30 pm at Science Center 530 |
| CMSA SPACETIME SEMINAR |
Pierpaolo Mastrolia (UNIVERSITY OF PADOVA) |
Feynman Integrals and Intersection Theory, Pt. 2 |
" |
November 14, 2019, 2:30 pm at CMSA, 20 Garden St, G02 |
| THURSDAY SEMINAR |
Elden Elmanto and Tom Bachmann (HARVARD UNIVERSITY/MIT) |
Cancellation leftovers and homotopy invariance of presheaves with framed transfers |
" |
November 14, 2019, 3:00 - 4:20 pm at Science Center 507 |
| CMSA CONDENSED MATTER/MATH SEMINAR |
Michael Pretko (U COLORADO) |
Advances in Fracton Physics: Dualities, Field Theories, and Classification |
In this talk, I will give short informal explanations of three topics in the field of fractons with some interesting mathematical structure. I will begin with a detailed discussion of fracton-elasticity duality, relating the properties of tensor gauge theories to the elastic description of two-dimensional crystals. I will emphasize the role of symmetries in this duality, and also discuss how the duality extends to three dimensions, giving rise to âhigher-formâ analogues of fracton conservation laws. Next, I will discuss recent advances on the field theory description of fractons, showing how fractons can be obtained by gauging field theories with a âvectorâ global symmetry. Finally, I will describe recent work towards classifying fracton phases in terms of their fusion theory, which can be described as a module over the group ring of translations" |
November 14, 2019, 11:50 am - 1:00 pm at CMSA, 20 Garden St, G02 |
| BRANDEIS-HARVARD-MIT-NORTHEASTERN JOINT COLLOQUIUM |
Ellen Eischen (U OREGON) |
Some congruences and consequences in number theory and beyond |
In the mid-1800s, Kummer observed some striking congruences between certain values of the Riemann zeta function, which have important consequences in algebraic number theory, in particular for unique factorization in certain rings. In spite of its potential, this topic lay mostly dormant for nearly a century until it was revived by Iwasawa in the mid-1950s. Since then, advances in arithmetic geometry and number theory (in particular, for modular forms, certain analytic functions that play a central role in number theory) have enabled substantial extension to congruences in the context of other arithmetically significant data, and this has remained an active area of research. In this talk, I will survey old and new tools for studying such congruences. I will conclude by introducing some unexpected challenges that arise when one tries to take what would seem like immediate next steps beyond the current state of the art" |
November 14, 2019, 4:30 pm- 5:30 pm at Science Center Hall E |
| JOINT CMSA AND DEPARTMENT OF MATHEMATICS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Gourab Ray (UNIVERSITY OF VICTORIA) |
Logarithmic variance of height function of square-ice |
A homomorphism height function on a finite graph is a integer-valued function on the set of vertices constrained to have adjacent vertices take adjacent integer values. We consider the uniform distribution over all such functions defined on a finite subgraph of Z^2 with predetermined values at some fixed boundary vertices. This model is equivalent to the height function of the six-vertex model with a = b = c = 1, i.e. to the height function of square-ice. Our main result is that in a subgraph of Z^2 with zero boundary conditions, the variance grows logarithmically in the distance to the boundary. This establishes a strong form of roughness of the planar uniform homomorphisms. Joint work with: Hugo Duminil Copin, Matan Harel, Benoit Laslier and Aran Raoufi" |
November 13, 2019, 3:15 - 4:15 pm at CMSA, 20 Garden St, G02 |
| HARVARD LOGIC COLLOQUIUM |
Matthew Foreman (UNIVERSITY OF CALIFORNIA AT IRVINE) |
When is time forward isomorphic to time backward? |
When is forward time is isomorphic to backward time for a given dynamical system? When the acting group is Z, this asks when a transformation T is (measure theoretically) isomorphic to its inverse. It was not until 1951, that Anzai refuted a conjecture of Halmos and von Neumann by exhibiting the first example of a transformation where T is not isomorphic to its inverse. In this talk, I show that there is a a one-to-one computable method of associating to each 01 formula in number theory, a computable measure preserving diffeomorphism T of the two-torus so that is true if and only if T is measure theoretically isomorphic to Tô1 . The class of problems is large enough to include the Riemann Hypothesis, Goldbachâs Conjecture and statements such as âZermelo-Frankel Set Theory (Z FC) is consistent. In consequence, each of these formulas is equivalent to whether T = Tô1 for a diffeomorphism of T2 canonically associated to that formula. Thus there is an ergodic diffeomorphism of the two-torus TRH such that TRH = Tô1 RH if and only if the Riemann Hypothesis holds, and a different ergodic diffeomorphism TGC such that TGC = Tô1 GC if and only if Goldbachâs conjecture holds and so forth. Moreover there is a canonical diffeomorphism T such that the question T = Tô1 is independent of ZFC" |
November 13, 2019, 4:30 - 5:30 pm at Logic Center, 2 Arrow St, Rm 420 |
| CMSA QUANTUM MATTER AND QUANTUM FIELD THEORY SEMINAR |
Michael Pretko (U COLORADO) |
Introduction to Fractons |
A fracton is an exotic new type of emergent quasiparticle with restricted mobility. While a single fracton is strictly immobile in isolation, they can often come together to form certain mobile bound states. In this talk, I will give a birdâs-eye overview on the current state of the field of fractons. I will begin with the theoretical formalism for fractons in terms of symmetric tensor gauge theories, which possess unusual higher moment conservation laws. I will then outline some physical realizations of fractons, such as spin models and topological crystalline defects, the latter of which arises through a novel field theory duality. Finally, I will discuss some of the most interesting phenomenology of fracton systems, such as their non-ergodic and gravitational behavior. " |
November 13, 2019, 10:30 am - 12:00 pm at CMSA, 20 Garden St, G02 |
| CMSA FLUID DYNAMICS SEMINAR |
Martin Lellep (PHILIPPS UNIVERSITY OF MARBURG, GERMANY) |
Predictions of relaminarisation in turbulent shear flows using deep learning |
Given the increasing performance of deep learning algorithms in tasks such as classification during the last years and the vast amount of data that can be generated in turbulence research, I present one application of deep learning to fluid dynamics in this talk. We train a deep learning machine learning model to classify if turbulent shear flow becomes laminar a certain amount of time steps ahead in the future. Prior to this, we use a 2D toy example to develop an understanding how the performance of the deep learning algorithm depends on hyper parameters and how to understand the errors. The performance of both algorithms is high and therefore opens up further steps towards the interpretation of the results in future work." |
November 13, 2019, 2:10 - 3:00 pm *note special time* at CMSA, 20 Garden St, G02 *note different room* |
| CMSA COLLOQUIUM |
Heather Harrington (UNIVERSITY OF OXFORD) |
Algebra, Geometry and Topology of ERK Enzyme Kinetics |
In this talk I will analyse ERK time course data by developing mathematical models of enzyme kinetics. I will present how we can use differential algebra and geometry for model identifiability and topological data analysis to study these the wild type dynamics of ERK and ERK mutants. This work is joint with Lewis Marsh, Emilie Dufresne, Helen Byrne and Stanislav Shvartsman" |
November 13, 2019, 4:30 - 5:30 pm at CMSA, 20 Garden St, G10 |
| CMSA GENERAL RELATIVITY SEMINAR |
Eric Woolgar (UNIVERSITY OF ALBERTA) |
Conditions of curvature-dimension type in Lorentzian geometry and in black hole topology |
Curvature-dimension inequalities are modifications of a Ricci curvature bound or, in the language of relativity, an energy condition. They have proved useful in applications of Fourier analysis to diffusion processes. As tools to prove theorems in Riemannian geometry and general relativity, they are often as powerful as the usual Ricci curvature bounds and can yield new results. Applications include static Einstein metrics, near-extremal-horizon geometry, and scalar-tensor gravity. I will discuss an application of a Riemannian curvature-dimension bound to horizon topology, and use Lorentzian curvature-dimension bounds to prove some singularity theorems and splitting theorems. Parts of the talk are based on joint work with Marcus Khuri, Will Wylie, and Greg Galloway." |
November 13, 2019, 1:00 - 2:00 pm at CMSA, 20 Garden St, G02 |
| NUMBER THEORY SEMINAR |
Daxin Xu (CALTECH) |
Bessel F-isocrystals for reductive groups |
I will first review the Frobenius structure on the classical Bessel differential equation \begin{displaymath} (x\frac{d}{dx})^{2} u -xu =0, \end{displaymath} whose Frobenius traces are classical Kloosterman sums \begin{displaymath} \textnormal{Kl}(a):= \sum_{xy=a \in \mathbb{F}_p^{\times}} \exp(\frac{2\pi i}{p}(x+y)). \end{displaymath} Recently, there are two generalizations of this story (corresponding to $\GL_2$-case) for reductive groups: one is due to Frenkel and Gross from the viewpoint of the Bessel differential equation; another one, due to Heinloth, Ng\^o and Yun, uses the geometric Langlands correspondence to produce $\ell$-adic sheaves. I will report my joint work with Xinwen Zhu, where we study the $p$-adic aspect of this theory and unify previous two constructions. \end{document" |
November 13, 2019, 3:00 pm at Science Center 507 |
| OPEN NEIGHBORHOOD SEMINAR |
Ellen Eischen (U OREGON) |
An Introduction to the Bernoulli Numbers, from Pythagoras to Present |
Consider these basic questions: What can we say about finite sums of powers of consecutive whole numbers? What can we say about whole number solutions to polynomial equations? What about factorizations into primes? What about values of the Riemann zeta function? In interesting families of examples â elementary and sophisticated, ancient and modern â Bernoulli numbers unify these seemingly unrelated questions. After an introduction to the Bernoulli numbers, we will explore related developments for these intertwined problems, which lead to central challenges in number theory and beyond" |
November 13, 2019, 4:30 pm at Science Center 507 |
| INFORMAL GEOMETRY & DYNAMICS SEMINAR |
David Dumas (UNIVERSITY OF ILLINOIS AT CHICAGO) |
Experimental study of a meromorphic analogue of TeichmĂŒller space |
The harmonic maps parameterization identifies the TeichmĂŒller space of a compact surface with the vector space of holomorphic quadratic differentials (on some base complex structure). There is an analogue of this picture for meromorphic quadratic differentials where the corresponding hyperbolic structures have additional moduli at each pole, which are called Stokes data. We discuss computer experiments in which we compute Stokes data for polynomial quadratic differentials on the plane and compare the results to those predicted by a remarkable conjecture of Gaiotto-Moore-Neitzke. We also discuss analogous comparisons for cubic differentials. In all of these cases our results support the Gaiotto-Moore-Neitzke conjectures. This is joint work with Andrew Neitzke" |
November 13, 2019, 4:30 pm at Science Center 530 |
| CMSA SPACETIME SEMINAR |
Pierpaolo Mastrolia (UNIVERSITY OF MUNICH) |
Feynman Integrals and Intersection Theory |
" |
November 12, 2019, 3:30 pm at CMSA, 20 Garden St, G02 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Yichen Huang (MIT) |
Renyi entanglement entropy in quantum many-body systems |
We present two concrete examples where the Renyi rather than just the von Neumann entanglement entropy is necessary in order to obtain certain insights into quantum many-body systems. In the first example, we consider systems supporting ballistic information propagation and diffusive transport. It is well known that the linear-in-time growth of the von Neumann entanglement entropy (starting from a product state) is a probe of the former. Perhaps surprisingly, we show that the Renyi entanglement entropy (with Renyi index greater than 1) grows diffusively (i.e., as a square root of time) and is consequently a probe of the latter. In the second example, we study the problem of approximating local properties of a quantum many-body state using matrix product and projected entangled pair representations in one and two dimensions, respectively. We prove that area laws for the Renyi entanglement entropy (with Renyi index less than 1) lead to nontrivial upper bounds on the bond dimension. The bounds only depend on the accuracy of the desired approximation but not the system size. References: https://arxiv.org/abs/1902.00977 https://arxiv.org/abs/1903.10048 " |
November 12, 2019, 3:30 pm at Jefferson 356 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Yu-Shen Lin (BOSTON UNIVERSITY) |
On the SYZ Mirror Symmetry of Log Calabi-Yau Surfaces |
The Strominger-Yau-Zaslow conjecture predicts the existence of special Lagrangians fibration in Calabi-Yau manifolds near large complex structure limit. The SYZ conjecture has been an important guiding principle for mirror symmetry and many of the implications are verified. In this talk, I will report on the recent progress on the SYZ fibration on certain log Calabi-Yau surfaces using the Lagrangian mean curvature flow and the theory of J-holomorphic curves. As a bi-product, we produce many new special Lagrangian submanifolds. I will also explain the applications in mirror symmetry, including the tropical/holomorphic correspondence for log Calabi-Yau surfaces and a mathematical realization of renormalization process of Hori-Vafa. Part of the talk is based on the joint work with T. Collins, A. Jacob and S-C. Lau, T-J. Lee" |
November 12, 2019, 4:15 pm - 5:15 pm at Science Center 507 |
| SYMPLECTIC GEOMETRY SEMINAR |
Yingdi Qin (BERKELEY AND HARVARD) |
Coisotropic branes in symplectic tori |
Homological mirror symmetry (HMS) asserts that the Fukaya category of a symplectic manifold is derived equivalent to the category of coherent sheaves on the mirror complex manifold. Without suitable enlargement (split closure) of the Fukaya category, certain objects of it are missing to prevent HMS from being true. Kapustin and Orlov conjectured that coisotropic branes should be included into the Fukaya category from a physics view point. In this talk, I will construct for linear symplectic tori a version of Fukaya category including coisotropic branes and show that the usual Fukaya category embeds fully faithfully into it" |
November 08, 2019, 2:00 pm - 3:00 pm at Science Center 530 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Lisa Piccirillo (BRANDEIS/MIT) |
Knot traces and PL embeddings |
It remains at the forefront of 4-manifold topology to construct simple closed 4-manifolds with distinct smooth structures. Towards that end, it is of interest to construct simple 4-manifolds with boundary with very distinct smooth structures. For all genera g, we produce pairs of homeomorphic smooth 4-manifolds Z and Z which are homotopy equivalent to a genus g surface and which have smooth structures distinguished by several formal properties: Z is diffeomorphic to a genus g knot trace and Z is not, Z admits a smooth spine and Z does not admit a piecewise linear spine. When g = 0, Z is geometrically simply connected and Z is not. In particular our Z are simple spineless 4-manifolds, which gives an alternative to Levine and Lidmanâs recent solution to Problem 4.25 on Kirbyâs list. This is joint work in progress with Kyle Hayden" |
November 08, 2019, 3:30 pm at Science Center 507 |
| CMSA GENERAL RELATIVITY SEMINAR |
Pei-Ken Hung (MIT) |
Stability of the modified wave map gauge |
In this talk, I will discuss a wave equation for one forms in the Schwarzschild spacetime which is the linearization of a modified wave map gauge. The equation behaves like a damped wave equation and we obtain robust estimates. In particular, it allows us to show the stability of the modified wave map equation. This is on-going joint work with S. Brendle. " |
November 08, 2019, 10:30 am - 11:30 am at Science Center 530 |
| THURSDAY SEMINAR |
Elden Elmanto and Tom Bachmann () |
The Framed Cancellation Theorem + Moving Leftovers |
" |
November 07, 2019, 3:00 pm - 5:00 pm at Science Center 507 |
| CMSA CONDENSED MATTER/MATH SEMINAR |
Mathias Scheurer (HARVARD UNIVERSITY) |
Gauge theories for the cuprates: thermal Hall effect and optimal doping |
Recent experiments [1] have revealed an enhanced thermal Hall effect in the pseudogap phase of several different cuprate compounds. The large signal even persists in the undoped system and, thus, challenges our understanding of the square-lattice antiferromagnet fundamentally. In the first part of the talk, I will analyze possible mechanisms that can give rise to a thermal Hall effect in the antiferromagnet [2,3]. In particular, I will discuss the possibility [3] that the magnetic field can drive the NĂ©el state close to a transition to a phase where NĂ©el order coexists with a chiral spin liquid. A spinon lattice model for this transition is shown to give rise to a large thermal Hall conductivity that also features a magnetic-field and temperature dependence similar to experiment. We will derive the low-energy continuum field theory for the transition, which is characterized by an emergent global SO(3) symmetry and has four different formulations that are all related by dualities. If time permits, I will present, in the second part of the talk, a non-Abelian gauge theory that we propose [4] as an effective field theory for the cuprates near optimal doping. In this theory, spin-density-wave order is fractionalized into Higgs fields while all low-energy fermionic excitations are electron-like and gauge neutral. The conventional Fermi-liquid state corresponds to the confining phase of the theory at large doping and there is a quantum phase transition to a Higgs phase, describing the pseudogap, at low doping. It will be shown that the topological order of the Higgs phase is very naturally intertwined with charge-density-wave, Ising-nematic, and scalar spin-chirality order. We will also discuss the quantum critical point of the model" |
November 07, 2019, 11:50 am at CMSA, 20 Garden St, G10 |
| CMSA FLUID DYNAMICS SEMINAR |
Federico Toschi (EINDHOVEN UNIVERSITY OF TECHNOLOGY ) |
Deep learning and reinforcement learning for turbulence |
This talk tells two stories. Chapter 1: We investigate the capability of a state-of-the-art deep neural model at learning features of turbulent velocity signals. Deep neural network (DNN) models are at the center of the present machine learning revolution. The set of complex tasks in which they over perform human capabilities and best algorithmic solutions grows at an impressive rate and includes, but it is not limited to, image, video and language analysis, automated control, and even life science modeling. Besides, deep learning is receiving increasing attention in connection to a vast set of problems in physics where quantitatively accurate outcomes are expected. We consider turbulent velocity signals, spanning decades in Reynolds numbers, which have been generated via shell models for the turbulent energy cascade. Given the multi-scale nature of the turbulent signals, we focus on the fundamental question of whether a deep neural network (DNN) is capable of learning, after supervised training with very high statistics, feature extractors to address and distinguish intermittent and multi-scale signals. Can the DNN measure the Reynolds number of the signals? Which feature is the DNN learning? Chapter 2: Thermally driven turbulent flows are common in nature and in industrial applications. The presence of a (turbulent) flow can greatly enhance the heat transfer with respect to its conductive value. It is therefore extremely important -in fundamental and applied perspective- to understand if and how it is possible to control the heat transfer in thermally driven flows. In this work, we aim at maintaining a RayleighâBĂ©nard convection (RBC) cell in its conductive state beyond the critical Rayleigh number for the onset of convection. We specifically consider controls based on local modifications of the boundary temperature (fluctuations). We take advantage of recent developments in Artificial Intelligence and Reinforcement Learning (RL) to find -automatically- efficient non-linear control strategies. We train RL agents via parallel, GPU-based, 2D lattice Boltzmann simulations. Trained RL agents are capable of increasing the critical Rayleigh number of a factor 3 in comparison with state-of-the-art linear control approaches. Moreover, we observe that control agents are able to significantly reduce the convective flow also when the conductive state is unobtainable. This is achieved by finding and inducing complex flow fields" |
November 06, 2019, 3:00 pm - 4:00 pm at CMSA, 20 Garden St, G10 |
| CMSA COLLOQUIUM |
Kevin Costello (PERIMETER INSTITUTE) |
A unified perspective on integrability |
Two dimensional integrable field theories, and the integrable PDEs which are their classical limits, play an important role in mathematics and physics. I will describe a geometric construction of integrable field theories which yields (essentially) all known integrable theories as well as many new ones. Billiard dynamical systems will play a surprising role. Based on work (partly in progress) with Gaiotto, Lee, Yamazaki, Witten, and Wu" |
November 06, 2019, 4:30 pm- 5:30 pm at CMSA, 20 Garden St, G10 |
| CMSA QUANTUM MATTER AND QUANTUM FIELD THEORY SEMINAR |
Dan Freed (U TEXAS) |
M-theory is time-reversal invariant |
In joint work with Mike Hopkins we prove that there is no parity anomaly in M-theory in the low-energy field theory approximation. There are two sources of anomalies: the Rarita-Schwinger field and the cubic form for the C-field. I will explain the general principles behind these anomalies, since they apply in many problems. Then I ll turn to the specific computations we did to verify this anomaly cancellation. They include topologial and geometric methods for computing eta-invariants as well as homotopy-theoretic techniques for computing bordism groups" |
November 06, 2019, 10:30 am - 12 pm at CMSA, 20 Garden St, G10 |
| JOINT CMSA AND DEPARTMENT OF MATHEMATICS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Bruno Nachtergaele (UC DAVIS) |
The transmission time and local integrals of motion for disordered spin chains |
We investigate the relationship between zero-velocity Lieb-Robinson bounds and the existence of local integrals of motion (LIOMs) for disordered quantum spin chains. We also study the effect of dilute random perturbations on the dynamics of many-body localized spin chains. Using a notion of transmission time for propagation in quantum lattice systems we demonstrate slow propagation by proving a lower bound for the transmission time. This result can be interpreted as a robustness property of slow transport in one dimension. (Joint work with Jake Reschke" |
November 06, 2019, 3:15 pm - 4:15 pm at CMSA, 20 Garden St, G02 |
| NUMBER THEORY SEMINAR |
Kestutis Cesnavicius (CNRS/PARIS-SUD ) |
Purity for flat cohomology |
The absolute cohomological purity for Ă©tale cohomology of Gabber--Thomasson implies that an Ă©tale cohomology class on a regular scheme extends uniquely over a closed subscheme of large codimension. I will discuss the corresponding phenomenon for flat cohomology. The talk is based on joint work with Peter Scholze" |
November 06, 2019, 3:00 pm - 4:00 pm at Sci Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
HĂ©lĂšne Esnault (FREIE UNIVERSITĂ€T BERLIN/INSTITUTE FOR ADVANCED STUDY) |
Special loci of rank one local systems |
Joint with Moritz Kerz. We show a structure theorem on those loci which enables us to deduce several consequences, one of which being Hard Lefschetz in rank one in positive characteristic" |
November 05, 2019, 3:00 pm - 4:00 pm at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Kyeongsu Choi (MIT) |
The Gauss curvature flow - the shape of worn stones |
The Gauss curvature flow was introduced to model the shape of worn stones. It is a parabolic Monge-Ampere type flow for convex hypersurfaces, involving regularity issues for fully nonlinear equations and free boundary problems, and involving several entropy. In this talk, we will discuss the free boundary problem concerning worn stone with flat sides, and the optimal regularity of non-concave fully nonlinear equations. When time permits, we also talk about the singularity analysis, especially about the relations to the affine geometry at the critical case, to fully nonlinear equations at the super-critical case, and to convex geometry and spectral analysis at the sub-critical case" |
November 05, 2019, 4:15 pm - 5:15 pm at Science Center 507 |
| CMSA SPECIAL SEMINAR |
Sawomir Kodziej (JAGIELLONIAN UNIVERSITY) |
Weak subsolutions and solutions of the Monge-Ampere equation |
I shall discuss the complex Monge-Ampere equation in strictly pseudoconvex domain in C^n and on compact Hermitian manifolds reviewing the results and open questions concerning the problem: when the existence of a subsolution implies the existence of a solution in a class of admissible functions of given regularity" |
November 04, 2019, 2:30 pm at CMSA, 20 Garden St, G10 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Elana Kalashnikov (HARVARD UNIVERSITY) |
Mirror symmetry and automorphisms |
I will discuss joint work with Chiodo investigating the mirror symmetry of Calabi--Yau hypersurfaces in weighted projective spaces. I will show how given such a hypersurface endowed with a finite order automorphism of a specific type, the traditional cohomological mirror statement can be both specialised and broadened to take into account the weights of the action of the automorphism and the cohomology of its fixed locus. The main tool is Berglund--Hubsch--Krawitz duality. When the automorphism is an involution, this allows us to construct generalisations of Borcea--Voisin orbifolds in any dimension and with any number of factors (joint work with Chiodo and Veniani). For odd prime order automorphisms and dimension 2 orbifolds, this implies mirror symmetry for the associated lattice polarised K3 surfaces" |
November 04, 2019, 12:00 pm - 1:00 pm at CMSA, 20 Garden St, G10 |
| CMSA GENERAL RELATIVITY SEMINAR |
Peter Hintz (MIT) |
Linear stability of slowly rotating Kerr black holes |
I will describe joint work with Dietrich HĂ€fner and AndrĂĄs Vasy in which we study the asymptotic behavior of linearized gravitational perturbations of Schwarzschild and slowly rotating Kerr black hole spacetimes. We show that solutions of the linearized Einstein equation decay at an inverse polynomial rate to a stationary solution (given by an infinitesimal variation of the mass and angular momentum of the black hole), plus a pure gauge term. Our proof uses a detailed description of the low energy resolvent of an associated wave equation on symmetric 2-tensors" |
November 01, 2019, 10:30 am - 11:30 am at Science Center 530 |
| CMSA SPACETIME SEMINAR |
George Lusztig (MIT) |
Total positivity in Springer fibres |
" |
November 01, 2019, 1:30 pm-2:30 pm at Science Center 232 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Ko Honda (UCLA) |
Convex hypersurface theory in higher-dimensional contact topology |
Convex surface theory and bypasses are extremely powerful tools for analyzing contact 3-manifolds. In particular they have been successfully applied to many classification problems. After briefly reviewing convex surface theory in dimension three, we explain how to generalize many of their properties to higher dimensions. This is joint work with Yang Huang. Future schedule is found here: https://scholar.harvard.edu/gerig/semina" |
November 01, 2019, 3:30 pm at Science Center 507 |
| HARVARD-MIT-MSR COMBINATORICS SEMINAR |
Xuhua He () |
The m=2 amplituhedron |
" |
November 01, 2019, 3:30 pm - 4:30 pm at Science Center 232 |
| CMSA SPACETIME SEMINAR |
Junjie Rao (ALBERT EINSTEIN INSTITUTE) |
All-loop Mondrian Reduction of 4-particle Amplituhedron at Positive Infinity |
" |
October 31, 2019, 2:30 pm at CMSA, 20 Garden St, G10 |
| THURSDAY SEMINAR |
Elden Elmanto and Tom Bachmann () |
Reconstruction |
" |
October 31, 2019, 3:00 pm - 5:00 pm at Science Center 507 |
| CMSA CONDENSED MATTER/MATH SEMINAR |
Patrick Lee (MIT) |
Gapless spin liquid and emergent gauge theory |
I shall review the emergence of gauge theory as a description of quantum spin liquid, particularly the gapless variety. The matter field plays a key role in stabilizing the deconfined phase. I shall also discuss the current experimental status of gapless spin liquid candidates, including the recently âre-discoveredâ example of TaS2" |
October 31, 2019, 11:50 am at CMSA, 20 Garden St, G10 |
| GROSS-SIEBERT PROGRAM SEMINAR |
Charles Wang (HARVARD UNIVERSITY) |
Introduction to Theta Functions |
Charles will give an introduction to theta functions in the context of the Gross-Siebert program." |
October 31, 2019, 4:00 pm at Science Center 232 |
| CMSA QUANTUM MATTER AND QUANTUM FIELD THEORY SEMINAR |
Chong Wang (PERIMETER INSTITUTE) |
A theory of deconfined pseudo-criticality |
" |
October 30, 2019, 10:30 am - 12:00 pm at CMSA, 20 Garden St, G02 |
| JOINT CMSA AND DEPARTMENT OF MATHEMATICS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Aram Harrow (MIT) |
Random quantum circuits, phase transitions and complexity |
Random unitary dynamics are a toy model for chaotic quantum dynamics and also have applications to quantum information theory and computing. Recently, random quantum circuits were the basis of Google s announcement of quantum computational supremacy, meaning performing a task on a programmable quantum computer that would difficult or infeasible for any classical computer. Google s approach is based on the conjecture that random circuits are as hard to classical computers to simulate as a worst-case quantum computation would be. I will describe evidence in favor of this conjecture for deep random circuits and against this conjecture for shallow random circuits. (Deep/shallow refers to the number of time steps of the quantum circuit.) For deep random circuits in Euclidean geometries, we show that quantum dynamics match the first few moments of the Haar measure after roughly the amount of time needed for a signal to propagate from one side of the system to the other. In non-Euclidean geometries, such as the Schwarzschild metric in the vicinity of a black hole, this turns out not to be always true. I will also explain how shallow quantum circuits are easier to simulate when the gates are randomly chosen than in the worst case. This uses a simulation algorithm based on tensor contraction which is analyzed in terms of an associated stat mech model" |
October 30, 2019, 3:15 pm - 4:15 pm at CMSA, 20 Garden St, G02 |
| NUMBER THEORY SEMINAR |
Yifeng Liu (YALE UNIVERSITY ) |
Isolation of L^2 spectrum and Gan-Gross-Prasad conjecture |
In this talk, we introduce a new technique for isolating components on the spectral side of the trace formula. By applying it to the Jacquet--Rallis relative trace formula, we complete the proof of the global Gan--Gross--Prasad conjecture and its refinement Ichino--Ikeda conjecture for unitary groups of corank 1 in the stable case, as well as obtain some other applications for base change and L-functions. This is based on a joint work with Raphaël Beuzart-Plessis, Wei Zhang, and Xinwen Zhu" |
October 30, 2019, 3:00 pm at Science Center 530 |
| CMSA COLLOQUIUM |
Nima Arkani-Hamed (IAS) |
Spacetime, Quantum Mechanics and Positive Geometry at Infinity |
" |
October 30, 2019, 4:30 pm- 5:30 pm at CMSA, 20 Garden St, G10 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Max Jordan Zimet (BLACKHOLE INITIATIVE) |
K3 metrics from little string theory |
Calabi--Yau manifolds have played a central role in both string theory and mathematics for decades, but in spite of this no Ricci-flat metric on a compact non-toroidal Calabi--Yau manifold is known. I will discuss a new physically motivated approach toward the determination of such metrics for K3 surfaces. The key remaining step is the determination of a BPS spectrum of a heterotic little string theory on $T^2$. I will use string dualities to provide a number of mathematical reformulations of this problem, ranging from open string reduced Gromov--Witten theory for the mirror K3 surface (in accordance with the SYZ conjecture) to Donaldson--Thomas theory for auxiliary Calabi--Yau threefolds. Finally, I will discuss new approximations to K3 metrics near the semi-flat limit that require only a minimal knowledge of this BPS spectrum" |
October 28, 2019, 12:00 pm - 1:00 pm at CMSA, 20 Garden St, G02 |
| CMSA GENERAL RELATIVITY SEMINAR |
Christina Sormani (CUNY) |
Scalar Curvature and Intrinsic Flat Convergence |
After reviewing the definition of intrinsic flat convergence, I will present open problems on the almost rigidity or stability of classic rigidity theorems for manifolds with scalar curvature bounds and survey partial results towards these conjectures" |
October 25, 2019, 10:30 am - 11:30 am at Science Center 530 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Alex Waldron (MICHIGAN STATE UNIVERSITY) |
G_2-instantons on the 7-sphere |
I ll discuss a forthcoming paper studying families of G_2-instantons on S^7, focusing on those which are obtained by pulling back asd instantons on S^4 via the quaternionic Hopf fibration. In the charge-1 case this yields a smooth and complete 15-dimensional family. The situation for higher charge is more complicated, but we are able to compute all the infinitesimal deformations. Future schedule is found here: https://scholar.harvard.edu/gerig/semina" |
October 25, 2019, 3:30 pm at Sci Center 507 |
| CMSA CONDENSED MATTER/MATH SEMINAR |
Andrew Turner (MIT) |
General F-theory models with SU(3) x SU(2) x U(1) / Z_6 symmetry |
We construct a general form for an F-theory Weierstrass model over any base giving a 6D or 4D supergravity theory with gauge group SU(3) x SU(2) x U(1) / Z_6 and associated generic matter. The concept of âgeneric matterâ can be rigorously defined in 6D supergravity and generalizes naturally to four dimensions for F-theory models. We describe general F-theory models with this gauge group and the associated generic matter content, which fit into two distinct classes, and present an explicit Weierstrass model that realizes these models as two distinct branches. We also discuss, as a special case, the class of models recently studied by Cvetic, Halverson, Lin, Liu, and Tian, for which we demonstrate explicitly the possibility of unification through an SU(5) unHiggsing" |
October 24, 2019, 11:50 am at CMSA, 20 Garden St, G10 |
| THURSDAY SEMINAR |
Jeremy Hahn (MIT) |
Framings and the recognition principle |
" |
October 24, 2019, 3:00 pm - 5:00 pm at Science Center 507 |
| GROSS-SIEBERT PROGRAM SEMINAR |
Maxim Jeffs (HARVARD UNIVERSITY) |
A Gentle Introduction to Scattering |
I will give a gentle introduction to scattering in the context of the Gross-Siebert program, motivated from the perspective of symplectic geometry." |
October 24, 2019, 3:00 pm at Science Center 232 |
| CMSA FLUID DYNAMICS SEMINAR |
Kimee Moore (HARVARD UNIVERSITY) |
Using magnetic fields to investigate Jupiter's fluid interior |
The present-day interior structure of a planet is an important reflection of the formation and subsequent thermal evolution of that planet. However, despite decades of spacecraft missions to a variety of target bodies, the interiors of most planets in our Solar System remain poorly constrained. In this talk, I will discuss how actively generated planetary magnetic fields (dynamos) can provide important insights into the interior properties and evolution of fluid planets. Using Jupiter as a case study, I will present new results from the analysis of in situ spacecraft magnetometer data from the NASA Juno Mission (currently in orbit about Jupiter). The spatial morphology of Jupiterâs magnetic field shows surprising hemispheric asymmetry, which may be linked to the dissolution of Jupiterâs rocky core in liquid metallic hydrogen. I also report the first definitive detection of time-variation (secular variation) in a planetary dynamo beyond Earth. This time-variation can be explained by the advection of Jupiterâs magnetic field by the zonal winds, which places a lower bound on the velocity of Jupiterâs winds at depth. These results provide an important complement to other analysis techniques, as gravitational measurements are currently unable to uniquely distinguish between deep and shallow wind scenarios, and between solid and dilute core scenarios. Future analysis will continue to resolve Jupiterâs interior, providing broader insight into the physics of giant planets, with implications for the formation of our Solar System." |
October 23, 2019, 3:00 pm - 4:00 pm at CMSA, 20 Garden St, G10 |
| OPEN NEIGHBORHOOD SEMINAR |
Marius Lemm (HARVARD UNIVERSITY) |
Why doesn't an electron fall into the nucleus? |
In physics class at school, we are taught that matter is composed of atoms. We learn that every atom has at its center a positively-charged nucleus, around which negatively-charged electrons orbit, just like planets orbiting the un. However, we also learn that positive and negative charges attract. So... why doesn t an electron simply fall into the nucleus? This is no small question as the answer holds the key to the stability of all matter around us. It turns out that the answer lies in quantum mechanics. This lecture will give a crash course on the mathematics describing quantum mechanics and in particular pin down the notion of uncertainty principle mathematically. It will conclude with a proof that a quantum-mechanical electron does not fall into the nucleus, hopefully prompting a sigh of relief from the audience" |
October 23, 2019, 4:30 pm at Science Center 507 |
| INFORMAL GEOMETRY & DYNAMICS SEMINAR |
Martin Bridgeman (BOSTON COLLEGE) |
The Weil-Petersson gradient flow for renormalized volume |
Renormalized volume was introduced by Graham and Witten for conformally compact Einstein manifolds. Krasnov-Schlenker studied it for convex compact hyperbolic 3-manifolds and proved many of its fundamental properties. In a series of papers, we study the Weil-Petersson gradient flow of the renormalized volume function $V_R$ on the space of convex compact structures $CC(N)$ of a 3-manifold $N$. For $\partial N$ incompressible, we use the flow to show that the infimum of $V_R$ on $CC(N)$ is the Gromov norm of $N$. For $N$ acylindrical, we introduce a surgered flow and show that starting at any $M \in CC(N)$ the flow limits to $M_{geod}$, the unique manifold with totally geodesic convex core boundary. Using this, we prove a lower bound on the convex core volume function $V_C$ on $CC(N)$ given by $V_C(M)-V_C(M_geod) \geq Kd_WP(\partial M,\partial M_geod) + C$. This is joint work with Jeff Brock and K. Bromberg" |
October 23, 2019, 4:30 pm at Science Center 530 |
| NUMBER THEORY SEMINAR |
Evan O'Dorney (PRINCETON UNIVERSITY ) |
Reflection theorems generalizing the Ohno-Nakagawa identities |
Scholz s celebrated 1932 reflection principle, relating the 3-torsion in the class groups of Q(âD) and Q(â-3D), can be viewed as an equality among the numbers of cubic fields of different discriminants. In 1997, Y. Ohno discovered (quite by accident) a reflection identity relating the number of cubic *rings* of discriminants D and -27D, where D is not necessarily squarefree. In my talk, I will present a new method for proving this identity, based on Poisson summation on adelic cohomology (in the style of Tate s thesis). I will describe my recent progress in extending it to rings of other ranks" |
October 23, 2019, 3:00 pm at Science Center 507 |
| CMSA QUANTUM MATTER/QUANTUM FIELD THEORY SEMINAR |
Chong Wang (PERIMETER) |
Unquantized quantum anomalies: electric polarization, Luttinger theorem and correlated Weyl semimetals |
" |
October 23, 2019, 10:30 am - 12:00 pm at CMSA, 20 Garden St, G10 |
| JOINT CMSA AND DEPARTMENT OF MATHEMATICS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Souvik Dhara (MIT) |
A new universality class for critical percolation on networks with heavy-tailed degrees |
The talk concerns critical behavior of percolation on finite random networks with heavy-tailed degree distribution. In a seminal paper, Aldous (1997) identified the scaling limit for the component sizes in the critical window of phase transition for the ErdĆ`s-RĂ©nyi random graph. Subsequently, there has been a surge in the literature identifying two universality classes for the critical behavior depending on whether the asymptotic degree distribution has a finite or infinite third moment. In this talk, we will present a completely new universality class that arises in the context of degrees having infinite second moment. Specifically, the scaling limit of the rescaled component sizes is different from the general description of multiplicative coalescent given by Aldous and Limic (1998). Moreover, the study of critical behavior in this regime exhibits several surprising features that have never been observed in any other universality classes so far. This is based on joint works with Shankar Bhamidi, Remco van der Hofstad, Johan van Leeuwaarden" |
October 23, 2019, 3:15 pm - 4:15 pm at CMSA, 20 Garden St, G02 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Juven Wang (CMSA, HARVARD UNIVERSITY) |
Quantum 4d Yang-Mills Theories and Time-Reversal Symmetric 5d Higher-Gauge TQFT |
We explore 4d Yang-Mills gauge theories (YM) living as boundary conditions of 5d gapped short/long-range entangled (SRE/LRE) topological states. Specifically, we explore 4d time-reversal symmetric pure YM of an SU(2) gauge group with a second-Chern-class topological term at Ξ=Ï (SU(2)Ξ=Ï YM), by turning on background fields for both the time-reversal (i.e., on unorientable manifolds) and 1-form center global symmetry. We comment on that such 4d Yang-Mills dynamics cannot be trivially confined gapped. The work is based mainly on https://arxiv.org/abs/1904.00994, also https://arxiv.org/abs/1812.11967 and https://arxiv.org/abs/1810.00844. We explore 4d Yang-Mills gauge theories (YM) living as boundary conditions of 5d gapped short/long-range entangled (SRE/LRE) topological states. Specifically, we explore 4d time-reversal symmetric pure YM of an SU(2) gauge group with a second-Chern-class topological term at Ξ=Ï (SU(2)Ξ=Ï YM), by turning on background fields for both the time-reversal (i.e., on unorientable manifolds) and 1-form center global symmetry. We comment on that such 4d Yang-Mills dynamics cannot be trivially confined gapped. The work is based mainly on https://arxiv.org/abs/1904.00994, also https://arxiv.org/abs/1812.11967 and https://arxiv.org/abs/1810.00844. We explore 4d Yang-Mills gauge theories (YM) living as boundary conditions of 5d gapped short/long-range entangled (SRE/LRE) topological states. Specifically, we explore 4d time-reversal symmetric pure YM of an SU(2) gauge group with a second-Chern-class topological term at Ξ=Ï (SU(2)Ξ=Ï YM), by turning on background fields for both the time-reversal (i.e., on unorientable manifolds) and 1-form center global symmetry. We comment on that such 4d Yang-Mills dynamics cannot be trivially confined gapped. The work is based mainly on https://arxiv.org/abs/1904.00994, also https://arxiv.org/abs/1812.11967 and https://arxiv.org/abs/1810.00844. This talk is related to my IAS seminar: https://www.youtube.com/watch?v=GUMheJboWB" |
October 22, 2019, 3:30 pm at Jefferson 356 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Francois Greer (STONY BROOK UNIVERSITY) |
Lagrangian spheres which are not vanishing cycles |
Let X be a smooth projective variety with its induced Kahler structure. If X admits a degeneration to a nodal variety, then X contains a Lagrangian sphere as the vanishing cycle. Donaldson asked whether the converse holds. We answer this question in the negative for Calabi-Yau threefolds and discuss related examples from Teichmuller theory" |
October 22, 2019, 3:00 pm - 4:00 pm at Science Center 507 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Man-Wai Cheung (HARVARD UNIVERSITY) |
Compactification for cluster varieties without frozen variables of finite type |
Cluster varieties are blow up of toric varieties. They come in pairs $(A,X)$, with $A$ and $X$ built from dual tori. Compactifications of $A$, studied by Gross, Hacking, Keel, and Kontsevich, generalize the polytope construction of toric varieties while the compactifications of X, studied by Fock and Goncharov, generalize the fan construction. The conjecture is that the $A$ and the $X$ cluster varieties are mirrors to each other. Together with Tim Magee, we have shown that there exists a positive polytope for the type $A$ cluster varieties which give us a hint to the Batyrev--Borisov construction" |
October 21, 2019, 12:20 - 1:10 pm *note special time at CMSA, 20 Garden St, G10 |
| CMSA GENERAL RELATIVITY SEMINAR |
Jordan Keller (BHI) |
Angular Momentum and Center-of-Mass at Null Infinity |
We calculate the limits of the quasi-local angular momentum and center-of-mass defined by Chen-Wang-Yau for a family of spacelike two-spheres approaching future null infinity in an asymptotically flat spacetime admitting a Bondi-Sachs expansion. Our result complements earlier work of Chen-Wang-Yau, where the authors calculate the quasi-local energy and linear momentum at null infinity. Working in the center-of-mass frame, i.e. assuming vanishing of linear momentum at null infinity, we obtain explicit expressions for the angular momentum and center-of-mass at future null infinity in terms of the observables appearing in the Bondi-Sachs expansion of the spacetime metric. This is joint work with Ye-Kai Wang and Shing-Tung Yau" |
October 18, 2019, 10:30 am - 11:30 am at Science Center 530 |
| CMSA SPACETIME SEMINAR |
Sebastian Franco (THE CITY COLLEGE OF NEW YORK) |
Graded quivers, generalized dimer models, and toric geometry |
" |
October 18, 2019, 2:30 pm at CMSA, 20 Garden St, G02 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Laurent CÎté (STANFORD) |
Rigidity of cotangent fibers of Riemann surfaces |
I will discuss joint work with Georgios Dimitroglou Rizell which studies symplectic rigidity phenomena for fibers in cotangent bundles of Riemann surfaces. Our work is motivated by analogies to Arnoldâs celebrated Nearby Lagrangian Conjecture and by work of Ekholm and Smith in higher dimensions. We crucially use several special properties of pseudo-holomorphic curves in dimension 4 as well as some fairly recent developments in the analysis of punctured pseudo-holomorphic curves. I will review these developments, highlighting in particular why certain pseudo-holomorphic curve techniques are particularly effective in dimension 4. Future schedule is found here: https://scholar.harvard.edu/gerig/semina" |
October 18, 2019, 3:30 pm at Science Center 507 |
| THURSDAY SEMINAR |
Elden Elmanto (HARVARD UNIVERSITY) |
A framed correspondences primer via Milnor-Witt K-theory |
" |
October 17, 2019, 3:00 pm - 5:00 pm at Science Center 507 |
| JOINT CMSA AND DEPARTMENT OF MATHEMATICS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Wei-Kuo Chen (UNIVERSITY OF MINNESOTA) |
The generalized TAP free energy |
Spin glasses are disordered spin systems initially invented by theoretical physicists with the aim of understanding some strange magnetic properties of certain alloys. In particular, over the past decades, the study of the Sherrington-Kirkpatrick (SK) mean-field model via the replica method has received great attention. In this talk, I will discuss another approach to studying the SK model proposed by Thouless-Anderson-Palmer (TAP). I will explain how the generalized TAP correction appears naturally and give the corresponding generalized TAP representation for the free energy. Based on a joint work with D. Panchenko and E. Subag" |
October 16, 2019, 3:15 pm at CMSA, 20 Garden St, G02 |
| LOGIC COLLOQUIUM |
Gabriel Goldberg (UC BERKELEY) |
Generalizations of the Ultrapower Axiom |
The Ultrapower Axiom (UA) is a set theoretic principle motivated by inner model theory. Under UA, it is possible to develop certain parts of large cardinal theory that are intractable under the standard ZFC axioms. Is UA consistent with all large cardinal axioms? Since UA is necessarily compatible with any large cardinal axiom that admits a canonical inner model theory, this question is likely to be intertwined with the longstanding open problem of constructing canonical inner models with very large cardinals. In this talk, we present two natural generalizations of UA that are not motivated by inner model theory. The goal is to refute these principles from large cardinal axioms. We view this as a way of identifying interesting complex structure at key levels of the large cardinal hierarchy. It also serves to corroborate the intuition that the (apparent) consistency of UA with supercompact cardinals is evidence that inner model theory extends to this level" |
October 16, 2019, 4:30 pm - 5:30 pm (talk), 5:30 pm -6:30 pm (reception) at CLogic Center, 2 Arrow St, Rm 420 |
| CMSA QUANTUM MATTER/QUANTUM FIELD THEORY SEMINAR |
Kantaro Ohmori (SUNY SCGP) |
Anomaly Obstructions to Symmetry Preserving Gapped Phases: Discrete symmetry case |
Anomalies are renormalization group invariants and constrain the dynamics of quantum field theories. In this talk we show that certain anomalies for discrete global generalized symmetries imply that the underlying theory either spontaneously breaks its global symmetry or is gapless. This is done by observing that a symmetry preserving unitary TQFT is not compatible with the anomaly whose inflow action evaluates nontrivially on a certain manifold" |
October 16, 2019, 10:30 am at CMSA, 20 Garden St, G02 |
| CMSA COLLOQUIUM |
Aram Harrow (MIT) |
Monogamy of entanglement and convex geometry |
The SoS (sum of squares) hierarchy is a flexible algorithm that can be used to optimize polynomials and to test whether a quantum state is entangled or separable. (Remarkably, these two problems are nearly isomorphic.) These questions lie at the boundary of P, NP and the unique games conjecture, but it is in general open how well the SoS algorithm performs. I will discuss how ideas from quantum information (the monogamy property of entanglement) can be used to understand this algorithm. Then I will describe an alternate algorithm that relies on apparently different tools from convex geometry that achieves similar performance. This is an example of a series of remarkable parallels between SoS algorithms and simpler algorithms that exhaustively search over carefully chosen sets. Finally, I will describe known limitations on SoS algorithms for these problems" |
October 16, 2019, 4:00 pm - 5:00 pm at CMSA, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Bejamin Matschke (BOSTON UNIVERSITY) |
Proofs by Example |
We study the proof scheme proof by example in which a general statement can be proved by verifying it for a single example. This strategy can indeed work if the statement in question is an algebraic identity and the example is generic. This talk addresses the problem of constructing a practical example, which is sufficiently generic, for which the statement can be verified efficiently, and which allows for a numerical margin of error. Our method is based on diophantine geometry, in particular an arithmetic Bezout theorem, an arithmetic Nullstellensatz, and a new effective Liouville-Lojasiewicz type inequality for algebraic varieties. As an application we discuss theorems from plane geometry and how to prove them by example" |
October 16, 2019, 3:00 pm at Science Center 507 |
| CMSA SPACETIME SEMINAR |
Sergey Fomin (UNIVERSITY OF MICHIGAN) |
Morsifications and mutations (joint work with P. Pylyavskyy, E. Shustin, and D. Thurston) |
" |
October 15, 2019, 3:30 pm at CMSA, 20 Garden St, G10 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Shubham Dwivedi (U WATERLOO) |
A gradient flow of isometric $G_2$ structures |
We will talk about a flow of isometric $G_2$ structures. We consider the negative gradient flow of the energy functional restricted to the class of $G_2$ structures inducing a given Riemannian metric. We will discuss various analytic aspects of the flow including global and local derivative estimates, a compactness theorem and a local monotonicity formula for the solutions. We also study the evolution equation of the torsion and show that under a modification of the gauge and of the relevant connection, it satisfies a nice reaction-diffusion equation. After defining an entropy functional we will prove that low entropy initial data lead to solutions that exist for all time and converge smoothly to a $G_2$ structure with divergence free torsion. We will also discuss finite time singularities and show that at the singular time the flow converges to a smooth $G_2$ structure outside a closed set of finite 5- dimensional Hausdorff measure. Finally, we will prove that if the singularity is Type-I then a sequence of blow-ups of a solution has a subsequence which converges to a shrinking soliton of the flow. This is a joint work with Panagiotis Gianniotis (University of Athens) and Spiro Karigiannis (University of Waterloo)" |
October 15, 2019, 4:15 pm - 5:15 pm at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Jonathan Wise (UNIVERSITY OF COLORADO) |
The universal compactified Picard group and Grothendieck's theorem in tropical geometry |
The Picard group of a smooth, proper algebraic curve is a smooth algebraic group with proper components. If the curve degenerates to acquire nodes then it may not be possible to find a simultaneous degeneration of its Picard group that has proper components and retains a group structure. However, in logarithmic geometry it is possible to find a family, called the logarithmic Picard group, that has both of these properties and extends the algebraic Picard group. I will describe some of the basic properties of the logarithmic Picard group and what algebro-geometric information it contains. As an application, we will recover a theorem of Grothendieck about the monodromy action on the first cohomology of a family of smooth, proper algebraic curves" |
October 15, 2019, 3:00 pm at Science Center 507 |
| CMSA GENERAL RELATIVITY SEMINAR |
Graham Cox (MEMORIAL UNIVERSITY) |
Blowup solutions of Jangâs equation near a spacetime singularity |
Jang s equation is a semilinear elliptic equation define on an initial data set. It was shown by Schoen and Yau that the (non)existence of global solutions is closely related to the existence of marginally outer trapped surfaces (MOTS), which are quasi-local analogues of black hole boundaries. As a result, Jang s equation can be used to prove the existence of MOTS by imposing appropriate geometric conditions on the initial data set. These proofs proceed by contradiction: one assumes there is a global solution, then proves that its existence is not compatible with the given geometric assumptions. In this talk I will outline a constructive approach to proving the existence of MOTS. In particular, I will consider a distinguished family of spacelike hypersurfaces in the maximally extended Schwarzschild spacetime, and prove that Jang s equation admits no global solutions once the hypersurfaces become sufficiently close to the r=0 singularity. This suggests a general strategy for relating spacetime singularities to the presence of MOTS. This is joint with Amir Aazami. " |
October 11, 2019, 10:30 am - 11:30 am at Science Center 530 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
AgustĂn Moreno (AUGSBURG) |
Bourgeois contact structures: tightness, fillability and applications |
Starting from a contact manifold and a supporting open book decomposition, an explicit construction by Bourgeois provides a contact structure in the product of the original manifold with the two-torus. In this talk, we will discuss recent results concerning rigidity and fillability properties of these contact manifolds. For instance, it turns out that Bourgeois contact structures are, in dimension 5, always tight, independent on the rigid/flexible classification of the original contact manifold. Moreover, Bourgeois manifolds associated to suitable monodromies provide new examples of weakly but not strongly fillable contact 5-manifolds. We also present the following application in any dimension: the standard contact structure in the unit cotangent bundle of the n-torus, which is a Bourgeois manifold, admits a unique aspherical filling up to diffeomorphism. This is joint work with Jonathan Bowden and Fabio Gironella. Future schedule is found here: https://scholar.harvard.edu/gerig/semina" |
October 11, 2019, 3:30 pm at Science Center 507 |
| CMSA CONDENSED MATTER/MATH SEMINAR |
Julio Parra Martinez (UCLA) |
GSO projections and D-brane classification via SPT phases |
I will explain how a choice of fermionic SPT phases on the string worldsheet gives rise to the different GSO projections. This point of view not only easily explains why there are essentially two type II and 0 theories, but also predicts an eight-fold classification of unoriented Pin- type 0 theories. A similar analysis for unoriented Type II strings requires introducing Double Pin (DPin) structures, and confirms that there is an essentially unique choice of the type I worldsheet theory. By considering the implications of the bulk SPTs on the boundary of opens strings we provide an alternative route to the K-theoretic classification of D-branes, and clarify some of their properties. As an example, I will describe the classification of D-branes in the unoriented Pin- type 0 theories, in which all higher real K-groups play a role" |
October 10, 2019, 11:50 am - 1:00 pm at CMSA, 20 Garden St, G10 |
| THURSDAY SEMINAR |
Dexter Chua (HARVARD UNIVERSITY) |
Introduction to Motivic Homotopy Theory |
" |
October 10, 2019, 3:00 pm - 5:00 pm at Science Center 507 |
| CMSA SPACETIME SEMINAR |
Yutin Huang (NATIONAL TAIWAN UNIVERSITY) |
Dualities of Planar Ising Networks and the Positive Orthogonal Grassmannian |
" |
October 10, 2019, 3:30 pm - 4:30 pm at CMSA, 20 Garden St, G10 |
| GROSS-SIEBERT PROGRAM SEMINAR |
Mandy Cheung (HARVARD UNIVERSITY) |
Gross-Siebert Construction Examples |
Mandy will be giving some examples of the Gross-Siebert construction for integral affine manifolds with singularities. Note new time of 4:05 p" |
October 10, 2019, 4:05 pm at Science Center 232 |
| OPEN NEIGHBORHOOD SEMINAR |
Kate Stange (COLORADO) |
Quantum computers and the future of cryptography |
When quantum computers are engineered to scale, quantum algorithms will be able to break our current cryptographic protocols. How do quantum computers work and how do they accomplish this? And what should we do about it? I ll introduce the basics of quantum computing, explain how a quantum computer can factor big numbers and break current cryptography, and then I ll introduce some of the front-runners for the future of quantum-safe cryptography (including elliptic curve isogeny-based cryptography), and explain why we think these might be secure" |
October 09, 2019, 4:30 pm at Science Center 507 |
| CMSA QUANTUM MATTER/QUANTUM FIELD THEORY SEMINAR |
Peter Koroteev (UC BERKELEY) |
On Quiver W-algebras and Defects from Gauge Origami |
Using Nekrasovâs gauge origami framework, we study two different versions of the BPS/CFT correspondence â first, the standard AGT duality and, second, the quiver W algebra construction which has been developed recently by Kimura and Pestun. The gauge origami enables us to work with both dualities simultaneously and find exact matchings between the parameters. In our main example of an A-type quiver gauge theory, we show that the corresponding quiver qW-algebra and its representations are closely related to a large-n limit of spherical gl(n) double affine Hecke algebra whose modules are described by instanton partition functions of a defect quiver theory" |
October 09, 2019, 10:30 am - 12:00 pm at CMSA, 20 Garden St, G10 |
| CMSA COLLOQUIUM |
Hans Lindblad (JOHNS HOPKINS UNIVERSITY) |
Global Existence and Scattering for Einstein's equations and related equations satisfying the weak null condition |
Einstein s equations in harmonic or wave coordinates are a system of nonlinear wave equations for a Lorentzian metric, that in addition satisfy the preserved wave coordinate condition. Christodoulou-Klainerman proved global existence for Einstein vacuum equations for small asymptotically flat initial data. Their proof avoids using coordinates since it was believed the metric in harmonic coordinates would blow up for large times. John had noticed that solutions to some nonlinear wave equations blow up for small data, whereas Klainerman came up with the null condition , that guaranteed global existence for small data. However Einstein s equations do not satisfy the null condition. Hormander introduced a simplified asymptotic system by neglecting angular derivatives which we expect decay faster due to the rotational invariance, and used it to study blowup. I showed that the asymptotic system corresponding to the quasilinear part of Einstein s equations does not blow up and gave an example of a nonlinear equation of this form that has global solutions even though it does not satisfy the null condition. Together with Rodnianski we introduced the weak null condition requiring that the corresponding asymptotic system have global solutions and we showed that Einstein s equations in wave coordinates satisfy the weak null condition and we proved global existence for this system. Our method reduced the proof to a fraction and has now been used to prove global existence also with matter fields. Recently I derived precise asymptotics for the metric which involves logarithmic corrections to the radiation field of solutions of linear wave equations. We are further imposing these asymptotics at infinity and solve the equations backwards to obtain global solutions with given data at infinity. " |
October 09, 2019, 4:30 - 5:30 pm at CMSA, 20 Garden St, G10 |
| JOINT CMSA AND DEPARTMENT OF MATHEMATICS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Ruth J. Williams (UNIVERSITY OF CALIFORNIA, SAN DIEGO & CMSA VISITOR) |
Stability of a Fluid Model for Fair Bandwidth Sharing with General File Size Distributions |
Massoulie and Roberts introduced a stochastic model for a data communication network where file sizes are generally distributed and the network operates under a fair bandwidth sharing policy. It has been a standing problem to prove stability of this general model when the average load on the system is less than the network s capacity. A crucial step in an approach to this problem is to prove stability of an associated measure-valued fluid model. We shall describe prior work on this question done under various strong assumptions and indicate how to prove stability of the fluid model under mild conditions. This talk is based on joint work with Yingjia Fu" |
October 09, 2019, 3:15 - 4:15 pm at CMSA, 20 Garden St, G02 |
| INFORMAL GEOMETRY AND DYNAMICS SEMINAR |
Saul Schleimer (UNIVERSITY OF WARWICK) |
From veering triangulations to pseudo-Anosov flows (and back again) |
The question of classifying flows in three-manifolds dates back to (at least) Smale s 1967 BAMS article. One important class, first studied by Fenley, are the pseudo-Anosov flows without perfect fits. Agol and Gueritaud showed that each such yields a veering triangulation of a cusped three-manifold. We prove the converse. The proof is very long, so I will give an overview and draw lots of pictures. Questions are most welcome! This is joint work with Henry Segerman" |
October 09, 2019, 4:30 pm at Science Center 530 |
| CMSA FLUID DYNAMICS SEMINAR |
Samuel Rudy (MIT) |
Data-driven methods for discovery of partial differential equations and forecasting |
A critical challenge in many modern scientific disciplines is deriving governing equations and forecasting models from data where derivation from first principals is intractable. The problem of learning dynamics from data is complicated when data is corrupted by noise, when only partial or indirect knowledge of the state is available, when dynamics exhibit parametric dependencies, or when only small volumes of data are available. In this talk I will discuss several methods for constructing models of dynamical systems from data including sparse identification for partial differential equations with or without parametric dependencies and approximation of dynamical systems governing equations using neural networks. Limitations of each approach and future research directions will also be discussed" |
October 09, 2019, 3:00 pm at CMSA, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Stefan Patrikis (UTAH) |
Geometric lifts of odd Galois representations |
Let G be a reductive group. Following Gross, and generalizing Serre s classical notion in the two-dimensional case, I will define what it means for a G-valued representation of the Galois group of a (totally real) number field to be odd. This notion provides a natural setting for studying generalizations of the familiar properties of odd two-dimensional Galois representations. I will then describe recent joint work with N. Fakhruddin and C. Khare on the existence of geometric lifts of odd, G-irreducible representations, with an emphasis on novel examples for both classical and exceptional groups" |
October 9, 2019, 3:00 pm - 4:00 pm at Science Center 507 |
| HARVARD LOGIC COLLOQUIUM |
Justin Moore (CORNELL UNIVERSITY) |
What makes the continuum â”2 |
One of the basic goals of mathematics is to classify. Usually, we do not have choice in the matter: classifications and their limitations can usually be established based on the accepted axioms of mathematics. In some cases, however the existence of pathologies and exotic examples can neither be proven nor refuted within . From a foundational point of view we have the option to make a choice. This talk will discuss the influence of this choice on the size of the continuum" |
October 09, 2019, 4:30 - 5:30 pm at Logic Center, 2 Arrow St, Rm 420 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Daren Cheng (U CHICAGO) |
Bubble tree convergence of conformally cross product preserving maps |
We study a class of weakly conformal maps, called Smith maps, which parametrize associative 3-folds in 7-manifolds equipped with G2-structures. These maps satisfy a system of first-order PDEs generalizing the Cauchy-Riemann equation for J-holomorphic curves, and we are interested in their bubbling phenomena. Specifically, we first prove an epsilon-regularity theorem for Smith maps in W^{1, 3}, and then explain how that combines with conformal invariance to yield bubble trees of Smith maps from sequences of such maps with uniformly bounded 3-energy. When the G2-structure is closed, we show that both the 3-energy and the homotopy are preserved in the bubble tree limit. The result can be viewed as an associative analogue of the bubble tree convergence theorem for J-holomorphic curves. This is joint work with Spiro Karigiannis and Jesse Madnick" |
October 8, 2019, 4:15 pm - 5:15 pm at Sci Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Ananth Shankar (MIT) |
Picard ranks of families of K3 surfaces in positive characteristic |
Consider a generically ordinary family of K3 surfaces in characteristic p > 2. Under a mild technical hypothesis, we prove that there exist infinitely many specializations under which the Picard rank is greater than the generic Picard rank. This is joint work with Davesh Maulik and Yunqing Tang" |
October 8, 2019, 3:00 pm - 4:00 pm at Science Center 507 |
| CMSA MATH PHYSICS SEMINAR |
Xiao Zheng (BOSTON UNIVERSITY) |
Equivariant disc potentials and the SYZ mirror construction |
In this talk, I will introduce an equivariant mirror construction using a Morse model of equivariant Lagrangian Floer theory, formulated in a joint work with Kim and Lau. In case of semi-Fano toric manifold, our construction recovers the $T$-equivariant Landau--Ginzburg mirror found by Givental. For toric Calabi--Yau manifold, the equivariant disc potentials of certain immersed Lagrangians are closely related to the open Gromov--Witten invaraints of Aganagic--Vafa branes, which were studied by Katz--Liu, Graber--Zaslow, Fang--Liu--Zong and many others using localization techniques. The later result is a work in progress joint with Hong, Kim and Lau" |
October 07, 2019, 12:00 pm - 1:00 pm at CMSA, 20 Garden St, G10 |
| CMSA SPECIAL SEMINAR |
Liang Kong (SHENZHEN INSTITUTE OF QUANTUM SCIENCES AND ENGINEERING, SOUTHERN UNIVERSITY OF SCIENCE AND TECHNOLOGY) |
A unified mathematical theory of both gapped and gapless boundaries of 2+1D topological orders |
It was well known that a gapless boundary of a 2+1D topological order is different from and significantly richer than a gapped boundary. In this talk, however, we will propose a unified mathematical theory of both gapped and gapless boundaries of 2+1D topological orders. In particular, we will show that observables on the 1+1D world sheet of a chiral gapless boundary in the long wave length limit form an enriched fusion category, the Drinfeld center of which is precisely the unitary modular tensor category associated to the bulk. If time permits, we will also briefly discuss some consequences of this result, including a theory of non-chiral gapless boundaries, applications to boundary topological phase transitions, 0+1D defects between different gapless boundaries and a generalized boundary-bulk relation. This is joint work with Hao Zheng." |
October 4, 2019, 3:00 pm at CMSA, 20 Garden St, G10 |
| CMSA CONDENSED MATTER/MATH SEMINAR |
Ryan Thorngren (CMSA) |
Domain Walls and the CPT Theorem |
I will describe how in a relativistic quantum field theory, symmetry-broken domain walls enjoy a curious remnant of the broken symmetry obtained by a combination with the unbreakable CPT symmetry. There is an anomaly-matching condition relating the symmetry-preserving bulk phase to the anomaly on the wall. This condition is related to an interesting property of manifold cobordisms called the Smith isomorphism. I will prove some generalizations of the Smith isomorphism theorem and discuss some physics applications to superfluids and gauge theories. This is joint work with Itamar Hason and Zohar Komargodski" |
October 03, 2019, 12:00 pm - 1:00 pm at CMSA, 20 Garden St, G10 |
| THURSDAY SEMINAR |
Lucy Yang (HARVARD UNIVERSITY) |
Classical infinite loop space theory + epsilon |
" |
October 3, 2019, 3:00 pm - 5:00 pm at Science Center 507 |
| JOINT CMSA AND DEPARTMENT OF MATHEMATICS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Jian Ding (UNIVERSITY OF PENNSYLVANIA) |
Distances associated with Liouville quantum gravity |
I will review some recent progresses on distances associated with Liouville quantum gravity, which is a random measure obtained from exponentiating a planar Gaussian free field. The talk is based on works with Julien Dubédat, Alexander Dunlap, Hugo Falconet, Subhajit Goswami, Ewain Gwynne, Ofer Zeitouni and Fuxi Zhang in various combinations" |
October 3, 2019, 4:30 pm- 5:30 pm at CMSA Building, 20 Garden St, G02 |
| GROSS-SIEBERT PROGRAM SEMINAR |
Maxim Jeffs (HARVARD UNIVERSITY) |
Hocus-Pocus with the Focus-Focus Locus |
I will be giving a motivational talk on the symplectic perspective on integral affine manifolds with singularities and wall-crossing in dimension 2" |
October 03, 2019, 3:30 pm at Science Center 232 |
| CMSA SPACETIME SEMINAR |
Simon Caron-Huot (MCGILL UNIVERSITY) |
Poincare Duals of Feynman Integrals |
" |
October 03, 2019, 2:30 pm at CMSA, 20 Garden St, G10 |
| CMSA COLLOQUIUM |
Spiro Karigiannis (UNIVERSITY OF WATERLOO ) |
Cohomologies on almost complex manifolds and their applications |
We define three cohomologies on an almost complex manifold (M, J), defined using the Nijenhuis-Lie derivations induced from the almost complex structure J and its Nijenhuis tensor N, regarded as vector-valued forms on M. One of these can be applied to distinguish non-isomorphic non-integrable almost complex structures on M. Another one, the J-cohomology, is familiar in the integrable case but we extend its definition and applicability to the case of non-integrable almost complex structures. The J-cohomology encodes whether a complex manifold satisfies the del-delbar-lemma, and more generally in the non-integrable case the J-cohomology encodes whether (M, J) satisfies a generalization of this lemma. We also mention some other potential cohomologies on almost complex manifolds, related to an interesting question involving the Nijenhuis tensor. This is joint work with Ki Fung Chan and Chi Cheuk Tsang. " |
October 2, 2019, 4:30 pm- 5:30 pm at CMSA, 20 Garden St, G10 |
| CMSA QUANTUM MATTER/QUANTUM FIELD THEORY SEMINAR |
Zhen Bi (MIT) |
Novel quantum criticality beyond Landau-Ginzburg-Wilson-Fisher paradigm |
The infrared behavior of 3 + 1-D non-abelian gauge fields with massless matter fields is an extremely important and intensively studied topic in particle physics. In this talk, we asking the following question from a condensed matter perspective: given some deconfined gauge theory in 3 + 1-D, what phase transition can this theory describe? It turns out to be a fruitful way to think about these gauge theories and provides many explicit examples for several novel quantum critical phenomena. 1. We present several examples of Deconfined Quantum Critical Points (DQCP) between Symmetry Protected Topological phases in 3 + 1-D for both bosonic and fermionic systems. 2. We find situations in which the same phase transition allows for multiple universality classes controlled by distinct fixed points. 3. We exhibit the possibility - which we dub âunnecessary quantum critical pointsâ - of stable generic continuous phase transitions within the same phase. 4. We present examples of interaction driven band-theory forbidden continuous phase transitions between two distinct band insulators. 5. We find an example for a Landau-allowed quantum phase transition, however, with a critical theory that is beyond Landau description." |
October 02, 2019, 10:30 am - 12:00 pm at CMSA, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Ananth Shankar (MIT) |
Isogenies between abelian varieties in positive and mixed characteristic |
I will speak about various results pertaining to isogenies between abelian varieties, including the Hecke orbit conjecture and the question of finding abelian varieties not isogenous to Jacobians. This is based on joint work with Tsimerman, Maulik-Tang, and Kisin-Lam-Srinivasan." |
October 2, 2019, 3:00 pm at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Julian Scheuer (FREIBURG) |
The Minkowski inequality in de Sitter space |
The classical Minkowski inequality in the Euclidean space provides a lower bound on the total mean curvature of a hypersurface in terms of the surface area, which is optimal on round spheres. In this talk we present a curvature flow approach to prove a properly defined analogue in the Lorentzian de Sitter space" |
October 01, 2019, 4:15 pm - 5:15 pm at Sci Center 507 |
| CMSA MATH PHYSICS SEMINAR |
Dmitry Tonkonog (HARVARD UNIVERSITY) |
Floer theory and rigid subsets of symplectic manifolds |
Suppose we are given a symplectic manifold. What general things can we say about the dynamics of its symplectomorphisms? A classical way to explore this question is to find rigid subsets: subsets that cannot be displaced from themselves by any symplectomorphism. This has inspired many developments in Floer theory, including recent ones. I will survey the topic, and prove that Lagrangian skeleta of divisor complements of Calabi--Yau manifolds are rigid. This partially reports on joint work with Umut Varolgunes, as well as other things I learned from him" |
September 30, 2019, 12:00 pm - 1:00 pm at CMSA, 20 Garden St, G10 |
| HARVARD-MIT-MSR COMBINATORICS SEMINAR |
Chris Eur (UC BERKELEY) |
Simplicial generation of Chow rings of matroids |
How does the recent breakthrough in matroid theory, the Hodge theory of matroids, relate to the type A combinatorics of matroids? We give an answer via a new presentation of the Chow ring of a matroid, whose variables now admit a combinatorial interpretation as matroid truncations and display behaviors akin to nef classes on smooth projective varieties. We discuss various applications, including the recovery of the Hodge theory of matroids as developed by Adiprasito, Huh, and Katz. This is joint work with Spencer Backman and Connor Simpson" |
September 27, 2019, 3:30 pm at Sci Center 507 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Jon Bloom (BROAD INSTITUTE) |
Principal component analysis for topologists |
Geometrically, PCA finds the k-dimensional subspace nearest a point cloud in m-dimensional Euclidean space. Numerically, PCA also specifies a basis for this subspace, the principal directions of the data. Deep learning-ly, PCA is the shallowest of autoencoder models, that of a linear autoencoder (LAE) which learns the subspace but not the basis. I ll relate these views by considering the gradient dynamics of learning from the perspective of a simple F_2-perfect Morse function on the real Grassmannian. I ll then prove that L_2-regularized LAEs are symmetric at all critical points and recover the principal directions as singular vectors of the decoder, with implications for eigenvector algorithms and perhaps learning in the brain. If asked, I ll speculate on a role for Morse homology in deep learning. Based on Loss Landscapes of Regularized Linear Autoencoders (ICML 2019) with Daniel Kunin, Aleksandrina Goeva, and Cotton Seed at the Broad Institute. Resources here: https://github.com/danielkunin/Regularized-Linear-Autoencoders Future schedule is found here: https://scholar.harvard.edu/gerig/semina" |
September 27, 2019, 3:30 pm at Science Center 507 |
| CMSA CONDENSED MATTER/MATH SEMINAR |
Shu-Heng Shao (IAS) |
Anomalies and Charged Operators |
We study the implications of t Hooft anomaly for conformal field theory. Using the modular bootstrap, universal bounds on (1+1)-dimensional bosonic conformal field theories with an internal Z2 global symmetry are derived. We find that there is a universal upper bound on the lightest Z2 odd operator if the symmetry is anomalous, but there is no bound if the symmetry is non-anomalous. We further discuss the implications for the Weak Gravity Conjecture in AdS3/CFT2. Finally we present a conjecture on more general anomalies that cannot be matched by TQFTs, a notion known as the symmetry-protected gaplessness in condensed matter physics" |
September 26, 2019, 12:00 pm - 1:00 pm at CMSA, 20 Garden St, G10 |
| GROSS-SIEBERT PROGRAM SEMINAR |
Dmitry Tonkonog (HARVARD UNIVERSITY) |
The Gross-Siebert Construction, Part 1 |
Dmitry Tonkonog will explain the first step of the Gross-Siebert smoothing construction, where the integral affine base has no singularities (also called Mumford s construction)" |
September 26, 2019, 3:30 pm at Science Center 232 |
| CMSA SPACETIME SEMINAR |
Tomasz Taylor (NORTHEASTERN) |
Celestial Amplitudes |
" |
September 26, 2019, 2:30 pm at CMSA, 20 Garden St, G10 |
| CMSA COLLOQUIUM |
Pavel Etingof (MIT) |
Double affine Hecke algebras |
Double affine Hecke algebras (DAHAs) were introduced by I. Cherednik in the early 1990s to prove Macdonald s conjectures. A DAHA is the quotient of the group algebra of the elliptic braid group attached to a root system by Hecke relations. DAHAs and their degenerations are now central objects of representation theory. They also have numerous connections to many other fields -- integrable systems, quantum groups, knot theory, algebraic geometry, combinatorics, and others. In my talk, I will discuss the basic properties of double affine Hecke algebras and touch upon some applications" |
September 25, 2019, 4:30 pm- 5:30 pm at CMSA, 20 Garden St, G10 |
| CMSA MATH PHYSICS SEMINAR |
Fenglong You (UNIVERSITY OF ALBERTA) |
Gluing Periods for DHT Mirrors |
Let $X$ be a Calabi--Yau manifold that admits a Tyurin degeneration to a union of two quasi-Fano varieties $X_1$ and $X_2$ intersecting along a smooth anticanonical divisor $D$. Doran--Harder--Thompson conjectured that the Landau--Ginzburg mirrors of $(X_1,D)$ and $(X_2,D)$ can be glued to obtain the mirror of $X$. In this talk, I will explain how periods on the mirrors of $(X_1,D)$ and $(X_2,D)$ are related to periods on the mirror of $X$. The relation among periods relates different Gromov--Witten invariants via their respective mirror maps. This is joint work with Charles Doran and Jordan Kostiuk" |
September 25, 2019, 12:00 pm - 1:00 pm at CMSA, 20 Garden St, G10 |
| CMSA FLUID DYNAMICS SEMINAR |
Yantao Yang (PEKING UNIVERSITY) |
Double diffusive convection and thermohaline staircases |
Double diffusive convection (DDC), i.e. the buoyancy-driven flow with fluid density depending on two scalar components, is omnipresent in many natural and engineering environments. In ocean this is especially true since the seawater density is mainly determined by temperature and salinity. In upper water of both (sub-) tropical and polar oceans, DDC causes the intriguing thermohaline staircases, which consist of alternatively stacked convection layers and sharp interfaces with high gradients of temperature and salinity. In this talk, we will focus on the fingering DDC usually found in (sub-)tropical ocean, where the mean temperature and salinity decrease with depth. We numerically investigate the formation and the transport properties of finger structures and thermohaline staircases. Moreover, we show that multiple states exit for the exactly same global condition, and individual finger layers and finger layers within staircases exhibit very different transport behaviors." |
September 25, 2019, 3:00 pm - 4:00 pm at CMSA, 20 Garden St, G10 |
| JOINT CMSA AND DEPARTMENT OF MATHEMATICS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Jeff Schenker (MICHIGAN STATE UNIVERSITY) |
An ergodic theorem for homogeneously distributed quantum channels with applications to matrix product states |
Quantum channels represent the most general physical evolution of a quantum system through unitary evolution and a measurement process. Mathematically, a quantum channel is a completely positive and trace preserving linear map on the space of $D\times D$ matrices. We consider ergodic sequences of channels, obtained by sampling channel valued maps along the trajectories of an ergodic dynamical system. The repeated composition of these maps along such a sequence could represent the result of repeated application of a given quantum channel subject to arbitrary correlated noise. It is physically natural to assume that such repeated compositions are eventually strictly positive, since this is true whenever any amount of decoherence is present in the quantum evolution. Under such an hypothesis, we obtain a general ergodic theorem showing that the composition of maps converges exponentially fast to a rank-one -- entanglement breaking channel. We apply this result to describe the thermodynamic limit of ergodic matrix product states and prove that correlations of observables in such states decay exponentially in the bulk. (Joint work with Ramis Movassagh" |
September 25, 2019, 3:15 pm at CMSA, 20 Garden St, G02 |
| CMSA QUANTUM MATTER AND QUANTUM FIELD THEORY SEMINAR |
Juven Wang (CMSA) |
Higher-Rank Tensor Field Theory of Non-Abelian Fracton and Embeddon |
We introduce a new class of tensor field theories in any dimension that has an interesting mixing between symmetric-tensor gauge theory and anti-symmetric tensor topological field theory. The gauge group can be continuous and non-abelian. Our theory may be a new gem sitting in the virgin territory outside the familiar gauge theories -- outside the paradigm of Maxwell theory in 1865 and Yang-Mills theory in 1954. We discuss its relation to the non-abelian generalization of Fracton in condensed matter, and Embeddon that we will introduce. This will be an informal talk, based on upcoming work, jointly with Kai Xu (Harvard)" |
September 25, 2019, 10:30 am - 12:00 pm at CMSA, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Tony Feng (MIT) |
Steenrod operations and the Artin-Tate pairing |
In 1966 Artin and Tate constructed a canonical pairing on the Brauer group of a surface over a finite field, and conjectured it to be alternating. This duality has analogous incarnations across arithmetic and topology, namely the Cassels-Tate pairing for a Jacobian variety, and the linking form on a 5-manifold. I will explain a proof of the conjecture, which is based on a surprising connection to Steenrod operations." |
September 25, 2019, 3:00 pm at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Carl Lian (COLUMBIA) |
Enumerating pencils with moving ramification on curves |
We consider the general problem of enumerating branched covers of the projective line from a fixed general curve subject to ramification conditions at possibly moving points. Our main computations are in genus 1; the theory of limit linear series allows one to reduce to this case. We first obtain a simple formula for a weighted count of pencils on a fixed elliptic curve E, where base-points are allowed. We then deduce, using an inclusion-exclusion procedure, formulas for the numbers of maps E->P^1 with moving ramification conditions. A striking consequence is the invariance of these counts under a certain involution. Our results generalize work of Harris, Logan, Osserman, and Farkas-Moschetti-Naranjo-Pirola" |
September 24, 2019, 4:15 pm - 5:15 pm at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Remy van Dobben de Bruyn (PRINCETON UNIVERSITY ) |
A variety that cannot be dominated by one that lifts |
The recent proofs of the Tate conjecture for K3 surfaces over finite fields start by lifting the surface to characteristic 0. Serre showed in the sixties that not every variety can be lifted, but the question whether every motive lifts to characteristic 0 is open. We give a negative answer to a geometric version of this question, by constructing a smooth projective variety that cannot be dominated by a smooth projective variety that lifts to characteristic 0" |
September 24, 2019, 3:00 pm at Sci Center 507 |
| HARVARD-MIT-MSR COMBINATORICS SEMINAR |
Julianna Tymoczko (SMITH COLLEGE) |
Hessenberg varieties, combinatorial constructions of equivariant cohomology, and the Stanley-Stembridge conjecture |
The elementary symmetric functions form a well-known basis for the entire space of symmetric functions. The conjecture that the chromatic symmetric function of any (3+1)-free poset can be written as a nonnegative linear combination of elementary symmetric functions is often called the Stanley-Stembridge conjecture. We describe recent progress towards proving the Stanley-Stembridge conjecture that uses a combinatorial representation of a geometric object called a Hessenberg variety" |
September 20, 2019, 3:30 pm - 4:30 pm at Sci Center 530 |
| CMSA GENERAL RELATIVITY SEMINAR |
Martin Lesourd (BHI) |
Existence of minimal or marginally outer trapped surfaces from quasi-local mass |
I will describe work in progress with Aghil Alaee and Shing-Tung Yau in which sufficient conditions for the existence of minimal or marginally outer trapped surfaces inside a domain are expressed in terms of the quasi-local mass of the domain" |
September 20, 2019, 10:30 am - 11:30 am at Sci Center 530 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Yi Ni (CALTECH) |
Thurston norm minimizing Seifert surfaces |
Let K be a null-homologous knot in a closed 3-manifold Y, and F be a Seifert surface. One can cap off the boundary of F with a disk in the zero surgery on K to get a closed surface F_0. If we know that F is Thurston norm minimizing, we can ask whether F_0 is also Thurston norm minimizing. A classical theorem of Gabai says that the answer is Yes when Y is the 3-sphere. Gabai s theorem can be generalized to many other 3-manifolds using Heegaard Floer homology. In this talk, we will discuss a sufficient condition for F_0 to be Thurston norm minimizing. Future schedule is found here: https://scholar.harvard.edu/gerig/semina" |
September 20, 2019, 3:30 pm at Science Center 507 |
| THURSDAY SEMINAR |
Peter Haine (MIT) |
Local complete intersections, the cotangent complex, and the Hilbert scheme of framed points |
" |
September 19, 2019, 3:00 - 5:00 PM at Science Center 507 |
| GROSS-SIEBERT PROGRAM SEMINAR |
Charles Wang (HARVARD UNIVERSITY) |
Introduction to Toric Degenerations |
Charles Wang will give an introduction to toric degenerations and their dual intersection complexes." |
September 19, 2019, 3:30 pm at Science Center 232 |
| CMSA SPACETIME SEMINAR |
Chuck Doran (UNIVERSITY OF ALBERTA) |
Calabi-Yau geometry of the N-loop sunset Feynman integrals |
I will present an overview of the algebraic and transcendental features of the computation of N-loop sunset Feynman integrals. Starting from the realization of arbitrary Feynman graph hypersurfaces as (generalized) determinantal varieties, we describe the Calabi-Yau subvarieties of permutohedral varieties that arise from the N-loop sunset Feynman graphs and some key features of their geometry and moduli. These include: (1) an iterated fibration structure which allows one to bootstrap both periods and Picard-Fuchs equations from lower N cases; (2) specialization to and interpretation of coincident mass loci (jump loci) in moduli; (3) a significant generalization of the Griffiths-Dwork algorithm via creative telescoping and (4) the realization of Calabi-Yau pencils as Landau-Ginzburg models mirror to weak Fano varieties. Details of each of these will be discussed in later lectures this semester. This is joint work with Pierre Vanhove and Andrey Novoseltsev" |
September 19, 2019, 2:30 pm at CMSA, 20 Garden St, G10 |
| BRANDEIS-HARVARD-MIT-NORTHEASTERN JOINT COLLOQUIUM |
Will Sawin (COLUMBIA UNIVERSITY) |
The Twin Primes and Chowla conjectures in F_q[T] |
The twin primes conjecture predicts that there are infinitely many consecutive pairs of odd numbers that are both prime. It is closely related to Chowla s conjecture, which, among other things, counts the number of consecutive pairs of numbers with an odd number of prime factors. We can consider analogues of these questions where the natural numbers are replaced with polynomials over a finite field. In joint work with Mark Shusterman, we prove strong forms of both analogous conjectures under mild conditions on the finite field. The proof relies on powerful geometric tools as well as, at a crucial point, a simple algebraic trick involving derivatives of polynomials" |
September 19, 2019, Tea at 4:00 pm, Talk at 4:30 pm at Science Center Hall E |
| NUMBER THEORY SEMINAR |
Wei Zhang (MIT) |
The arithmetic fundamental lemma for diagonal cycles |
This is an update on the talk I gave almost 10 years ago in this seminar. The arithmetic Gan-Gross-Prasad (AGGP) conjecture, a high dimensional generalization of the Gross-Zagier theorem, relates the height pairing of arithmetic diagonal cycles on certain product Shimura varieties to the first central derivative of Rankin-Selberg tensor product L-functions. The arithmetic fundamental lemma conjecture, proposed about 10 years ago, arises from the relative trace formula approach to the AGGP conjecture. I will recall the statement of the arithmetic fundamental lemma and present (a sketch of) a proof" |
September 18, 2019, 3:00 pm at Sci Center 507 |
| CMSA COLLOQUIUM |
Bill Helton (UC SAN DIEGO) |
A taste of noncommutative convex algebraic geometry |
The last decade has seen the development of a substantial noncommutative (in a free algebra) real and complex algebraic geometry. The aim of the subject is to develop a systematic theory of equations and inequalities for (noncommutative) polynomials or rational functions of matrix variables. Such issues occur in linear systems engineering problems, in free probability (random matrices), and in quantum information theory. In many ways the noncommutative (NC) theory is much cleaner than classical (real) algebraic geometry. For example, A NC polynomial, whose value is positive semidefinite whenever you plug matrices into it, is a sum of squares of NC polynomials. A convex NC semialgebraic set has a linear matrix inequality representation. The natural Nullstellensatz are falling into place. The goal of the talk is to give a taste of a few basic results and some idea of how these noncommutative problems occur in engineering. The subject is just beginning and so is accessible without much background. Much of the work is joint with Igor Klep who is also visiting CMSA for the Fall of 2019. " |
September 18, 2019, 4:30 pm- 5:30 pm at CMSA, 20 Garden St, G10 |
| CMSA FLUID DYNAMICS SEMINAR |
Jiawei Zhuang (HARVARD UNIVERSITY) |
The computational cost of fluid simulations grows rapidly with grid resolution. With the recent slow-down of Moore's Law, it can take many decades for 10x higher resolution grids to become affordable. To break this major barrier in high-performance scientific computing, we used a data-driven approach to learn an optimal numerical solver that can retain high-accuracy at much coarser grids. We applied this method to 2-D turbulent advection and achieved 4x effective resolution than traditional high-order flux-limited advection solvers. The machine learning component is tightly integrated with traditional finite-volume schemes and can be trained via an end-to-end differentiable programming framework. The model can achieve near-peak FLOPs on CPUs and accelerators via convolutional filters. |
The computational cost of fluid simulations grows rapidly with grid resolution. With the recent slow-down of Moore s Law, it can take many decades for 10x higher resolution grids to become affordable. To break this major barrier in high-performance scientific computing, we used a data-driven approach to learn an optimal numerical solver that can retain high-accuracy at much coarser grids. We applied this method to 2-D turbulent advection and achieved 4x effective resolution than traditional high-order flux-limited advection solvers. The machine learning component is tightly integrated with traditional finite-volume schemes and can be trained via an end-to-end differentiable programming framework. The model can achieve near-peak FLOPs on CPUs and accelerators via convolutional filters" |
September 18, 2019, 3:00 pm at CMSA, 20 Garden St, G10 |
| CMSA QUANTUM MATTER AND QUANTUM FIELD THEORY SEMINAR |
Po-Shen Hsin (CALTECH) |
Lorentz symmetry fractionalization and duality in (2+1)d |
I will introduce a discrete transformation in bosonic QFTs with Z2 one-form symmetry using the concept of symmetry fractionalization in condensed matter physics. I will then discuss some applications including boson/fermion dualities in (2+1)d" |
September 18, 2019, 10:30 am - 12 pm at CMSA, 20 Garden St, G10 |
| LOGIC SEMINAR |
Sebastien Vasey (HARVARD UNIVERSITY) |
The Weak Diamond |
The weak diamond is a combinatorial guessing principle which came out of Shelah s work on Whitehead s problem. It was introduced by Devlin and Shelah. As opposed to the usual diamond, weak diamond follows from the continuum hypothesis, and even just from strict monotonicity of cardinal exponentiation. I will give an introduction to the principle. Time permitting, I will also discuss using the weak diamond to obtain amalgamation properties in abstract model theory" |
September 18, 2019, 4:00 pm - 5:00 pm at Logic Center, Room 420, 2 Arrow Street |
| DIFFERENTIAL GEOMETRY SEMINAR |
Xin Zhou (UCSB) |
Existence of hypersurfaces with prescribed mean curvature |
I will present some results on the construction of closed hypersurfaces with prescribed mean curvature (PMC) in closed manifolds. In particular, I will start by reporting a joint work with Jonathan Zhu, in which we proved the existence of PMC hypersurfaces for a large class of prescribing functions by min-max method. I will also talk about Morse index bounds for those min-max PMC hypersurfaces. This topic is related to Problem 59 in Professor Yau s famous 1982 problem section" |
September 17, 2019, 4:15 pm - 5:15 pm at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Geoffrey Smith (HARVARD UNIVERSITY) |
Stability conditions and the irrationality of surfaces |
The degree of irrationality of a variety is the minimal degree of a dominant rational map from the variety to a projective space of the same dimension. In this talk, I will discuss one relatively new method of bounding the degree of irrationality of some surfaces, using a connection between the irrationality of the surface and the tilt stability of certain rank three sheaves on threefolds. This method is sufficient, for instance, to show that the degree of irrationality of a very general genus 5 K3 surface is 4" |
September 17, 2019, 3:00 pm at Science Center 507 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Eirik Eik Svanes (KING'S COLLEGE LONDON AND ICTP) |
On coupled moduli problems and effective topological theories |
I will discuss recent developments in understanding coupled moduli spaces for geometries which appear naturally in string theory. Focusing on heterotic geometries and SU(3) and G2 structure compactifications in particular, which also come equipped with a gauge sector, I will describe how the moduli are captured by effective quasi-topological theories derived from the heterotic supergravity. In the case of SU(3) structure compactifications the topological theory in question is a natural generalization of holomorphic Chern--Simons theory or Donaldson--Thomas theory. In the case of heterotic G2 structures we will see that the moduli problem is a lot more coupled, and the moduli space has no intrinsic fibration structure in general" |
September 16, 2019, 12 pm - 1 pm at CMSA, 20 Garden St, G10 |
| CMSA GENERAL RELATIVITY SEMINAR |
Martin Lesourd (BHI) |
Shi-Tam's Existence of Minimal Surfaces from Quasi-Local Mass |
Thorne s hoop conjecture is an intuitive hypothesis intended to capture necessary and sufficient conditions for the existence of a black hole region. The first result in this direction was Schoen-Yau 83 and later Yau 01, which give sufficient conditions for the existence of an apparent horizon within a 3-dimensional initial data set. Shi-Tam 07 have done something analogous in the Riemannian context and obtained the existence of minimal surfaces from conditions on quasi-local mass. We shall review the main ideas of their proof" |
September 13, 2019, 10:30 am - 11:30 am at CMSA, 20 Garden St, G02 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Dmitry Tonkonog (HARVARD UNIVERSITY) |
Floer-theoretic heaviness and Lagrangian skeleta |
I will talk on what I have learned from Umut Varolgunes, and on our work in preparation. In 2007, Entov and Polterovich introduced the notion of heavy and superheavy subsets of symplectic manifolds; such subsets have remarkable symplectic rigidity properties. One can define a variant version of (super)heaviness using relative symplectic homology studied by Varolgunes. I will explain this story, and prove that Lagrangian skeleta of symplectic divisor complements of Calabi-Yau s are superheavy in this sense" |
September 13, 2019, 3:30 - 4:30 pm at Science Center 507 |
| GROSS-SIEBERT PROGRAM SEMINAR |
Denis Auroux (HARVARD UNIVERSITY) |
Introduction to SYZ Mirror Symmetry |
Denis Auroux will give an introduction to SYZ mirror symmetry and an overview of the Gross-Siebert program" |
September 12, 2019, 3:30 pm at Science Center 232 |
| THURSDAY SEMINAR |
Michael Hopkins (HARVARD UNIVERSITY) |
Infinite loop spaces in motivic homotopy theory: Overview |
" |
September 12, 2019, 3:00 - 5:00 pm at Science Center 507 |
| CMSA SPACETIME SEMINAR |
Pasha Pylyavskyy (UNIVERSITY OF MINNESOTA) |
Vector-relation configurations and plabic graphs |
" |
September 12, 2019, 2:30 pm at CMSA, 20 Garden St, G10 |
| JOINT CMSA AND DEPARTMENT OF MATHEMATICS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Subhabrata Sen (HARVARD UNIVERSITY) |
Sampling convergence for random graphs: graphexes and multigraphexes |
We will look at structural properties of large, sparse random graphs through the lens of sampling convergence (Borgs, Chayes, Cohn and Veitch Sampling convergence generalizes left convergence to sparse graphs, and describes the limit in terms of a graphex. We will introduce this framework and motivate the components of a graphex. Subsequently, we will discuss the graphex limit for several well-known sparse random (multi)graph models. This is based on joint work with Christian Borgs, Jennifer Chayes, and Souvik Dhara." |
September 11, 2019, 1:45 pm - 2:45 pm at CMSA, 20 Garden St, G02 |
| NUMBER THEORY SEMINAR |
Fabian Gundlach (HARVARD UNIVERSITY) |
Multiplication tables of Galois extensions |
How quickly can you specify a Galois extension (of Q, say) with Galois group G? For S_2-extensions, you only need to say one (rational) number. For S_3-extensions, Levi showed that a binary cubic form suffices. Wright and Yukie noticed that for S_4-extensions, two symmetric 3x3-matrices suffice, and for S_5-extensions, four skew-symmetric 5x5-matrices are enough. We explore a general strategy that reproduces these known examples and generates new parametrizations for other groups" |
September 11, 2019, 3:00 pm - 4:00 pm at Science Center 507 |
| BLACK HOLE INITIATIVE LECTURE |
Hanoch Gutfreund (HEBREW UNIVERSITY) |
Relatively Speaking: Einstein and Black Holes |
https://www.afhu.org/relativelyspeakin" |
September 11, 2019, 5:30 pm at Northwest Science Building, Room B103 |
| OPEN NEIGHBORHOOD SEMINAR |
Joe Harris (HARVARD UNIVERSITY) |
How many lines meet each of 4 given lines in 3-space, and why it matters |
" |
September 11, 2019, 4:30 pm at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Ziquan Zhuang (MIT) |
Birational superrigidity is not a locally closed property |
A Fano variety is said to be birationally superrigid if every birational map from it to a Mori fiber space is an isomorphism. In this talk, we investigate whether these exists a nice moduli for this very special class of Fano varieties. Such moduli would exist if birational superrigidity is a locally closed property in family. We show that this is not true in general by providing a counterexample" |
September 10, 2019, 3:00 pm at 2-147 MIT |
| DIFFERENTIAL GEOMETRY SEMINAR |
Ahil Alaee (CMSA) |
Geometric inequalities for quasi-local masses |
In this talk, we establish lower bounds for quasi-local masses in terms of charge, angular momentum, and horizon area. In particular, we treat three quasi-local masses based on a Hamiltonian approach, namely the Brown-York, Liu-Yau, and Wang-Yau masses. The geometric inequalities are motivated by analogous results for the ADM mass. They may be interpreted as localized versions of these inequalities, and are also closely tied to the conjectured Bekenstein bounds for entropy of macroscopic bodies. In addition, we give a new proof of the positivity property for the Wang-Yau mass which can be used to remove the spin condition in higher dimensions. Furthermore, we generalize a recent result of Lu and Miao to obtain a localized version of the Penrose inequality for the static Liu-Yau mass. This is joint work with Marcus Khuri and Shing-Tung Yau" |
September 10, 2019, 4:15 - 5:15 pm at Science Center 507 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Daniel Pomerleano (UNIVERSITY OF MASSACHUSETTS BOSTON) |
Intrinsic mirror symmetry via symplectic topology |
Given a maximally degenerate log Calabi--Yau variety $X$, I will describe how one can recover the birational class of the mirror manifold from a Floer theoretic invariant of $X$ (symplectic cohomology). I will then explain how this result relates to recent constructions in mirror symmetry due to Gross--Hacking--Keel and Gross--Siebert" |
September 09, 2019, 12:00 pm - 1:00 pm at CMSA, 20 Garden St, G10 |
| GROSS-SIEBERT PROGRAM SEMINAR |
() |
Organizational meeting |
This will be an organizational meeting for the Gross-Siebert program seminar: the seminar will focus on the Gross-Siebert construction of toric degenerations and theta functions, and their relations to homological mirror symmetry and cluster algebras. For more information, see the webpage http://math.harvard.edu/~jeffs/gsprogram.htm" |
September 05, 2019, 3:30 pm at Science Center 232 |
| CMSA SPECIAL SEMINAR |
Masaki Oshikawa (U TOKYO) |
Gauge invariance, polarization, and conductivity |
The large gauge transformation on a quantum many-body system under a periodic boundary condition has had numerous applications including generalizations of Lieb-Schultz-Mattis theorem. It is also deeply related to the electric polarization in insulators. I will discuss an application to a scaling of the fluctuation of the polarization in conductors, and also to general constraints on the electric conductivity" |
May 28, 2019, 10:30 am at CMSA, 20 Garden St, G10 |
| CMSA FLUID DYNAMICS SEMINAR |
Jörn Dunkel (MIT) |
Symmetry breaking in active and quantum fluids |
Active biological fluids, such as bacterial and other microbial suspensions, exhibit striking spontaneous symmetry breaking phenomena, from the formation of vortex lattices to the emergence of large-scale unidirectional flows. Borrowing ideas from classical pattern formation theory, I will discuss generalized Navier-Stokes (GNS) equations as an analytically tractable minimal model of stress-driven active fluids. The GNS equations permit exact stress-free bulk solutions in planar and curved geometries, including Abrikosov-type lattices in 2D and Beltrami flows in 3D. A triad analysis shows that the combination of a generic linear instability and a standard advective nonlinearity can give rise to spontaneous chiral symmetry breaking that supports inverse energy transport in 3D. In the second part, we extend the underlying concepts to quantum fluids by deriving a higher-order generalization of the Gross-Pitaevskii equation to study supersolid crystals and quasi-crystals." |
May 22, 2019, 3:00 pm - 4:00 pm at CMSA, 20 Garden St, G10 |
| CMSA FLUID DYNAMICS SEMINAR |
Tamer A. Zaki (JOHNS HOPKINS UNIVERSITY) |
The Onset of Chaos in Shear Flows |
The manner in which infinitesimal disturbances can cause organized fluid motion to become chaotic is an intriguing phenomenon. In addition to being of great theoretical interest, laminar-to-turbulence transition is of significant importance due to its role in heat transfer, its influence on momentum mixing, and its effect on drag. In this work, we present complementary theoretical analyses, high-fidelity direct numerical simulations and data-enabled predictions of transition to turbulence in boundary layers. The proceedings of transition are not unique, and various pathways can ultimately lead to boundary-layer turbulence. In real-world applications, the presence of free-stream disturbances promotes early onset of turbulence, and transition is said to bypass other routes that have been traditionally examined using stability theory. Numerical simulations of this bypass transition process reveal that high-frequency disturbances from the free stream are expelled by the boundary-layer shear a phenomenon known as shear sheltering. Using asymptotic analysis, we develop a physical understanding of the mechanics of shear sheltering, and explain how low-frequency free-stream perturbations can permeate the mean shear. These elongated disturbances force the boundary layer resonantly and lead to the amplification of streaks. While the majority of the laminar streaks are innocuous, a small proportion undergoes a localized instability and breaks down to turbulence. Reports in the literature present conflicting views on the origin of streak breakdown as a matter that we address by performing secondary instability analyses of realistic streaks as well as using artificial neural networks. The predicted streak instabilities are shown to cause breakdown to turbulence in complementary direct numerical simulations." |
May 15, 2019, 3:00 pm - 4:00 pm at CMSA, 20 Garden St, G10 |
| CMSA METRIC LIMITS OF CALABI-YAU MANIFOLDS LECTURE SERIES |
Valentino Tosatti (NORTHWESTERN UNIVERSITY) |
A priori estimates |
I will give an introduction to the study of limits of Ricci-flat Kahler metrics on a compact Calabi-Yau manifold when the Kahler class degenerates to the boundary of the Kahler cone. Analytically, the problem is to prove suitable uniform a priori estimates for solutions of a degenerating family complex Monge-AmpĂšre equations, away from some singular set. Geometrically, this can be used to understand the Gromov-Hausdorff limit of these metrics. In the projective case, the limits possess an algebraic structure and are obtained from the initial manifold via contraction morphisms from Mori theory. I will discuss some results on this problem, in both the noncollapsing case and in the much harder collapsing case. I will also discuss a different source of examples, coming from work of McMullen and Cantat in complex dynamics on K3 surfaces" |
May 10, 2019, 3:00 pm - 4:00 pm at CMSA, 20 Garden St, G10 |
| CMSA TOPICAL ASPECTS OF CONDENSED MATTER SEMINAR |
Michael Zaletel (UC BERKELEY) |
Three-partite entanglement in CFTs and chiral topological orders |
While the entanglement entropy provides an essentially complete description of two-partite entanglement, multi-partite entanglement is far richer, with a concomitant zoo of possible measures. This talk will focus on applications of one such measure, the entanglement of purification, in many-body systems. I will first present a holographic prescription for calculating it which we can compare with numerical calculations. Interestingly, we find that a 1+1D CFT on a ring contains a universal number of GHZ states for any tri-partition of the ring. Using this result I ll conjecture a bulk entanglement diagnostic for 2+1D chiral orders, and solicit the audience s help in proving or disproving it" |
May 09, 2019, 10:30 am at CMSA, 20 Garden St, G10 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Igor Krylov (KOREA INSTITUTE FOR ADVANCED STUDY) |
Birational rigidity of low degree del Pezzo fibrations |
A Mori fiber space is called birationally rigid if, roughly speaking, it has only one Mori fiber space structure. I will talk about birational rigidity of singular del Pezzo fibrations. I will explain the essence of the method of proving birational rigidity: Noether-Fano method, also known as method of maximal singularities. I will discuss the differences in applying this to Fano varieties and Mori fiber spaces with a positive dimensional base" |
May 07, 2019, 3:00 pm at Science Center 507 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Dennis Borisov (AARHUS/CMSA) |
Global shifted potentials for -2-shifted symplectic structures |
I will explain the notion of shifted symplectic structures due to Pantev, Toen, Vaquie and Vezzosi, and then show that a derived scheme with a -2-shifted symplectic structure can be realized as critical locus of a globally defined -1-shifted potential. Joint work with Artan Sheshmani" |
May 06, 2019, 12 pm - 1 pm at CMSA, 20 Garden St, G10 |
| CMSA SPECIAL TALK |
Ming Hu (PICOWER INSTITUTE FOR LEARNING AND MEMORY, MIT) |
The Retinotopic Representation of the Visual Field in Early Visual Cortex - A Geometric View |
In this talk, I will first review the studies of neural representation of the external physical space in early visual system, namely retinotopic representation of the visual field. Then I ll introduce some of my recent works on rodent vision and show how the rodent visual cortex follows the same global principles of visual cortex maps in other species, with variations in local layout that possibly reflect the ecological adaption of vision in these species. Finally, I ll share my thinking of vision from a geometric perspective and its possible role for advancing our understanding of visual perceptio" |
May 06, 2019, 2:15 pm at CMSA, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Romyar Sharifi (UCLA) |
Iwasawa modules in higher codimension |
Classically speaking, Iwasawa theory concerns the growth of p-parts of class groups in towers of number fields of p-power degree. One considers an inverse limit of such groups as a finitely generated, torsion module over a completed pro-p group ring of the tower. Often, this growth can be slow enough that the support of this unramified module lies in codimension two and higher, while invariants like characteristic ideals which one hopes might be described through L-values fail to measure anything beyond codimension one. The typical way around this is to allow ramification at enough primes over p to make the module larger. Yet, the original modules are certainly of arithmetic interest. I ll discuss how, over CM fields, these unramified Iwasawa modules and others satisfy nice reflection principles and how p-adic L-functions tell us something about them. More generally, I ll explain how p-adic L-functions can be used to describe quotients of exterior powers of Iwasawa modules of restricted ramification. This is joint work with F. Bleher, T. Chinburg, R. Greenberg, M. Kakde, and M. Taylor, building on prior joint work of these authors and G. Pappas." |
May 01, 2019, 3:00 - 4:00 pm at Science Center 507 |
| CMSA FLUID DYNAMICS SEMINAR |
David Sondak (IACS, HARVARD UNIVERSITY) |
Towards Machine Learning for Cataloguing Optimal Solutions in Turbulent Convection |
Fluids have had a profound impact on scientific and engineering pursuits. They impact life at its most basic levels (e.g. biological fluids) but are also found in astrophysical environments (e.g. solar physics). Moreover, understanding and working with fluids has significant implications for engineering systems. For example, fluids are good at transporting energy in the form of heat. In order to work efficiently with fluids, engineers and scientists must be able to predict forces that fluids exert on their surroundings. This is a major challenge, further confounded by the phenomenon of turbulence in which fluid flows are disordered and erratic. Understanding and predicting turbulent flows is a major open problem in classical physics with numerous practical applications. In this talk, optimal solutions that maximize heat transport in turbulent Rayleigh-BĂ©nard convection are presented. The talk begins with an overview of fluid mechanics, turbulence, and Rayleigh-BĂ©nard convection before introducing the idea of optimal solutions, their computation, and their relevance to turbulence. The second half of the talk will focus on methods for detecting the signature of these optimal solutions. Machine learning algorithms may provide new routes forward for detecting the optimal solutions in a turbulent flow. The talk will close with an application of autoencoders on a turbulent dataset in an effort to discern some of the building-blocks of turbulence." |
May 01, 2019, 3:00 pm - 4:00 pm at CMSA, 20 Garden St, G02 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Shawn Xingshan Cui (VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY) |
Four dimensional topological quantum field theories from G-crossed braided categories |
We construct a state-sum type invariant of smooth closed oriented 4-manifolds out of a G-crossed braided spherical fusion category (G-BSFC) for G a finite group. The construction can be extended to obtain a (3+1)-dimensional topological quantum field theory (TQFT). The invariant of 4-manifolds generalizes several known invariants in literature such as the Crane-Yetter invariant from a ribbon fusion category and Yetter s invariant from homotopy 2-types. Furthermore, a cohomology class in H4(G,U(1)) can be introduced to produce a different invariant, which reduces to the twisted Dijkgraaf-Witten theory in a special case. Very recently, Reutter and Douglas generalized the above construction to spherical fusion 2-categories, which is expected to produce the most general (3+1)-TQFTs of state-sum type." |
April 30, 2019, 3:00 pm at Jefferson 356 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Adam Jacob (UC DAVIS) |
Adiabatic limits of Yang-Mills connections on collapsing K3 surfaces |
In this talk I will discuss the vector bundle analogue of the degeneration problem for Ricci flat K3 surfaces considered by Gross-WIlson (and later Gross-Tosatti-Zhang). Namely, given an elliptically fibered K3 surface equipped with complex vector bundle, what are the convergence properties of a family of SU(n) ASD Yang-Mills connections as the elliptic fibers collapse? Under certain geometric assumptions, I will demonstrate W^{1,p} convergence away from a finite number of fibers, and show how the limit is uniquely determined by the sequence of holomorphic structures. This is joint work with Ved Datar and Yuguang Zhang" |
April 30, 2019, 5:45 pm at CMSA, 20 Garden St, G10 |
| OPEN NEIGHBORHOOD SEMINAR |
Alissa Crans (LOYOLA MARYMOUNT) |
Matrices, Reflections, and Knots, oh my! |
Motivated by questions arising in starkly different contexts, quandles have been discovered and rediscovered over the past century. The axioms defining a quandle simultaneously encode the three Reidemeister moves from classical knot theory and capture the essential properties of conjugation. Thus, on the one hand, quandles are a fruitful source of applications to knots and knotted surfaces; in particular they provide a complete invariant of knots. On the other, they inspire independent interest as algebraic structures; for instance, the set of operation preserving maps from one quandle to another admits a natural quandle structure in a large class of cases. We will illustrate the history of this theory through numerous examples and survey recent developments. (This talks will be accessible to members of the department at all levels." |
April 29, 2019, 4:30 pm at Science Center 507 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Zili Zhang (UNIVERSITY OF MICHIGAN) |
P=W, a strange identity for Dynkin diagrams |
Start with a compact Riemann surface X with marked points and a complex reductive group G. According to Hitchin-Simpson s nonabelian Hodge theory, the pair (X,G) comes with two new complex varieties: the character variety M_B and the Higgs moduli M_D. I will present some aspects of this story and discuss an identity P=W indexed by affine Dynkin diagrams - occurring in the singular cohomology groups of M_D and M_B, where P and W dwell. Based on joint work with Junliang Shen" |
April 29, 2019, 12:00 pm - 1:00 pm at CMSA, 20 Garden St, G02 |
| CMSA SPECIAL SEMINAR |
Maissam Barkeshli (UNIVERSITY OF MARYLAND) |
Relative anomalies in (2+1)D symmetry enriched topological states |
It has recently been understood that some patterns of symmetry fractionalization in topologically ordered phases of matter are anomalous, in the sense that they can only occur at the surface of a higher dimensional symmetry-protected topological (SPT) state. In this talk I will explain some recent advances in our understanding of how to compute relative anomalies between different symmetry fractionalization classes in (2+1)D topological states. The theory applies to general types of symmetries, including symmetries that permute anyon types and space-time reflection symmetries. This allows us to compute anomalies for more general types of space-time reflection symmetries than previously known methods." |
April 26, 2019, 10:30 am at CMSA, 20 Garden St, G10 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Jennifer Hom (GEORGIA TECH) |
Heegaard Floer and homology cobordism |
We show that the three-dimensional homology cobordism group admits an infinite-rank summand. It was previously known that the homology cobordism group contains an infinite-rank subgroup and a Z-summand. The proof relies on the involutive Heegaard Floer homology package of Hendricks-Manolescu and Hendricks-Manolescu-Zemke. This is joint work with I. Dai, M. Stoffregen, and L. Truong. Future schedule is found here: https://scholar.harvard.edu/gerig/semina" |
April 26, 2019, 3:30 pm at Science Center 507 |
| CMSA GENERAL RELATIVITY SEMINAR |
Armando Cabrera Pacheco (UNIVERSITĂ€T TĂŒBINGEN) |
Asymptotically flat extensions with charge |
Inspired by the Mantoulidis and Schoen construction, we obtain time-symmetric black hole initial data sets for the Einstein--Maxwell equations satisfying the dominant energy condition, such that their horizon boundary geometry is prescribed, and their total masses and total charges are controlled. We also formulate a notion of boundary Bartnik mass in this context and compute its value for minimal Bartnik data. This talk is based on a joint work with A. Alaee and C. Cederbaum" |
April 26, 2019, 2:30-3:30 pm at CMSA, 20 Garden Street, G02 |
| CMSA SPECIAL SEMINAR |
Zhouli Xu (MIT) |
The intersection form of spin 4-manifolds and Pin(2)-equivariant Mahowald invariants |
A fundamental problem in 4-dimensional topology is the following geography question: which simply connected topological 4-manifolds admit a smooth structure? After the celebrated work of Kirby-Siebenmann, Freedman, and Donaldson, the last uncharted territory of this geography question is the 11/8-Conjecture . This conjecture, proposed by Matsumoto, states that for any smooth spin 4-manifold, the ratio of its second-Betti number and signature is least 11/8. Furuta proved the 10/8+2 -Theorem by studying the existence of certain Pin(2)-equivariant stable maps between representation spheres. In this talk, we will present a complete solution to this problem by analyzing the Pin(2)-equivariant Mahowald invariants of powers of certain Euler classes in the RO(Pin(2))-graded equivariant stable homotopy groups of spheres. In particular, we improve Furuta s result into a 10/8+4 -Theorem. Furthermore, we show that within the current existing framework, this is the limit. For the proof, we use the technique of cell-diagrams, known results on the stable homotopy groups of spheres, and the j-based Atiyah-Hirzebruch spectral sequence. This is joint work with Michael Hopkins, Jianfeng Lin and XiaoLin Danny Shi" |
April 26, 2019, 1:30 pm-2:30 pm at CMSA, 20 Garden St, G10 |
| JOINT CMSA AND DEPARTMENT OF MATHEMATICS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Benjamin Fehrman (OXFORD UNIVERSITY) |
Pathwise well-posedness of nonlinear diffusion equations with nonlinear, conservative noise |
We present a pathwise well-posedness theory for stochastic porous media and fast diffusion equations driven by nonlinear, conservative noise. Such equations arise in the theory of mean field games, approximate the Dean-Kawasaki equation in fluctuating fluid dynamics, describe the fluctuating hydrodynamics of the zero range process, and model the evolution of a thin film in the regime of negligible surface tension. Motivated by the theory of stochastic viscosity solutions, we pass to the equation s kinetic formulation, where the noise enters linearly and can be inverted using the theory of rough paths. The talk is based on joint work with Benjamin Gess" |
April 25, 2019, 4:30 pm- 5:30 pm at CMSA, 20 Garden St, G10 |
| CMSA FLUID DYNAMICS SEMINAR |
Neel Patel (UNIVERSITY OF MICHIGAN) |
Local Existence and Blow-Up for SQG Patches |
We consider the evolution of sharp temperature fronts in the two-dimensional surface quasi-geostrophic (SQG) equation. This equation has been used as a model for atmospheric or oceanic flows and has structural similarity with the 3D Euler equation. The I-patch problem for studies the evolution of patch solutions to a family of transport equations, where α = 0 and α = 1 correspond to the Euler vortex patches and the SQG sharp temperature fronts respectively. Previously, finite time singularities have been demonstrated on the half-plane setting for the family of functions 0 < α < 1/12 by first establishing local well-posedness of the system for that range and then constructing a blow-up solution. In this talk, we extend that result to 0 < α < 1/3 by exploring a new cancellation in the patch contour equation. Furthermore, this cancellation can be used to prove a singularity criterion of lower regularity than the numerical results for SQG patches and to prove lower regularity local existence results for the extended family of equations 0 < α < 2" |
April 25, 2019, 12 pm - 1 pm at CMSA, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Yiannis Sakellaridis (RUTGERS ) |
A new paradigm for the comparison of trace formulas |
Trace formulas are the mainstream method for proving Langlands functoriality, relating the local and automorphic spectra of different groups; in the generalization provided by the relative trace formula, groups can be replaced by appropriate homogeneous spaces. However, the endoscopic paradigm of comparisons has nearly reached its limits. In this talk, I will introduce a new paradigm for comparing relative trace formulas, in order to prove instances of (relative) functoriality and relations between periods of automorphic forms and L-functions. More precisely, for an affine spherical variety X=H\G of rank one, I will prove that there is an explicit integral transfer operator which transforms the orbital integrals of the relative trace formula for H\G/H to the orbital integrals of the Kuznetsov formula for PGL(2) or SL(2), equipped with suitable non-standard test functions. The operator is determined by the L-value associated to the square of the H-period integral, and the proof uses a deep theory of Friedrich Knop on the cotangent bundles of spherical varieties, viewed as Hamiltonian manifolds. If time permits, I will also discuss other instances of such non-standard comparisons, including Venkatesh s thesis that gave a beyond endoscopy proof of functoriality from tori to SL(2), and Hankel transforms which encode the functional equations of L-functions." |
April 24, 2019, 3:00 - 4:00 pm at Science Center 507 |
| TOPOLOGICAL ASPECTS OF CONDENSED MATTER SEMINAR |
Michael Freedman (MICROSOFT STATION Q) |
Quantum cellular automata in higher dimensions |
I ll discuss joint work with Matt Hastings on local endomorphisms of the operator algebra. We found these have a cohomological invariant similar to that of an incompressible flow" |
April 24, 2019, 10:30 am at CMSA Building, 20 Garden St, G10 |
| CMSA FLUID DYNAMICS SEMINAR |
Heng Xiao (VIRGINIA TECH) |
Turbulence Modeling in the Age of Data: From Data Assimilation to Machine Learning |
Many complex systems are characterized by physics at a wide range of scales, for which first-principle-based high-fidelity models resolving all the scales are prohibitively expensive to run. Consequently, practical simulations have primarily relied on low-fidelity models with approximate closure models, which introduce large model-form uncertainties and diminish their predictive capabilities. Turbulent flows are a classical example of such complex physical systems, where numerical solvers with turbulence closure models are widely used in industrial flow simulations. In light of the decades-long stagnation in traditional turbulence modeling, data-driven methods have been proposed as a promising alternative. We present a comprehensive framework for using data to reduce model uncertainties in turbulent flow simulations. For online, continuously streamed monitoring data, we use data assimilation and Bayesian inference to reduce model-form uncertainties; For offline data from a database of flows, we proposed a physics-informed machine learning approach to reduce model discrepancies. In both cases, we emphasized enforcing physical constraints in the data-driven modeling. More information: https://www.aoe.vt.edu/people/faculty/xiaoheng/personal-page/publications.htm" |
April 24, 2019, 3:00 - 4:00 pm at CMSA, 20 Garden St, G10 |
| CMSA COLLOQUIUM |
Shengwu Li (HARVARD UNIVERSITY) |
Credible Mechanisms |
Consider an extensive-form mechanism, run by an auctioneer who communicates sequentially and privately with agents. Suppose the auctioneer can deviate from the rules provided that no single agent detects the deviation. A mechanism is credible if it is incentive-compatible for the auctioneer to follow the rules. We study the optimal auctions in which only winners pay, under symmetric independent private values. The first-price auction is the unique credible static mechanism. The ascending auction is the unique credible strategy-proof mechanism" |
April 24, 2019, 4:30 pm- 5:30 pm at CMSA, 20 Garden St, G10 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Yi-Hong Zhang (TSINGHUA UNIVERSITY) |
Quantum many-body computation on a small quantum computer |
What can we do on a small scale near-term noisy quantum computer with O(10) qubits? We propose a variational scheme to study ground state properties of quantum many-body systems with fewer qubits. Studying ground state of quantum magnets and quantum chemistry problems in this way will be one of few killer applications of a near-term quantum computer" |
April 23, 2019, 3:00 pm at Jefferson 356 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Kalina Mincheva (YALE UNIVERSITY ) |
Tropical Algebra |
Tropical geometry provides a new set of purely combinatorial tools, which has been used to approach classical problems. In tropical geometry most algebraic computations are done on the classical side - using the algebra of the original variety. The theory developed so far has explored the geometric aspect of tropical varieties as opposed to the underlying (semiring) algebra and there are still many commutative algebra tools and notions without a tropical analogue. In the recent years, there has been a lot of effort dedicated to developing the necessary tools for commutative algebra using different frameworks, among which prime congruences, tropical ideals, tropical schemes. These approaches allows for the exploration of the properties of tropicalized spaces without tying them up to the original varieties and working with geometric structures inherently defined in characteristic one (that is, additively idempotent) semifields. In this talk we explore the relationship between tropical ideals and congruences and what they remember about the geometry of a tropical variety. This is joint work with D. Jo\ o" |
April 23, 2019, 3:00 pm at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Yu-Wei Fan (HARVARD UNIVERSITY) |
Systolic inequality for K3 surfaces via stability conditions |
We propose a natural generalization of Loewner s torus systolic inequality from the perspective of Calabi-Yau geometry. We ask whether the square of the minimum volume of special Lagrangians in a Calabi-Yau manifold is bounded above by the total volume of the Calabi-Yau. We introduce the categorical analogues of systole and volume in terms of Bridgeland stability conditions, which enables us to formulate the mirror question under mirror symmetry. Finally, we give an affirmative answer to the mirror question for K3 surfaces of Picard rank one" |
April 23, 2019, 4:00 pm at Science Center 507 |
| LOGIC SEMINAR |
Sebastien Vasey (HARVARD UNIVERSITY) |
Weak factorization systems and stable independence |
We exhibit a bridge between the theory of weak factorization systems, a categorical concept used in algebraic topology and homological algebra, and the model-theoretic notion of stable independence. Roughly speaking, we show that the cofibrantly generated weak factorization systems (those that are, in a precise sense, generated by a set) are exactly those that give rise to stable independence notions. This two way connection yields a powerful new tool to build tame and stable abstract elementary classes. In particular, we generalize a construction of Baldwin-Eklof-Trlifaj to prove that the category of flat modules with flat monomorphisms has a stable independence notion, and explain how this connects to the fact that every module has a flat cover. Joint work with JiĆĂ RosickĂœ and Michael Lieberman" |
April 22, 2019, 5:40 pm at Science Center 507 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Yang Zhou (CMSA) |
Quasimap wall-crossing for GIT quotients |
For a large class of GIT quotients X=W//G, Ciocan-Fontanine--Kim--Maulik have developed the theory of epsilon-stable quasimap invariants. They are conjecturally equivalent to the Gromov--Witten invariants of X via explicit wall-crossing formulae, which have been proved in many cases, including targets with good torus action and complete intersections in a product of projective spaces. In this talk, we will give a proof for all targets in all genera. The main ingredient is the construction of some moduli space with C^* action whose fixed-point loci precisely correspond to the terms in the wall-crossing formulae" |
April 22, 2019, 12:00 pm - 1:00 pm at CMSA, 20 Garden St, G10 |
| CMSA GENERAL RELATIVITY SEMINAR |
Lydia Bieri (UNIVERSITY OF MICHIGAN) |
Logarithmic or Not Logarithmic |
In General Relativity, we describe isolated gravitating systems by asymptotically flat solutions of the Einstein equations. For various classes of initial data corresponding classes of solutions have been constructed in the nonlinear stability proofs when slightly moving away from Minkowski spacetime. Many of the null asymptotic results still hold when one replaces the small initial data by large initial data. Therefore, these solutions have become an interesting and important source to understand gravitational waves and memory as observed at null infinity. Lately, discussions have flared up whether logarithmic terms are present at highest order in crucial components of the Riemannian curvature and shear of the spacetime and whether such terms would give a tail effect for ordinary memory. There is a large literature (older and newer) on terms of this sort. In this talk, I will address some of my recent work that proves that for asymptotically flat solutions of the Einstein equations the crucial curvature and shear components do not have logarithmic terms at highest order, but logarithmic terms naturally show up at lower order. From this it follows that there is no divergent memory caused by logarithmic terms. However, in my earlier work, considering spacetimes with very slow decay, the ordinary memory diverges (though not logarithmically but faster) and null memory is always finite. Last but not least, these logarithmic terms do show up at leading order of certain other curvature and geometric components for specific decay of the initial data. These mathematical results are in accordance with a physical argument that I will present as well." |
April 19, 2019, 9:30 am - 10:30 am at CMSA, 20 Garden St, G02 |
| CMSA METRIC LIMITS OF CALABI-YAU MANIFOLDS LECTURE SERIES |
Valentino Tosatti (NORTHWESTERN UNIVERSITY) |
Noncollapsing degenerations II |
I will give an introduction to the study of limits of Ricci-flat Kahler metrics on a compact Calabi-Yau manifold when the Kahler class degenerates to the boundary of the Kahler cone. Analytically, the problem is to prove suitable uniform a priori estimates for solutions of a degenerating family complex Monge-AmpĂšre equations, away from some singular set. Geometrically, this can be used to understand the Gromov-Hausdorff limit of these metrics. In the projective case, the limits possess an algebraic structure and are obtained from the initial manifold via contraction morphisms from Mori theory. I will discuss some results on this problem, in both the noncollapsing case and in the much harder collapsing case. I will also discuss a different source of examples, coming from work of McMullen and Cantat in complex dynamics on K3 surfaces" |
April 19, 2019, 3:00 - 4:00 pm at CMSA Building, 20 Garden St, G10 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Aliakbar Daemi (SIMONS CENTER) |
Exotic Structures, Homology Cobordisms and Chern-Simons Functional |
An exotic structure on a smooth manifold X is another smooth manifold which is homeomorphic but not diffeomorphic to X. There are many closed 4-manifolds which admit exotic smooth structures. However, it is still an open question whether there are exotic structures on simple closed 4-manifolds such as the 4-dimensional sphere (smooth Poincare conjecture) and S^1xS^3. Motivated by the latter case, Akbulut asked whether there are an integral homology sphere Y with non-trivial Rokhlin invariant and a simply connected homology cobordism from Y to itself. In this talk, I will introduce various invariants of homology cobordism classes of 3-manifolds and discuss some of their topological applications. In particular, we answer Akbulutâs question for various integral homology spheres and propose a plan to completely address his conjecture" |
April 19, 2019, 3:30 pm at Science Center 507 |
| GENDER INCLUSIVITY IN MATHEMATICS SEMINAR |
Gelonia Dent (BROWN UNIVERSITY) |
Seeing Myself in Science: How Identity and Representation Impact Retention in STEM |
" |
April 18, 2019, 3:30 pm at Emerson 105 |
| CMSA COLLOQUIUM |
Yi-Zhuang You (UCSD) |
Machine Learning Physics: From Quantum Mechanics to Holographic Geometry |
Inspired by the third wave of artificial intelligence (AI), machine learning has found rapid applications in various topics of physics research. Perhaps one of the most ambitious goals of machine learning physics is to develop novel approaches that ultimately allows AI to discover new concepts and governing equations of physics from experimental observations. In this talk, I will present our progress in applying machine learning technique to reveal the quantum wave function of Bose-Einstein condensate (BEC) and the holographic geometry of conformal field theories. In the first part, we apply machine translation to learn the mapping between potential and density profiles of BEC and show how the concept of quantum wave function can emerge in the latent space of the translator and how the Schrodinger equation is formulated as a recurrent neural network. In the second part, we design a generative model to learn the field theory configuration of the XY model and show how the machine can identify the holographic bulk degrees of freedom and use them to probe the emergent holographic geometry. [1] C. Wang, H. Zhai, Y.-Z. You. Uncover the Black Box of Machine Learning Applied to Quantum Problem by an Introspective Learning Architecture https://arxiv.org/abs/1901.11103 [2] H.-Y. Hu, S.-H. Li, L. Wang, Y.-Z. You. Machine Learning Holographic Mapping by Neural Network Renormalization Group https://arxiv.org/abs/1903.00804 [3] Y.-Z. You, Z. Yang, X.-L. Qi. Machine Learning Spatial Geometry from Entanglement Features https://arxiv.org/abs/1709.0122" |
April 17, 2019, 4:30 pm- 5:30 pm at CMSA, 20 Garden St, G10 |
| CMSA FLUID DYNAMICS SEMINAR |
Maziar Raissi (NVIDIA) |
Hidden Physics Models: Machine Learning of Non-Linear Partial Differential Equations |
A grand challenge with great opportunities is to develop a coherent framework that enables blending conservation laws, physical principles, and/or phenomenological behaviors expressed by differential equations with the vast data sets available in many fields of engineering, science, and technology. At the intersection of probabilistic machine learning, deep learning, and scientific computations, this work is pursuing the overall vision to establish promising new directions for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data. To materialize this vision, this work is exploring two complementary directions: (1) designing data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and non-linear differential equations, to extract patterns from high-dimensional data generated from experiments, and (2) designing novel numerical algorithms that can seamlessly blend equations and noisy multi-fidelity data, infer latent quantities of interest (e.g., the solution to a differential equation), and naturally quantify uncertainty in computations. The latter is aligned in spirit with the emerging field of probabilistic numerics" |
April 17, 2019, 3:00 - 4:00 pm at CMSA, 20 Garden Street, G02 |
| NUMBER THEORY SEMINAR |
Brian Smithling (JOHNS HOPKINS UNIVERSITY) |
On Shimura varieties for unitary groups |
Shimura varieties attached to unitary similitude groups are a well-studied class of PEL Shimura varieties. There are also natural Shimura varieties attached to (honest) unitary groups; these lack a moduli interpretation, but they have other advantages (e.g., they give rise to interesting cycles of the sort that appear in the arithmetic Gan-Gross-Prasad conjecture). I will describe some variant Shimura varieties which enjoy good properties from both of these classes. This is joint work with M. Rapoport and W. Zhang" |
April 17, 2019, 3:00 pm at Science Center 507 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Emil Prodan (YESHIVA UNIVERSITY) |
Pushing index theorems into the Sobolev |
The classification table of topological condensed matter systems is often and erroneously said to reflect the K-theories of the underlying algebras of observables. In fact, the groups appearing in that table are much smaller than the K-groups. In this talk, I will explain how the classification table is rather related to index theorems derived from the pairing of the relevant K-theories with Alain Connes cyclic cohomology. As an example, I will work out the case of Class A of the classification table in arbitrary even dimension, following [1]. The algebra of observables is the disordered non-commutative torus and the task is to prove an index theorem for the top pairing which can be pushed into a certain non-commutative Sobolev space, which turns out to cover the regime of strong disorder, relevant to the experiments. As we shall see, the algebraic side of the program supplies guidance but it is analysis that eventually finishes the job. 1. E Prodan, H. Schulz-Baldes, Bulk and Boundary Topological Invariants: From K-Theory to Physics, (Springer, Berlin, 2016)" |
April 16, 2019, 3:00 pm at Jefferson 356 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Connor Mooney (UC IRVINE) |
Minimizers of convex functionals with small degeneracy set |
A classical problem in the calculus of variations is to determine the regularity of Lipschitz minimizers of $\int F(\nabla u)$, where $F$ is convex. When $F$ is smooth and uniformly convex, De Giorgi and Nash showed that minimizers are smooth. If the graph of $F$ contains a line segment, minimizers are no better than Lipschitz. In the intermediate case that $F$ is strictly convex but its second derivatives tend to zero or infinity on some set (which arises in many applications), it is reasonable to ask whether Lipschitz minimizers are $C^1$. We will discuss recent results that answer this question affirmatively in some cases and negatively in general, and highlight a connection between this problem and classical differential geometry" |
April 16, 2019, 4:00 pm at Science Center 507 |
| COLLOQUIUM |
Xinwen Zhu (CALTECH) |
Hilbert's twenty-first problem for p-adic varieties |
Hilbert s twenty-first problem, formulated to generalize Riemann s work on hypergeometric equations, concerns the existence of linear differential equations of Fuchsian type on the complex plane with specified singular points and monodromic group. Its modern solution, due to Deligne and known as the Riemann-Hilbert correspondence, establishes an equivalence between two different types of data on a complex algebraic manifold X: the representations of the fundamental group of X (topological data) and the linear systems of algebraic differential equations on X with regular singularieties (algebraic data). I will review this classical theory, and discuss some recent works towards similar problems for p-adic manifolds as well as a few interesting applications. The talk will be followed by a Tea Reception in the common room at 4:00PM" |
April 16, 2019, 3:00 pm at Science Center 507 |
| OPEN NEIGHBORHOOD SEMINAR |
Lauren Williams (HARVARD UNIVERSITY) |
Combinatorics of shallow water waves (via the KP hierarchy) |
I ll give a gentle introduction to the Grassmannian, and explain how its points give rise to soliton solutions of the KP equation (which model shallow water waves). I ll then describe how the combinatorics of the positive Grassmannian and its cell decomposition allows one to answer questions about shallow water waves. (This talk will be accessible to members of the department at all levels." |
April 15, 2019, 4:30 pm at Science Center 507 |
| LOGIC SEMINAR |
Rebecca Coulson (WEST POINT) |
Bipartite Metrically Homogeneous Graphs of Generic Type: Their Generic Theories and the Almost Sure Theories of their Ages |
The class of random graphs famously satisfies a zero-one law: every first-order sentence in the language of graphs is such that the proportion of finite graphs on n vertices which satisfy this sentence goes either to zero or to one as n goes to infinity. The almost-sure theory of the class of finite graphs matches the generic theory of its Fraisse limit - the Rado graph. Interestingly, the almost-sure theory of the class of finite triangle-free graphs does not match the theory of the generic triangle free graph. In this talk, we will discuss another class of graphs which are Fraisse limits defined by forbidden configurations, and we examine two such graphs in particular. We show that for one of the them, its generic theory does match the corresponding almost-sure theory, and that for the other, the generic theory does not match the corresponding almost-sure theory" |
April 15, 2019, 5:40 pm at Science Center 507 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Junliang Shen (MIT) |
Perverse sheaves in hyper-KĂ€hler geometry |
I will discuss the role played by perverse sheaves in the study of topology and geometry of hyper-KĂ€hler manifolds. Motivated by the P=W conjecture, we establish a connection between topology of Lagrangian fibrations and Hodge theory using perverse filtrations. Our method gives new structural results for topology of Lagrangian fibrations associated with hyper-KĂ€hler varieties. If time permits, I will also discuss connections to enumerative geometry of Calabi-Yau 3-folds. Based on joint work with Qizheng Yin" |
April 15, 2019, 12:00 - 1:00 pm at CMSA, 20 Garden Street, G02 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Joel Fish (UMASS BOSTON) |
Feral pseudoholomorphic curves and minimal sets |
I will discuss some recent joint work with Helmut Hofer, in which we define and establish properties of a new class of pseudoholomorhic curves (feral J-curves) to study certain divergence free flows in dimension three. In particular, we show that if H is a smooth, proper, Hamiltonian in R^4, then no regular non-empty energy level of H is minimal. That is, the flow of the associated Hamiltonian vector field has a trajectory which is not dense. Future schedule is found here: https://scholar.harvard.edu/gerig/semina" |
April 12, 2019, 3:30 pm at Science Center 507 |
| HARVARD-MIT-MSR COMBINATORICS SEMINAR |
Carly Klivans (BROWN UNIVERSITY) |
Flow-firing processes |
I will discuss a discrete non-deterministic flow-firing process for topological cell complexes. The process is a form of discrete diffusion; a flow is repeatedly diverted according to a discrete Laplacian. The process is also an instance of higher-dimensional chip-firing. I will motivate and introduce the system and then focus on two important features â whether or not the system is terminating and whether or not the system is confluent." |
April 12, 2019, 4:45 pm- 5:45 pm at Science Center 507 |
| CMSA METRIC LIMITS OF CALABI-YAU MANIFOLDS |
Valentino Tosatti (NORTHWESTERN UNIVERSITY) |
Noncollapsing degenerations |
I will give an introduction to the study of limits of Ricci-flat Kahler metrics on a compact Calabi-Yau manifold when the Kahler class degenerates to the boundary of the Kahler cone. Analytically, the problem is to prove suitable uniform a priori estimates for solutions of a degenerating family complex Monge-AmpĂšre equations, away from some singular set. Geometrically, this can be used to understand the Gromov-Hausdorff limit of these metrics. In the projective case, the limits possess an algebraic structure and are obtained from the initial manifold via contraction morphisms from Mori theory. I will discuss some results on this problem, in both the noncollapsing case and in the much harder collapsing case. I will also discuss a different source of examples, coming from work of McMullen and Cantat in complex dynamics on K3 surfaces" |
April 12, 2019, 3:00 pm at CMSA, 20 Garden St, G10 |
| GENDER INCLUSIVITY IN MATHEMATICS SEMINAR |
Genevieve Walsh (TUFTS UNIVERSITY) |
Geometric Topology and Group Theory |
" |
April 11, 2019, 4:30 pm - 6 pm at Science Center Hall C |
| CMSA GENERAL RELATIVITY SEMINAR |
Amir Babak Aazami (CLARK UNIVERSITY) |
KĂ€hler metrics via Lorentzian geometry in dimension 4 |
Given a Lorentzian 4-manifold (M, g) with two distinguished vector fields satisfying properties determined by their shear, twist and various Lie bracket relations, a family of KĂ€hler metrics gk is constructed on M. Under certain conditions g and gk share various properties, such as a Killing vector field or a vector field with geodesic flow. The Ricci and scalar curvatures of gk are computed in some cases in terms of data associated to g; in certain cases the KĂ€hler manifold (M, gk) will be complete and Einstein. Many classical spacetimes fit into this construction: warped products, for instance de Sitter spacetime, as well as gravitational plane waves and metrics of Petrov type D, such as Kerr and NUT metrics. This work is joint with Gideon Maschler" |
April 11, 2019, 3:00 - 4:00 pm at Science Center 411 |
| THURSDAY SEMINAR |
Sander Kupers and Mike Hopkins (HARVARD UNIVERSITY) |
Discussion of two points |
" |
April 11, 2019, 3:00 - 5:00 pm at Science Center 507 |
| JOINT CMSA AND DEPARTMENT OF MATHEMATICS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Rui Han (GEORGIA TECH) |
Spectral gaps in graphene structures |
We present a full analysis of the spectrum of graphene in magnetic fields with constant flux through every hexagonal comb. In particular, we provide a rigorous foundation for self-similarity by showing that for irrational flux, the spectrum of graphene is a zero measure Cantor set. We also show that for vanishing flux, the spectral bands have nontrivial overlap, which proves the discrete Bethe-Sommerfeld conjecture for the graphene structure. This is based on joint works with S. Becker, J. Fillman and S. Jitomirskaya" |
April 11, 2019, 4:30 pm at CMSA, 20 Garden St, G10 |
| COLLOQUIUM |
Pietro Veronesi (UNIVERSITY OF CHICAGO) |
Inequality Aversion, Populism, and the Backlash Against Globalization |
Motivated by the recent rise of populism in western democracies, we develop a model in which a populist backlash emerges endogenously in a growing economy. In the model, voters dislike inequality, especially the high consumption of elites. Economic growth exacerbates inequality due to heterogeneity in risk aversion. In response to rising inequality, rich-country voters optimally elect a populist promising to end globalization. Countries with more inequality, higher financial development, and current account deficits are more vulnerable to populism, both in the model and in the data. Evidence on who voted for Brexit and Trump in 2016 also supports the model" |
April 10, 2019, 2:30-3:30 pm at CMSA, 20 Garden Street, G10 |
| CMSA SPECIAL SEMINAR |
Juven Wang (IAS) |
Quantum 4d Yang-Mills and Time-Reversal Symmetric 5d TQFT: New Higher Anomalies to Anyonic-String/Brane Induced Topological Link Invariants |
My talk will aim to be a friendly introduction for mathematicians, condensed matter friends, and QFT theorists alike --- I shall first review and warm up the use of higher symmetries and anomalies of gauge theories. Then I will present the results of recent work [arXiv:1904.00994]. We revisit [arXiv:1812.11968] and explore various 4d Yang-Mills gauge theories (YM) living as boundary conditions of 5d topological states. Specifically, we explore 4d time-reversal symmetric pure YM of an SU(2) gauge group with a second-Chern-class topological term at Ξ=Ï (SU(2)Ξ=Ï YM). We find their Fantastic Four Siblings with four sets of new higher anomalies associated with the Kramers singlet/doublet and bosonic/fermionic properties of Wilson lines. Via Weyl s gauge principle, by dynamically gauging the 1-form center symmetry, we transform a 5d bulk SPTs into a symmetry-enriched topologically ordered state (SETs) as 5d TQFT. Apply the tool introduced in [arXiv:1612.09298], we derive new exotic anyonic statistics of extended objects such as 2-worldsheet of strings and 3-worldvolume of branes, which physically characterize the 5d SETs. We discover new triple and quadruple link invariants potentially associated with the underlying 5d higher-gauge TQFTs, hinting a new intrinsic relation between non-supersymmetric 4d pure YM and topological links in 5d. We provide lattice simplicial complex and condensed matter regularizations and then comment on gauge dynamics" |
April 10, 2019, 10:30 am at CMSA, 20 Garden St, G10 |
| FLUID DYNAMICS SEMINAR |
Luc Deike (PRINCETON UNIVERSITY ) |
Wave breaking in ocean atmosphere interactions |
Breaking waves at the water surface is a striking example of turbulent mixing across a fluid interface. The impact of the jet generates turbulence, entrains air into the water and ejects droplets into the air. A fundamental understanding of the general multi-scale properties of the resulting air-water turbulent flow is necessary to develop more accurate gas transfer or spray generation parameterizations. I will discuss a multi-scale approach where air entrainment, bubble statistics and aerosol generation by bubble bursting is investigated by laboratory experiments and numerical simulations at small scale while ocean scale fluxes are obtained by up-scaling the results using statistical description of the wave and wave breaking field. This approach leads to semi-empirical formulations to be implemented in coupled ocean-wave models" |
April 10, 2019, 3:00 pm at Science Center 530 |
| NUMBER THEORY SEMINAR |
Naser Talebi Zadeh (UNIVERSITY OF WISCONSIN) |
The Siegel variance formula for quadratic forms |
We introduce a smooth variance sum associated to a pair of positive definite symmetric integral matrices $A_{m\times m}$ and $B_{n\times n}$, where $m\geq n$. By using the oscillator representation, we give a formula for this variance sum in terms of a smooth sum over the square norms of the $B$-th Fourier coefficients of the vector-valued holomorphic Siegel cusp forms which are Hecke eigenforms and obtained by the theta transfer from $O_A$ to $Sp_{n}$. By using the Ramanujan bound on the Fourier coefficients of the holomorphic forms when $n=1$, we give a sharp upper bound on this variance. As applications, we generalize the result of Sarnak \cite{Sarnak2}, and give an optimal bound on the diophantine exponent of integral points on any positive definite $d$-dimensional quadric, where $d\geq 3$ is odd. This also improves the bound of Ghosh, Gorodnick and Nevo~\cite{GGN} into an optimal bound. Furthermore, we show that almost all even unimodular lattices of dimension $m$ represent a given even number greater than $\frac{m}{2\pi e}$ with respect to Siegel s weights, and this bound is optimal." |
April 10, 2019, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Spiro Karigiannis (UNIVERSITY OF WATERLOO ) |
A curious system of second order nonlinear PDEs for U(m)-structures on manifolds |
" |
April 09, 2019, 3:00 pm at Science Center 232 |
| JOINT CMSA AND DEPARTMENT OF MATHEMATICS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Giulio Biroli (ENS) |
Large deviations for the largest eigenvalues and eigenvectors of spiked random matrices |
I consider matrices formed by a random $N\times N$ matrix drawn from the Gaussian Orthogonal Ensemble (or Gaussian Unitary Ensemble) plus a rank-one perturbation of strength $\theta$, and focus on the largest eigenvalue, $x$, and the component, $u$, of the corresponding eigenvector in the direction associated to the rank-one perturbation. I will show how to obtain the large deviation principle governing the atypical joint fluctuations of $x$ and $u$. Interestingly, for $\theta>1$, in large deviations characterized by a small value of $u$, i.e. $u<1-1/\theta$, the second-largest eigenvalue pops out from the Wigner semi-circle and the associated eigenvector orients in the direction corresponding to the rank-one perturbation. These results can be generalized to the Wishart Ensemble, and extended to the first $n$ eigenvalues and the associated eigenvectors. Finally, I will discuss motivations and applications of these results to the study of the geometric properties of random high-dimensional functionsâa topic that is currently attracting a lot of attention in physics and computer science" |
April 09, 2019, 12:00 - 1:00 pm at CMSA, 20 Garden Street, G02 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Alina Vdovina (UNIVERSITY OF NEWCASTLE, UK) |
Higher dimensional picture languages |
My main goal is to develop a theory of combinatorics of higher dimensional words, or higher dimensional picture languages. These languages are closely related to the theory of C*-algebras and can be viewed as natural generalizations of free monoids, whose elements can naturally be regarded as higher-dimensional strings. We will construct concrete models in any dimension using arithmetic geometry and theory of buildings. The work we are going to present fits very well to the picture language program suggested by A.Jaffe and Z.Liu, for example, to the question L(iii)(ii). [Mathematical picture language program, PNAS 115, no. 1 (2018), pp. 81-86" |
April 09, 2019, 4:30 pm at Jefferson 356 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Claus Koestler (UNIVERSITY COLLEGE CORK, IRELAND) |
Markovianity as a distributional system |
My talk should be accessible to a general mathematical audience. Markovianity is a stochastic phenomenon which does not care about the past - the presence âdictatesâ the future. Unexpectedly this phenomenon is closely linked to representations of the Thompson group F. My talk will introduce this new connection between randomness and symmetry which is valid for classical and quantum probability. I will explain the general result that every stationary (quantum) Markov chain induces a representation of the Thompson group F. Conversely, a large class of representations of F yields stationary (quantum) Markov chains. Finally, I will introduce âpartial spreadabilityâ as a new distributional symmetry, aiming at a de Finetti type characterization of Markovianity. The presented results are based on ongoing research with Rajarama Bhat, Gwion Evans, Rolf Gohm, Arundhathi Krishnan, Vijaya Kumar, and Stephen Wills" |
April 09, 2019, 3:00 pm at Jefferson 356 |
| TOPOLOGICAL ASPECTS OF CONDENSED MATTER SEMINAR |
Adam Nahum (OXFORD UNIVERSITY) |
Emergent statistical mechanics of entanglement in random unitary circuits |
I will talk about quantum-classical mappings for real-time observables in some simple many-body systems (random unitary circuits). Specifically I will discuss how (1) entanglement entropy growth and (2) two-point correlation functions in these systems can be related to partition functions for interacting random walks. If time permits I will mention a phase transition in the entanglement structure of a repeatedly measured quantum state" |
April 08, 2019, 10:00 am at CMSA, 20 Garden St, G10 |
| COLLOQUIUM |
Laura DeMarco (NORTHWESTERN UNIVERSITY) |
Complex dynamics and arithmetic equidistribution |
I will explain a notion of arithmetic equidistribution that has recently found application in the study of complex dynamical systems. It was first introduced about 25 years ago, by Szpiro-Ullmo-Zhang, to analyze the geometry and arithmetic of abelian varieties. In 2011, Matt Baker and I used the theory to study periodic points of maps on P^1. In this talk, I will explain some dynamical questions that were inspired by questions about elliptic curves, and then how the dynamical results allowed us to solve problems in the original setting of abelian varieties. The new results are joint with Holly Krieger and Hexi Ye" |
April 08, 2019, 3:00 pm at Science Center 507 |
| CMSA MATH PHYSICS SEMINAR |
Yoosik Kim (BOSTON UNIVERSITY) |
String polytopes and Gelfand-Cetlin polytopes |
The string polytope was introduced by Littelmann and Berenstein--Zelevinsky as a generalization of the Gelfand-Cetlin polytope in representation theory. For a connected reductive algebraic group $G$ over $\mathbb{C}$ and a dominant integral weight $\lambda$, a choice of a reduced word of the longest element in the Weyl group of G determines a string polytope. Depending on a reduced word of the longest element in the Weyl group, combinatorially distinct string polytopes arise in general. In this talk, I will explain how to classify the string polytopes that are unimodularly equivalent to Gelfand-Cetlin polytopes when $G = \mathrm{SL}_{n+1}(\mathbb{C})$ and $\lambda$ is a regular dominant integral weight. Also, I will explain a conjectural way obtaining SYZ mirrors respecting a cluster structure invented by Fomin--Zelevinsky. This talk is based on joint work with Yunhyung Cho, Eunjeong Lee, and Kyeong-Dong Park" |
April 08, 2019, 12:00 - 1:00 pm at CMSA, 20 Garden St, G10 |
| LOGIC SEMINAR |
Douglas Blue (HARVARD UNIVERSITY) |
Equivalence relations and effective cardinality |
I will survey the theory of definable equivalence relations with emphasis on dichotomy theorems about effective cardinalities" |
April 08, 2019, 5:40 pm at Science Center 507 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Melissa Liu (COLUMBIA UNIVERSITY) |
The Yang-Mills Equations over Klein Surfaces |
In The Yang-Mills equations over Riemann surfaces, Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory, and derived results on topology of the moduli space of algebraic bundles over a complex algebraic curve. In this talk, I will discuss Yang-Mills functional over a Klein surface (a 2-manifold equipped with a dianalytic structure) from the point of view of Morse theory, and derive results on topology of the moduli space of real or quaternionic vector bundles over a real algebraic curve. This is based on joint work with Florent Schaffhauser. Future schedule is found here: https://scholar.harvard.edu/gerig/semina" |
April 05, 2019, 3:30 pm at Science Center 507 |
| THURSDAY SEMINAR |
Ben Knudsen (HARVARD UNIVERSITY) |
Toward the immersion conjecture |
" |
April 04, 2019, 3:00 - 5:00 pm at Science Center 507 |
| CMSA GENERAL RELATIVITY SEMINAR |
Marcus Khuri (STONY BROOK UNIVERSITY) |
Stationary Vacuum Black Holes in Higher Dimensions |
A result of Galloway and Schoen asserts that horizon cross-sections must be of positive Yamabe invariant. In this talk we discuss results on a converse problem. That is, which manifolds of positive Yamabe invariant arise as horizon cross-sections in a stationary vacuum spacetime" |
April 04, 2019, 3:00 - 4:00 pm at CMSA, 20 Garden Street, G02 |
| JOINT CMSA AND DEPARTMENT OF MATHEMATICS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Paul Bourgade (NYU) |
Log-correlations and branching structures in analytic number theory |
Fyodorov, Hiary and Keating have predicted the size of local maxima of L-function along the critical axis, based on analogous random matrix statistics. I will explain this prediction in the context of the log-correlated universality class and branching structures. In particular I will explain why the Riemann zeta function exhibits log-correlations, and outline the proof for the leading order of the maximum in the Fyodorov, Hiary and Keating prediction. Joint work with Arguin, Belius, Radziwill and Soundararajan" |
April 04, 2019, 4:30 pm- 5:30 pm at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Avner Ash (BOSTON COLLEGE) |
Resolutions of the Steinberg module for GL(n) |
The Steinberg module St(n,K) for the general linear group G of a number field K is the dualizing module for arithmetic subgroups of G. So St(n,K) can be used in studying the cohomology of arithmetic groups, and is especially suitable for computing Hecke operators. I will present several resolutions of St(n,Q) that are helpful in this regard. I will discuss applications to computations for congruence subgroups of SL(4,Z) (with Paul Gunnells and Mark McConnell) and some work related to Serre-type conjectures for GL(n,Z) (with Darrin Doud." |
April 04, 2019, 3:00 pm at Science Center Hall E *note different day and location* |
| CMSA FLUID DYNAMICS SEMINAR |
Christopher Rycroft (HARVARD UNIVERSITY) |
The reference map technique for simulating complex materials and multi-body interactions |
Conventional computational methods often create a dilemma for fluidâstructure interaction problems. Typically, solids are simulated using a Lagrangian approach with grid that moves with the material, whereas fluids are simulated using an Eulerian approach with a fixed spatial grid, requiring some type of interfacial coupling between the two different perspectives. Here, a fully Eulerian method for simulating structures immersed in a fluid will be presented. By introducing a reference map variable to model finite-deformation constitutive relations in the structures on the same grid as the fluid, the interfacial coupling problem is highly simplified. The method is particularly well suited for simulating soft, highly-deformable materials and many-body contact problems, and several examples will be presented. This is joint work with Ken Kamrin (MIT)" |
April 03, 2019, 4:00 pm at CMSA, 20 Garden Street, G10 |
| COLLOQUIUM |
Christopher Hacon (UNIVERSITY OF UTAH) |
On the geometry of Algebraic varieties |
Algebraic varieties are geometric objects defined by polynomial equations. The minimal model program (MMP) is an ambitious program that aims to classify algebraic varieties. According to the MMP, there are 3 building blocks: Fano varieties, Calabi-Yau varieties and varieties of general type which are higher dimensional analogs of Riemann Surfaces of genus 0,1 or at least 2 respectively. In this talk I will recall the general features of the MMP and discuss recent advances in our understanding of Fano varieties and varieties of general type" |
April 03, 2019, 3:00 pm at Science Center 507 |
| CMSA COLLOQUIUM |
Sarah Moshary (UNIVERSITY OF CHICAGO) |
Deregulation through Direct Democracy: Lessons from Liquor |
This paper examines the merits of state control versus private provision of spirits retail, using the 2012 deregulation of liquor sales in Washington state as an event study. We document effects along a number of dimensions: prices, product variety, convenience, substitution to other goods, state revenue, and consumption externalities. We estimate a demand system to evaluate the net effect of privatization on consumer welfare. Our findings suggest that deregulation harmed the median Washingtonian, even though residents voted in favor of deregulation by a 16% margin. Further, we find that vote shares for the deregulation initiative do not reflect welfare gains at the ZIP code level. We discuss implications of our findings for the efficacy of direct democracy as a policy tool" |
April 03, 2019, 2:30-3:30 pm at CMSA, 20 Garden Street, G10 |
| CMSA SPECIAL LECTURE SERIES ON DERIVED ALGEBRAIC/DIFFERENTIAL GEOMETRY |
Artan Sheshmani (CMSA) |
Examples and applications 2 (Part II) |
" |
April 02, 2019, 3:00 - 4:30 pm at CMSA, 20 Garden St, G10 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Mikael Rordam (UNIVERSITY OF COPENHAGEN) |
Highlights of the Classification of Simple Nuclear C*-Algebras |
" |
April 02, 2019, 3:00 pm at Jefferson 356 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Ao Sun (MIT) |
Local Entropy and Generic Multiplicity One Singularities of Mean Curvature Flow of Surfaces |
One of the central topics in mean curvature flow is understanding the singularities. In 1995, Ilmanen conjectured that the first singularity appeared in a smooth mean curvature flow of surfaces must have multiplicity one. Following the theory of generic mean curvature flow developed by Colding-Minicozzi, we prove that a closed singularity with high multiplicity is not generic, in the sense that we may perturb the flow so that this singularity with high multiplicity can never show up. In order to do this, we introduce the local entropy, which is an extension of the entropy used by Colding-Minicozzi to study the generic mean curvature flow" |
April 02, 2019, 4:00 pm at Science Center 507 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Magdalena Musat (UNIVERSITY OF COPENHAGEN) |
Quantum Correlations, Factorizable Channels, and the Connes Embedding Problem |
" |
April 02, 2019, 4:00 pm at Jefferson 356 |
| LOGIC SEMINAR |
Elliot Glazer (HARVARD UNIVERSITY AND ZHEJIANG UNIVERSITY) |
Set theory with randomness |
Probabilistic intuition has historically been used to provide evidence for and against certain axioms, e.g. the Banach-Tarski paradox as evidence against AC and Freiling s argument against CH. I will demonstrate that these intuitions are incompatible with standard set theory even in the absence of choice by examining a certain paradoxical game with explicit winning strategies. I use this example to motivate a formal theory which adds probabilistic quantifiers to a weak base set theory. This theory clarifies the properties of randomness and its relationship with the structure of the universe" |
April 01, 2019, 5:40 pm at Science Center 507 |
| OPEN NEIGHBORHOOD SEMINAR |
John Mackey (CARNEGIE MELLON UNIVERSITY) |
Tournaments having the most cycles |
In celebration of March Madness, we will consider the problem of maximizing the number of cycles in round robin tournaments. A round robin tournament is a set of matches in which each contestant plays all other contestants. A cycle is a sequence of contestants, each beating the one that follows it, with the last beating the first. This problem is about three-fourths solved. Open problems and connections with the zeta function will be discussed. (This talk will be accessible to members of the department at all levels." |
April 01, 2019, 4:30 pm at Science Center 507 |
| CMSA MATH PHYSICS SEMINAR |
Athanassios S. Fokas (UNIVERSITY OF CAMBRIDGE) |
Asymptotics: the unified transform, a new approach to the Lindelöf Hypothesis, and the ultra-relativistic limit of the Minkowskian approximation of general relativity |
Employing standard, as well as novel techniques of asymptotics, three different problems will be discussed: (i) The computation of the large time asymptotics of initial-boundary value problems via the unified transform (also known as the Fokas method, www.wikipedia.org/wiki/Fokas_method)[1]. (ii) The evaluation of the large t-asymptotics to all orders of the Riemann zeta function[2], and the introduction of a new approach to the Lindelöf Hypothesis[3]. (iii) The proof that the ultra relativistic limit of the Minkowskian approximation of general relativity [4] yields a force with characteristics of the strong force, including confinement and asymptotic freedom[5]. [1] J. Lenells and A. S. Fokas. The Nonlinear Schrödinger Equation with t-Periodic Data: I. Exact Results, Proc. R. Soc. A 471, 20140925 (2015). J. Lenells and A. S. Fokas, The Nonlinear Schrödinger Equation with t-Periodic Data: II. Perturbative Results, Proc. R. Soc. A 471, 20140926 (2015). [2] A.S. Fokas and J. Lenells, On the Asymptotics to All Orders of the Riemann Zeta Function and of a Two-Parameter Generalization of the Riemann Zeta Function, Mem. Amer. Math. Soc. (to appear). [3] A.S. Fokas, A Novel Approach to the Lindelof Hypothesis, Transactions of Mathematics and its Applications (to appear). [4] L. Blanchet and A.S. Fokas, Equations of Motion of Self-Gravitating N-Body Systems in the First Post-Minkowskian Approximation, Phys. Rev. D 98, 084005 (2018). [5] A.S. Fokas, Super Relativistic Gravity has Properties Associated with the Strong Force, Eur. Phys. J. C (to appear)" |
April 01, 2019, 12:00 - 1:00 pm at CMSA, 20 Garden St, G10 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Chris Scaduto (SIMONS CENTER) |
Instantons and lattices of smooth 4-manifolds with boundary |
Given a 3-manifold Y, what are the possible definite intersection forms of smooth 4-manifolds with boundary Y? Donaldson s theorem says that if Y is the 3-sphere, then all such intersection forms are standard integer Euclidean lattices. I will survey some new progress on this problem, for other 3-manifolds, that comes from instanton Floer theory" |
March 29, 2019, 3:30 pm at Science Center 222 |
| JOINT CMSA AND DEPARTMENT OF MATHEMATICS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Xuwen Chen (UNIVERSITY OF ROCHESTER) |
The Derivation of the Energy-critical NLS from Quantum Many-body Dynamics |
We derive the 3D energy-critical quintic NLS from quantum many-body dynamics with 3-body interaction in the T^3 (periodic) setting. Due to the known complexity of the energy critical setting, previous progress was limited in comparison to the 2-body interaction case yielding energy subcritical cubic NLS. We develop methods to prove the convergence of the BBGKY hierarchy to the infinite Gross-Pitaevskii (GP) hierarchy, and separately, the uniqueness of large GP solutions. Since the trace estimate used in the previous proofs of convergence is the false sharp trace estimate in our setting, we instead introduce a new frequency interaction analysis and apply the finite dimensional quantum de Finetti theorem. For the large solution uniqueness argument, we discover the new HUFL (hierarchical uniform frequency localization) property for the GP hierarchy and use it to prove a new type of uniqueness theorem" |
March 28, 2019, 4:30 - 5:30 pm at CMSA, 20 Garden St, G02 |
| GENDER INCLUSIVITY IN MATHEMATICS SEMINAR |
Eunice Kim (TUFTS UNIVERSITY) |
Dynamical Systems and Physical Phenomena |
" |
March 28, 2019, 4:30 pm - 6 pm at Science Center Hall E |
| NUMBER THEORY SEMINAR |
Kai-Wen Lan (UNIVERSITY OF MINNESOTA, TWIN CITIES) |
Local systems of Shimura varieties: a comparison of two constructions |
Given a Shimura variety, we can construct two kinds of automorphic local systems, i.e., local systems attached to algebraic representations of certain associated algebraic group. The first one is based on the classical complex analytic construction using double quotients, while the second one is a p-adic analytic construction based on some recently developed p-adic analogue of the Riemann-Hilbert correspondence. I will explain how to compare these two constructions even when the Shimura variety is not of abelian type, and mention some applications. (This is based on joint work with Hansheng Diao, Ruochuan Liu, and Xinwen Zhu." |
March 27, 2019, 3:00 pm at Science Center 507 |
| CMSA COLLOQUIUM |
Tatyana Sharpee (SALK INSTITUTE FOR BIOLOGICAL STUDIES) |
Hyperbolic geometry of the olfactory space |
The sense of smell can be used to avoid poisons or estimate a foodâs nutrition content because biochemical reactions create many by-products. Thus, the presence of certain bacteria in the food becomes associated with the emission of certain volatile compounds. This perspective suggests that it would be convenient for the nervous system encode odors based on statistics of their co-occurrence within natural mixtures rather than based on the chemical structure per se. I will discuss how this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendograms, and more generally between points within hierarchical tree-like networks. We find that these coordinates, which were generated purely based on the statistics of odors in the natural environment, provide a contiguous map of human odor pleasantness. Further, a separate analysis of human perceptual descriptions of smells indicates that these also generate a three dimensional hyperbolic representation of odors. This match in geometries between natural odor statistics and human perception can help to minimize distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes" |
March 27, 2019, 5:15 pm - 6:15 pm at CMSA, 20 Garden St, G10 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Jinsong Wu (HARBIN INSTITUTE OF TECHNOLOGY, CHINA) |
Fourier analysis on fusion rings |
In our previous work, we study Fourier analysis on subfactors, modular tensor categories, locally compact quantum groups etc. In this talk, we will discuss Fourier analysis on fusion ring. Many inequalities will be obtained such as Hausdorff-Young inequality, uncertainty principles, Schur product theorem, Youngâs inequality, sum set estimate. However, some inequalities might not be true" |
March 26, 2019, 3:00 pm at Jefferson 356 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Changho Han (HARVARD UNIVERSITY) |
'Almost K3' stable log surfaces and curves of genus 4 |
The geometry of compact moduli spaces of log surfaces is mysterious in general. Thus, describing an example with its geometric properties is already valuable. To do so, we consider an almost K3 stable log surface, which is a pair where the log canonical divisor is positive but very close to 0. We study compactified moduli spaces of such log surfaces, constructed using the techniques of KollĂĄr, Shepherd-Barron, Alexeev, and Hacking. We completely describe such a compactification of the moduli space of (X, D) where X is a quadric surface and D is a canonical genus 4 curve, obtaining a new birational model of the moduli space M_4 of smooth curves of genus 4. This is joint work with Anand Deopurkar" |
March 26, 2019, 3:00 pm at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Tian-Jun Li (MINNESOTA) |
Geometry of symplectic log Calabi-Yau surfaces |
This is a survey on the geometry of symplectic log Calabi-Yau surfaces, which are the symplectic analogues of Looijenga pairs. We address the classification up to symplectic deformation, the relations between symplectic circular sequences and anti-canonical sequences, contact trichotomy, and symplectic fillings. This is a joint work with Cheuk Yu Mak" |
March 26, 2019, 4:00 pm at Science Center 507 |
| CMSA SPECIAL LECTURE SERIES ON DERIVED ALGEBRAIC/DIFFERENTIAL GEOMETRY |
Artan Sheshmani (CMSA) |
Examples and applications 2 (Part II) |
" |
March 26, 2019, 3:00 - 4:30 pm at CMSA, 20 Garden St, G10 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Eduardo Gonzalez (UNIVERSITY OF MASSACHUSETTS BOSTON) |
Stratifications in gauged Gromov-Witten theory |
Let G be a reductive group and X be a smooth projective G-variety. In classical geometric invariant theory (GIT), there are stratifications of X that can be used to understand the geometry of the GIT quotients X//G and their dependence on choices. In this talk, after introducing basic theory, I will discuss the moduli of gauged maps, their relation to the Gromov-Witten theory of GIT quotients X//G and work in progress regarding stratifications of the moduli space of gauged maps as well as possible applications to quantum K-theory. This is joint work with D. Halpern-Leistner, P. Solis and C. Woodward" |
March 25, 2019, 12:00 - 1:00 pm at CMSA, 20 Garden St, G10 |
| LOGIC SEMINAR |
Justin Cavitt (HARVARD UNIVERSITY) |
Large Cardinals and Simpler Proofs |
Extending ZFC by large cardinal axioms not only allows one to prove more theorems, but also allows one to give simpler proofs of ZFC theorems. For example, the proof of Borel determinacy assuming the existence of a measurable cardinal is much simpler than the proof assuming only ZFC. A theorem of Ehrenfeucht and Mycielski indicates that something similar happens whenever an undecidable theory is extended by a new axiom. In this talk, we will review this and related results and discuss potential applications to the large cardinal speedup phenomenon" |
March 25, 2019, 5:40 pm at Science Center 507 |
| HARVARD - MIT - MSR COMBINATORICS SEMINAR |
Jim Haglund (UNIVERSITY OF PENNSYLVANIA) |
Three faces of the Delta Conjecture |
The Delta Conjecture says that a certain symmetric function, expressed in terms of Macdonald polynomial operators, equals a weighted sum over Dyck lattice paths. It contains the well-known Shuffle Theorem of Carlsson and Mellit as a special case. There is also a third side to the problem that has emerged, centered around the goal of showing the symmetric function side also has a representation-theoretic interpretation. We will overview some of this work, including a recent conjecture of Mike Zabrocki which says the two sides of the Delta Conjecture equal the bigraded character of a generalization of the diagonal coinvariant ring. We will also discuss work of D Adderio, Iraci, and Wyngaerd, who have used plethystic calculus to prove special cases of the Delta Conjecture" |
March 22, 2019, 4:15 pm at Science Center 507 |
| CMSA SPECIAL LECTURE SERIES ON DERIVED ALGEBRAIC/DIFFERENTIAL GEOMETRY |
Artan Sheshmani (CMSA) |
Examples and applications 2 (Part I) |
" |
March 21, 2019, 3:00 - 4:30 pm at CMSA, 20 Garden St, G10 |
| CMSA FLUID DYNAMICS SEMINAR |
Paris Perdikaris (UNIVERSITY OF PENNSYLVANIA) |
Data-driven modeling of stochastic systems using physics-aware deep learning |
We present a probabilistic deep learning methodology that enables the construction of predictive data-driven surrogates for stochastic systems. Leveraging recent advances in variational inference, we put forth a scalable computational framework for discovering surrogate models from paired input-output observations of a system that may be stochastic in nature, originate from different information sources of variable fidelity, or be corrupted by complex noise processes. We also show how physical constraints can be employed as informative priors that introduce a regularization mechanism for effectively constructing robust deep learning models in cases where the cost of data acquisition is high and training data-sets are typically small. The effectiveness of the proposed methods is demonstrated through a series of canonical studies involving stochastic dynamical systems and nonlinear conservation laws" |
March 20, 2019, 3:00 PM - 4:00 PM at CMSA, 20 Garden Street, G10 |
| CMSA COLLOQUIUM |
Sonia Jaffe (MICROSOFT) |
Quality Externalities on Platforms: The Case of Airbnb |
We explore quality externalities on platforms: when buyers have limited information, a seller s quality affects whether her buyers return to the platform, thereby impacting other sellers future business. We propose an intuitive measure of this externality, applicable across a range of platforms. Guest Return Propensity (GRP) is the aggregate propensity of a seller s customers to return to the platform. We validate this metric using Airbnb data: matching customers to listings with a one standard deviation higher GRP causes them to take 17% more subsequent trips. By directing buyers to higher-GRP sellers, platforms may be able to increase overall seller surplus. (Joint work with Peter Coles, Steven Levitt, and Igor Popov.) " |
March 20, 2019, 4:30 - 5:30 pm at CMSA, 20 Garden St, G10 |
| CMSA SPECIAL LECTURE SERIES ON DERIVED ALGEBRAIC/DIFFERENTIAL GEOMETRY |
Artan Sheshmani (CMSA) |
Intersections of Lagrangians |
" |
March 19, 2019, 3:00 - 4:30 pm at CMSA, 20 Garden St, G10 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Emmy Murphy (NORTHWESTERN UNIVERSITY) |
Inductively collapsing Fukaya categories and flexibility |
A Weinstein manifold is a symplectic manifold which admits a Lagrangian skeleton, and associated to any Weinstein manifold is its wrapped Fukaya category, a powerful algebraic invariant. One important case is that the wrapped category of C^n is trivial. The talk will discuss a partial converse: if X is any Weinstein 6-manifold which is contractible, admitting an arboreal skeleton so that the wrapped category is inductively collapsing, then X is symplectomorphic to C^3. A large portion of the talk will be defining the notion of inductively collapsing: this is a purely algebraic condition, but it depends on a presentation of the wrapped category, which itself comes from a chosen Lagrangian skeleton. Future schedule is found here: https://scholar.harvard.edu/gerig/semina" |
March 15, 2019, 3:30 pm at Science Center 507 |
| JOINT CMSA AND DEPARTMENT OF MATHEMATICS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Anna Vershynina (UNIVERSITY OF HOUSTON) |
How fast can entanglement be generated in quantum systems? |
We investigate the maximal rate at which entanglement can be generated in bipartite quantum systems. The goal is to upper bound this rate. All previous results in closed systems considered entanglement entropy as a measure of entanglement. I will present recent results, where entanglement measure can be chosen from a large class of measures. The result is derived from a general bound on the trace-norm of a commutator, and can, for example, be applied to bound the entanglement rate for Renyi and Tsallis entanglement entropies" |
March 14, 2019, 5:45 pm at Science Center 232 *note different location* |
| CMSA GENERAL RELATIVITY SEMINAR |
Peter Hintz (MIT) |
Stability of Minkowski space and polyhomogeneity of the metric |
I will explain a new proof of the non-linear stability of the Minkowski spacetime as a solution of the Einstein vacuum equation. The proof relies on an iteration scheme at each step of which one solves a linear wave-type equation globally. The analysis takes place on a compactification of R^4 to a manifold with corners whose boundary hypersurfaces correspond to spacelike, null, and timelike infinity. I will describe how the asymptotic behavior of the metric can be deduced from the structure of simple model operators at these boundaries. Joint work with AndrĂĄs Vasy" |
March 14, 2019, 3:30 pm at Science Center 411 |
| BRANDEIS-HARVARD-MIT-NORTHEASTERN JOINT COLLOQUIUM |
Emmy Murphy (NORTHWESTERN UNIVERSITY) |
Flexibility in contact and symplectic geometry |
We discuss a number of h-principle phenomena which were recently discovered in the field of contact and symplectic geometry. In generality, an h-principle is a method for constructing global solutions to underdetermined PDEs on manifolds by systematically localizing boundary conditions. In symplectic and contact geometry, these strategies typically are well suited for general constructions and partial classifications. Some of the results we discuss are the characterization of smooth manifolds admitting contact structures, high dimensional overtwistedness, the symplectic classification of flexibile Stein manifolds, and the construction of exotic Lagrangians in C^n" |
March 14, 2019, Tea at 4:00 pm; Talk at 4:30 pm at Science Center Hall A |
| CMSA SPECIAL LECTURE SERIES ON DERIVED ALGEBRAIC/DIFFERENTIAL GEOMETRY |
Artan Sheshmani (CMSA) |
Lagrangians and Lagrangian fibrations |
" |
March 14, 2019, 3:00 - 4:30 pm at CMSA, 20 Garden St, G02 *note different room* |
| CMSA SPECIAL SEMINAR |
Albrecht Klemm (UNIVERSITY OF BONN) |
D-brane masses and the motivic Hodge conjecture |
We consider the one parameter mirror family W of the quintic in P^4. By mirror symmetry the even Dp-brane masses of the quintic M can be identified with four periods w.r.t to an integral symplectic basis of H_3(W,Z) at the point of maximal unipotent monodromy. We establish that the masses of the D4 and D2 branes at the conifold are given by the two algebraically independent values of the L-function of the weight four holomorphic Hecke eigenform with eigenvalue one of \Gamma_0(25), that was found by Chad Schoen in this context and whose coefficients a_p count the number of solutions of the mirror quinitic at the conifold over the finite number field F_p as was discovered by del la Ossa, Candelas and Villegas. Using the theory of periods and quasi-periods of \Gamma_0(N) and the special geometry pairing on Calabi-Yau 3 folds we can fix further values in the connection matrix between the maximal unipotent monodromy point and the conifold point." |
March 13, 2019, 12:15 - 1:15 pm at CMSA, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Samit Dasgupta (DUKE UNIVERSITY) |
On Brumer-Stark units |
In this talk I will discuss: 1) The Brumer-Stark conjecture, which purports the existence of p-units in abelian extensions of totally real fields with valuations at p related to special values of partial zeta functions; 2) The integral Gross-Stark conjecture, which gives a formula for the image of these units under the Artin reciprocity map associated to certain auxiliary extensions; 3) An exact formula for these units developed in my thesis and subsequent work. I will give an update on work in progress with Mahesh Kakde to attack these conjectures. Our key tool is the development of the theory of group-ring families of modular forms" |
March 13, 2019, 3:00 pm at Science Center 507 |
| CMSA COLLOQUIUM |
Greg Galloway (UNIVERSITY OF MIAMI) |
On the geometry and topology of initial data sets in General Relativity |
A theme of long standing interest (to the speaker!) concerns the relationship between the topology of spacetime and the occurrence of singularities (causal geodesic incompleteness). Many results concerning this center around the notion of topological censorship, which has to do with the idea that the region outside all black holes (and white holes) should be simple. The aim of the results to be presented is to provide support for topological censorship at the pure initial data level, thereby circumventing difficult issues of global evolution. The proofs rely on the recently developed theory of marginally outer trapped surfaces, which are natural spacetime analogues of minimal surfaces in Riemannian geometry. The talk will begin with a brief overview of general relativity and topological censorship. The talk is based primarily on joint work with various collaborators: Lars Andersson, Mattias Dahl, Michael Eichmair and Dan Pollack" |
March 13, 2019, 5:15 PM - 6:15 PM at CMSA, 20 Garden Street, G10 |
| CMSA SPECIAL LECTURE SERIES ON DERIVED ALGEBRAIC/DIFFERENTIAL GEOMETRY |
Artan Sheshmani (CMSA) |
Lagrangians and Lagrangian fibrations |
" |
March 12, 2019, 3:00 - 4:30 pm at CMSA, 20 Garden St, G10 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Jake Levinson (UNIVERSITY OF WASHINGTON) |
Boij-Söderberg Theory for Grassmannians |
The Betti table of a graded module over a polynomial ring encodes much of its structure and that of the corresponding sheaf on projective space. In general, it is hard to tell which tables of numbers can arise as Betti tables. An easier problem is to describe such tables up to positive scalar multiple: this is the cone of Betti tables. The Boij-Söderberg conjectures, proven by Eisenbud-Schreyer, gave a beautiful description of this cone and, as a bonus, a dual description of the cone of cohomology tables of sheaves. I will describe some extensions of this theory, joint with Nicolas Ford and Steven Sam, to the setting of GL-equivariant modules over coordinate rings of matrices. Here, the dual theory (in geometry) concerns sheaf cohomology on Grassmannians. The main result is an equivariant analog of the Boij-Söderberg pairing between Betti tables and cohomology tables. This is a bilinear pairing of cones, with output in the cone coming from the base case of square matrices, which we also fully characterize" |
March 12, 2019, 3:00 pm at Science Center 507 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Youwei Zhao (UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA) |
A review of the surface code from an experimental perspective |
I will review the surface code without the perfect syndrome assumption. I will give an experimental explanation of some details" |
March 12, 2019, 3:00 pm at Jefferson 356 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Yaiza Canzani (UNC) |
Understanding the growth of Laplace eigenfunctions |
In this talk we will discuss a new approach to understanding eigenfunction concentration. We characterize the features that cause an eigenfunction to saturate the standard supremum bounds in terms of the distribution of L^2 mass along geodesic tubes emanating from a point. We also show that the phenomena behind extreme supremum norm growth is identical to that underlying extreme growth of eigenfunctions when averaged along submanifolds. Using the description of concentration, we obtain quantitative improvements on the known bounds in a wide variety of settings" |
March 12, 2019, 4:00 PM at Science Center 507 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Yu Pan (MIT) |
Augmentations and exact Lagrangian cobordisms. |
Augmentations are tightly connected to embedded exact Lagrangian fillings. However, not all the augmentations of a Legendrian knot come from embedded exact Lagrangian fillings. In this talk, we introduce immersed exact Lagrangian fillings into the picture and show that all the augmentations come from possibly immersed exact Lagrangian fillings. In this way, we realize augmentations, which is an algebraic object, fully geometrically. This is a joint work with Dan Rutherford working in progress" |
March 11, 2019, 12:00 PM - 1:00 PM at CMSA, 20 Garden Street, G10 |
| COLLOQUIUM |
Bhargav Bhatt (UNIVERSITY OF MICHIGAN) |
Title: Interpolating p-adic cohomology theories |
Integration of differential forms against cycles on a complex manifold helps relate de Rham cohomology to singular cohomology, which forms the beginning of Hodge theory. The analogous story for p-adic manifolds, which is the subject of p-adic Hodge theory, is richer due to a wider variety of available cohomology theories (de Rham, etale, crystalline, and more) and torsion phenomena. In this talk, I will give a bird s eye view of this picture, guided by the recently discovered notion of prismatic cohomology that provides some cohesion to the story" |
March 11, 2019, 3:00 PM at Science Center 507 |
| CMSA SOCIAL SCIENCE APPLICATIONS FORUM |
Wes Pegden (CARNEGIE MELLON) |
Developing and applying theorems for the rigorous detection of gerrymandering in the real-world |
We will discuss the role of Markov Chains in the rigorous detection of political gerrymandering. Specifically, we will discuss theorems which enable Markov Chains to be used in a rigorous way in this context, without heuristic assumptions on the mixing time of the chain" |
March 11, 2019, 4:00 pm at CMSA, 20 Garden St, G02 |
| OPEN NEIGHBORHOOD SEMINAR |
Bill Dunham (HARVARD UNIVERSITY) |
A Recipe for Ï |
In recognition of the upcoming âPi Day, 2019,â we begin with a quick history of this illustrious constant, mentioning contributions from Archimedes, Newton, Leibniz, and Euler and carrying the story to the present day, where the value of Ï has been computed to trillions of places. Then, to add a bit of mathematics to the tale, we examine a result from Euler that features this constant in a starring role. In 1783, he sought the exact sum of the infinite series tanâĄ(Ïâ4)+1â2tanâĄ(Ïâ8)+1â4tanâĄ(Ïâ16)+1â8tanâĄ(Ïâ32)+... His solution was devilishly clever in an 18th-century kind of way and should bring our celebration of Ï to a fitting end. (This talk will be accessible to members of the department at all levels." |
March 11, 2019, 4:30 pm at Science Center 507 |
| CMSA SPECIAL SEMINAR |
Juven Wang (IAS) |
New Higher Anomalies and 3+1D Quantum Matter: From 4d Yang-Mills Gauge Theory to 2d CP^N Sigma Model |
This will be a one-hour-ish survey talk, in particular, focusing on overviewing my recent work: arXiv:1812.11968 and 1812.11955. We hypothesize a new and more complete set of anomalies of certain quantum field theories (QFTs) and then give an eclectic proof. First, we propose a set of t Hooft anomalies of 2d ââ^{Nâ 1}-sigma models at topological term Ξ=Ï, with N =2,3,4 and others, by enlisting all possible 3d cobordism invariants (as 3d Symmetry-Protected Topological [SPT] states, which are the interacting generalization of the renowned Topological Insulators/Superconductors) and selecting the matched terms. Second, we propose a set of t Hooft higher anomalies of 4d time-reversal symmetric SU(N)-Yang-Mills (YM) gauge theory at Ξ=Ï, via 5d cobordism invariants (as 5d higher Symmetry-Protected Topological states) such that compactifying YM theory on a 2-torus matches the constrained 3d cobordism invariants from sigma models. We generalize the (Thom-Madsen-Tillmann-)Freed-Hopkins s cobordism theory [arXiv:1604.06527] to higher-symmetry analog [arXiv:1812.11967] in order to compute the above cobordism invariants (the higher-SPT states). Based on algebraic/geometric topology, algebraic geometry methods, QFT analysis, manifold generator dimensional reduction, condensed matter inputs and additional physics criteria, we derive a correspondence between 5d and 3d new invariants, thus broadly prove a more complete anomaly-matching between 4d YM and 2d ââ^{Nâ 1} models via a twisted 2-torus reduction. Furthermore, we formulate a higher-symmetry generalization of symmetry-extension method (w/ Wen-Witten [arXiv:1705.06728]) as a higher-symmetry analog of Lieb-Schultz-Mattis theorem to constrain the low-energy dynamics of the above QFTs/Quantum Matter. If time permits, I will briefly mention my other related work: arXiv:1810.00844 and arXiv:1901.1153" |
March 11, 2019, 4:15 pm at CMSA, 20 Garden St, G10 |
| SOCIAL SCIENCE APPLICATIONS FORUM |
Pietro Bonaldi (CARNEGIE MELLON UNIVERSITY) |
Synthetic Regression Discontinuity - Causal Identification with Machine Learning |
" |
March 11, 2019, 2:30 PM at CMSA, 20 Garden Street, G02 |
| LOGIC SEMINAR |
Cameron Freer (MIT) |
Computability of exchangeable sequences, arrays, and graphs |
A sequence of random variables is exchangeable when its distribution is invariant to reorderings of the sequence. This notion of symmetry and its generalizations to arrays, graphs, and other structures, arise in many statistical contexts. Representation theorems due to de Finetti, Aldous-Hoover, and others, describe how exchangeable structures can be written in a way that exposes conditional independence, which is often important for computational purposes. However, these results are not obviously computable. We will present several positive and negative results examining the computable content of these theorems, and will also describe several implications for the design of probabilistic programming languages. Joint work with Nathanael Ackerman, Jeremy Avigad, Daniel Roy, and Jason Rute" |
March 11, 2019, 5:40 pm at Science Center 507 |
| CMSA METRIC LIMITS OF CALABI-YAU MANIFOLDS |
Valentino Tosatti (NORTHWESTERN UNIVERSITY) |
Proof of Yau's Theorem |
I will give an introduction to the study of limits of Ricci-flat Kahler metrics on a compact Calabi-Yau manifold when the Kahler class degenerates to the boundary of the Kahler cone. Analytically, the problem is to prove suitable uniform a priori estimates for solutions of a degenerating family complex Monge-AmpĂšre equations, away from some singular set. Geometrically, this can be used to understand the Gromov-Hausdorff limit of these metrics. In the projective case, the limits possess an algebraic structure and are obtained from the initial manifold via contraction morphisms from Mori theory. I will discuss some results on this problem, in both the noncollapsing case and in the much harder collapsing case. I will also discuss a different source of examples, coming from work of McMullen and Cantat in complex dynamics on K3 surfaces" |
March 08, 2019, 3:00 - 4:00 pm at CMSA, 20 Garden St, G10 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Thomas Walpuski (MICHIGAN STATE UNIVERSITY) |
Super-rigidity and Castelnuovoâs bound |
Castelnuovoâs bound is a very classical result in algebraic geometry. It asserts a sharp bound on the genus of a curve of degree d in n-dimensional projective space. It is an interesting question to ask whether analogues of Castelnuovoâs bound hold in almost complex geometry. There is a direct analogue in dimension four. In dimension at least eight genus bounds can be established for generic almost complex structures. These results leave open the case of dimension six. Bryan and Panharipande introduced the notion of super-rigidity of an almost complex structure. They also speculated that this condition might hold for a generic almost complex structure (compatible with a fixed symplectic structure). It had been believed for a long time that super-rigidity will play an important role in the proof of the GopakumarâVafa conjecture. However, it turned that Ionel and Parkerâs recent proof of this conjecture did not make use of it. Nevertheless, super-rigidity has important consequences. I will present one of these consequences, namely, a genus bound for index zero pseudo-holomorphic curves. This is joint work with Aleksander Doan and, heavily, relies on work by De Lellis, Spadaro, and Spolaor and ideas of Taubes . There has been a lot of progress towards establishing Bryan and Pandharipandeâs super-rigidity conjecture in the work of Wendl. In fact, based on his ideas, Aleksander Doan and I have developed an abstract framework for equivariant transversality/BrillâNoether type questions. Wendlâs work shows that the super-rigidity conjecture holds provided generic real Cauchy-Riemann operators satisfy an easy to state analytic condition. I will explain what this condition means and discuss a few cases in which this condition (or versions of it hold). Future schedule is found here: https://scholar.harvard.edu/gerig/semina" |
March 08, 2019, 3:30 PM at Science Center 507 |
| SOCIAL SCIENCE APPLICATIONS FORUM |
Jura Liaukonyte (CORNELL UNIVERSITY) |
Background Noise? TV Advertising Affects Real Time Investor Behavior |
Using minute-by-minute television advertising data covering approximately 326,000 ads, 301 firms, and $20 billion in ad spending, we study the real-time effects of TV advertising on investor search for online financial information and subsequent trading activity. Our identification strategy exploits the fact that viewers in different U.S. time zones are exposed to the same programming and national advertising at different times, allowing us to control for contemporaneous confounding events. We find that an average TV ad leads to a 3% increase in SEC EDGAR queries and an 8% increase in Google searches for financial information within 15 minutes of the airing of that ad. Such advertising effects spill over through horizontal and vertical product market links to financial information searches on closest rivals and suppliers. The ad-induced queries on the advertiser and its key rival lead to higher trading volumes of their respective stocks. For large advertisers, around 0.8% of daily trading volume can directly be attributed to advertising. This suggests that advertising, originally intended for consumers, has a sizable effect on financial markets" |
March 07, 2019, 2:30 PM at CMSA, 20 Garden Street, G02 |
| CMSA SPECIAL LECTURE SERIES ON DERIVED ALGEBRAIC/DIFFERENTIAL GEOMETRY: TUESDAYS & THURSDAYS BEGINNING FEBRUARY 5, 2019 |
Artan Sheshmani (CMSA) |
Lecture 4: Cotangent complexes |
Derived algebraic geometry is a branch of mathematics whose aim is to extend algebraic geometry to study of spaces which are locally defined over topological ring spectra (rather than commutative rings of polynomials) and hence they can come equipped with higher homotopical structure. An object in derived geometry comes with an infinity groupoid of internal symmetries as well as infinity algebra of functions (which we will define in detail during the course). One main application of study of derived algebraic spaces (derived schemes or stacks) has been to provide an algebraic description of configuration spaces in gauge theory. Take for instance the so-called BV-BRST complex which encodes the function algebra on the homological resolution of a locus of solutions to differential equation which encodes movement of particles in certain gauge theoretic mechanical system. The derived (or higher) differential geometry is also similar to differential geometry in higher homotopical setting. In derived differential geometry smooth manifolds are replaced with smooth infinity-stacks or (infinity, 1)-sheaves which live over their site. The course discusses both derived algebraic and derived differential geometries and aims to eventually study application of these two constructions in enumerative geometry of moduli stack of algebraic objects on Calabi-Yau or Fano manifolds (for instance Donaldson-Thomas theory of sheaves on Calabi-Yau 4 folds which have a priori ill-behaved non-perfect deformation-obstruction theories). Some of the main topics covered in the course are: Derived Artin Stacks and their cotangent complexes, De Rham complexes and S1 equivariant schemes (loop spaces), Cyclic homology, Shifted symplectic structures, Lagrangians and Lagrangian fibrations, Derived intersection theory and finally a derived analog of Uhlenbeck-Yau correspondences. The detail syllabus of the course and schedule is provided at: http://cmsa.fas.harvard.edu/derived-geometry" |
March 07, 2019, 3:00 - 4:30 pm at CMSA Building, 20 Garden St, G10 |
| CMSA GENERAL RELATIVITY SEMINAR |
Laura Donnay (BLACK HOLE INITIATIVE) |
Carrollian physics at the black-hole horizon |
In this talk, I will show that the near-horizon geometry of a black hole can be described as a Carrollian geometry emerging from an ultra-relativistic limit. The laws governing the dynamic of a black hole horizon, the null Raychaudhuri and Damour equations, are shown to be Carrollian conservation laws obtained by taking the ultra-relativistic limit of the conservation of an energy-momentum tensor. Vector fields preserving the Carrollian geometry of the horizon, dubbed Carrollian Killings, include BMS-like supertranslations and superrotations, and have non-trivial associated conserved charges. If time allows, I will discuss their relation with the infinite-dimensional horizon charges of the covariant phase space formalism" |
March 07, 2019, 3:00 PM - 4:00 PM at Science Center 411 |
| JOINT CMSA AND DEPARTMENT OF MATHEMATICS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Ilya Kachkovskiy (MICHIGAN STATE) |
Localization and delocalization for interacting 1D quasiperiodic particles |
We consider a system of two interacting one-dimensional quasiperiodic particles as an operator on $\ell^2(\mathbb Z^2)$. The fact that particle frequencies are identical, implies a new effect compared to generic 2D potentials: the presence of large coupling localization depends on symmetries of the single-particle potential. If the potential has no cosine-type symmetries, then we are able to show large coupling localization at all energies, even if the interaction is not small (with some assumptions on its complexity). If symmetries are present, we can show localization away from finitely many energies, thus removing a fraction of spectrum from consideration. We also demonstrate that, in the symmetric case, delocalization can indeed happen if the interaction is strong, at the energies away from the bulk spectrum. The result is based on joint works with Jean Bourgain and Svetlana Jitomirskaya" |
March 06, 2019, 4:15 pm at Science Center 411 *note unusual day and location* |
| NUMBER THEORY SEMINAR |
Nicholas Triantafillou (MIT) |
The Method of Chabauty-Coleman-Skolem for Restrictions of Scalars |
For a number field $K$ and a curve $C/K$, the Chabauty s method is a powerful $p$-adic tool for bounding/enumerating the set $C(K)$. The method typically requires that dimension of the Jacobian $J$ of $C$ is greater than the rank of $J(K)$. Since this condition often fails, especially when $[K:\mathbb Q]$ is large, several techniques have been proposed to augment Chabauty s method. For proper curves, Siksek introduced an analogue of Chabauty s method for the restriction of scalars $\text{Res}_{K/\mathbb Q} C$ that can succeed when the rank of $J(\mathcal O_{K,S})$ is as large as $[K:\mathbb Q]\cdot (\dim J - 1)$. Using an analogue of Chabauty s method for restrictions of scalars in the non-proper case, we study the power of this approach together with descent for computing $C = (\mathbb P^1\smallsetminus \{0,1,\infty\})(\mathcal O_{K,S})$. As an application, we show that if $3$ splits completely in $K$ then there are no solutions to the unit equation $x + y = 1$ with $x,y \in \mathcal O_{K}^{\times}$" |
March 06, 2019, 3:00 pm at Science Center 507 |
| CMSA COLLOQUIUM |
Philippe Sosoe (CORNELL UNIVERSITY) |
A sharp transition for Gibbs measures associated to the nonlinear Schrödinger equation |
In 1987, Lebowitz, Rose and Speer (LRS) showed how to construct formally invariant measures for the nonlinear Schrödinger equation on the torus. This seminal contribution spurred a large amount of activity in the area of partial differential equations with random initial data. In this talk, I will explain LRS s result, and discuss a sharp transition in the construction of the Gibbs-type invariant measures considered by these authors. (Joint work with Tadahiro Oh and Leonardo Tolomeo" |
March 06, 2019, 2:30-3:30 PM at CMSA, 20 Garden Street, G10 |
| CMSA FLUID DYNAMICS SEMINAR |
Zhong Yi Wan (MIT) |
Machine learning the kinematics of spherical particles in fluid flows |
Numerous efforts have been devoted to the derivation of equations describing the kinematics of finite-size spherical particles in arbitrary fluid flows. These approaches rely on asymptotic arguments to obtain a description of the particle motion in terms of a slow manifold. We present a novel approach that results in kinematic models with unprecedented accuracy compared with traditional methods. We apply a recently developed machine learning framework that relies on (i) an imperfect model, obtained through analytical arguments, and (ii) a long short-term memory (LSTM) recurrent neural network. The latter learns the mismatch between the analytical model and the exact velocity of the finite-size particle as a function of the fluid velocity that the particle has encountered along its trajectory. We show that training the model for one flow is sufficient to generate accurate predictions for any other arbitrary flow field, capturing the spectrum of the particle velocity, as well as the extreme event statistics. The proposed scheme paves the way for machine learning kinematic models for bubbles and aerosols using high-fidelity DNS simulations and experiments" |
March 06, 2019, 3:00 -4:00 PM at CMSA, 20 Garden Street, G02 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Kaifeng Bu (HARVARD UNIVERSITY AND ZHEJIANG UNIVERSITY) |
Efficient classical simulation of Clifford circuits with nonstabilizer input states |
I will talk about the problem of estimating the output probabilities of the Clifford circuits with any nonstabilizer input states. I will talk about some method of efficient classical simulation for this problem" |
March 05, 2019, 3:00 PM at Jefferson 356 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Tristan Collins (MIT) |
The Inverse Monge-Ampere flow |
I will discuss a new parabolic approach to the existence (and non-existence) of Kahler-Einstein metrics. I will discuss a conjectural picture relating the behaviour of the flow to the existence of optimal algebraic degenerations, and explain a proof of this picture in the setting of toric Kahler manifolds. This is joint work with T. Hisamoto, and R. Takahashi" |
March 05, 2019, 4:00 PM at Science Center 507 |
| COLLOQUIUM |
Mihnea Popa (NORTHWESTERN UNIVERSITY) |
D-modules in birational and complex geometry |
I will give an overview of techniques based on the theory of mixed Hodge modules, which lead to a number of applications of a rather elementary nature in birational and complex geometry, as well as in the study of singularities. One of the main points I will emphasize is the existence (and usefulness) of a package of vanishing and positivity theorems in the context of filtered D-modules of Hodge theoretic origin" |
March 04, 2019, 3:00 pm at Science Center 507 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Zhenkun Li (MIT) |
Cobordism and gluing maps in sutured monopoles and applications |
The sutured monopole Floer homology was constructed by Kronheimer and Mrowka on balanced sutured manifolds. Floer homologies on closed three manifolds are functors from oriented cobordism category to the category of modules over suitable rings. It is natural to ask whether the sutured monopole Floer homology can be viewed as a functor similarly. In the talk we will answer this question affirmatively. In order to study the above problem, we will need to use an important tool called the gluing maps. Gluing maps were constructed in the Heegaard Floer theory by Honda, Kazez and MatiÄ , while were previously unknown in the monopole theory. In the talk we will also explain how to construct such gluing maps in monopoles and how to use them to define a minus version of knot monopole Floer homology" |
March 04, 2019, 12:00 - 1:00 PM at CMSA, 20 Garden Street, G10 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Peter OzsvĂĄth (PRINCETON UNIVERSITY) |
Computing knot Floer homology |
I will explain how to use bordered Floer homology to obtain a practical, algebraic computation of knot Floer homology. This is joint work with ZoltĂĄn SzabĂł. Future schedule is found here: https://scholar.harvard.edu/gerig/semina" |
March 01, 2019, 3:30 PM at Science Center 507 |
| CMSA METRIC LIMITS OF CALABI-YAU MANIFOLDS LECTURE SERIES |
Valentino Tosatti (NORTHWESTERN UNIVERSITY) |
Introduction and Yau's Theorem |
I will give an introduction to the study of limits of Ricci-flat Kahler metrics on a compact Calabi-Yau manifold when the Kahler class degenerates to the boundary of the Kahler cone. Analytically, the problem is to prove suitable uniform a priori estimates for solutions of a degenerating family complex Monge-AmpĂšre equations, away from some singular set. Geometrically, this can be used to understand the Gromov-Hausdorff limit of these metrics. In the projective case, the limits possess an algebraic structure and are obtained from the initial manifold via contraction morphisms from Mori theory. I will discuss some results on this problem, in both the noncollapsing case and in the much harder collapsing case. I will also discuss a different source of examples, coming from work of McMullen and Cantat in complex dynamics on K3 surfaces" |
March 01, 2019, 3:00 -4:00 PM at CMSA, 20 Garden St, G10 |
| BRANDEIS-HARVARD-MIT-NORTHEASTERN JOINT COLLOQUIUM |
Robert Lazarsfeld (STONY BROOK) |
How irrational is an irrational variety? |
Recall that an algebraic variety is said to be rational if it contains a Zariski-open subset isomorphic to a Zariski-open subset of projective space. Subtle questions of rationality have seen a great deal of recent interest and progress, but most varieties arenât rational. I will survey a developing body of work in a complementary direction, centered around measures of irrationality for varieties whose non-rationality is known" |
February 28, 2019, Tea at 4:00 pm; Talk at 4:30 pm at Science Center Hall A |
| CMSA COLLOQUIUM |
Ian Martin (LSE) |
Sentiment and Speculation in a Market with Heterogeneous Beliefs |
We present a dynamic model featuring risk-averse investors with heterogeneous beliefs. Individual investors have stable beliefs and risk aversion, but agents who were correct in hindsight become relatively wealthy; their beliefs are overrepresented in market sentiment, so âthe marketâ is bullish following good news and bearish following bad news. Extreme states are far more important than in a homogeneous economy. Investors understand that sentiment drives volatility up, and demand high risk premia in compensation. Moderate investors supply liquidity: they trade against market sentiment in the hope of capturing a variance risk premium created by the presence of extremists. [with Dimitris Papadimitriou" |
February 27, 2019, 2:30-3:30 PM at CMSA, 20 Garden Street, G10 |
| NUMBER THEORY SEMINAR |
Charlotte Chan (PRINCETON UNIVERSITY) |
Affine Deligne--Lusztig varieties at infinite level for GLn |
Affine Deligne--Lusztig varieties have been of interest for some time because of their relation to Shimura varieties and the Langlands program. In this talk, we will construct a tower of affine Deligne--Lusztig varieties for GLn and its inner forms. We prove that its limit at infinite level is isomorphic to the semi-infinite Deligne--Lusztig variety of Lusztig and that its cohomology realizes certain cases of automorphic induction and Jacquet--Langlands. This is joint work with A. Ivanov." |
February 27, 2019, 3:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Ethan Cotterill (UNIVERSIDADE FEDERAL FLUMINENSE) |
Real inflection points of real linear series on real (hyper)elliptic curves (joint with I. Biswas and C. Garay LĂłpez) |
According to Plucker s formula, the total inflection of a linear series (L,V) on a complex algebraic curve C is fixed by numerical data, namely the degree of L and the dimension of V. Equipping C and (L,V) with compatible real structures, it is more interesting to ask about the total real inflection of (L,V). The topology of the real inflectionary locus depends in a nontrivial way on the topology of the real locus of C. We study this dependency when C is hyperelliptic and (L,V) is a complete series. We first use a nonarchimedean degeneration to relate the (real) inflection of complete series to the (real) inflection of incomplete series on elliptic curves; we then analyze the real loci of Wronskians along an elliptic curve, and formulate some conjectural quantitative estimates" |
February 26, 2019, 3:00 pm at Science Center B10 *note different location |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Fei Wei (HARVARD UNIVERSITY) |
Entropy of arithmetic functions and arithmetic compactifications |
A new notion of entropy of arithmetic functions is introduced. It is shown that all zero entropy arithmetic functions form a C*-algebra. This entropy also behaves nicely with respect to limits similar to Kolomogorovâs dynamical entropy and has many properties similar to Shannonâs entropy" |
February 26, 2019, 3:00 PM at Jefferson 356 |
| COLLOQUIUM |
Melanie Wood (UNIVERSITY OF WISCONSIN) |
Random groups from generators and relations, and unramified extensions of global fields |
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations, and in particular we study the limiting behavior of this model as n goes to infinity. The abelianization of this model is related to the Cohen-Lenstra heuristics, which predict the distribution of unramified abelian extensions of number fields. We use this model as a jumping off point to develop conjectures on the distribution of the Galois groups of the maximal unramified extensions of varying number fields or function fields. We give theorems in the function field case that support these new conjectures. This talk includes joint work with Yuan Liu" |
February 26, 2019, 3:00 pm at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Antoine Song (PRINCETON UNIVERSITY) |
Existence of infinitely many minimal hypersurfaces in closed manifolds |
In the early 80 s, S.-T. Yau conjectured that in any closed $3$-manifold there should be infinitely many minimal surfaces. I will review previous contributions to the question and present a proof of the conjecture, which builds on min-max methods developed by F. C. Marques and A. Neves. A key step is the construction by min-max theory of a sequence of closed minimal surfaces in a certain manifold N with non-empty stable minimal boundary, and I will explain how to achieve this via the construction of a non-compact manifold with cylindrical ends" |
February 26, 2019, 4:00 PM at Science Center 507 |
| CMSA SPECIAL SEMINAR |
Shinobu Hosono (GAKUSHUIN UNIVERSITY) |
Double cover family of K3 surfaces and mirror symmetry |
I will study a family K3 surfaces which are given as double covers of ${\mathbb P}^2$ branched along six lines in general position. Period integrals of this family satisfy the hypergeometric system E(3,6), i.e., Aomoto-Gel fand hypergeometric system on Grassmannian G(3,6), which were studied in detail by Matsumoto, Sasaki and Yoshida in the 90s. In this talk, I will focus on the parameter space of the E(3,6) system described naturally by GIT or Baily-Borel-Satake compactification. I will find that the E(3,6) system is" |
February 25, 2019, 1:00-2:00 PM at CMSA, 20 Garden Street, G10 |
| LOGIC SEMINAR |
Nathanael Ackerman (HARVARD UNIVERSITY) |
Entropy of Invariant Measures |
The entropy of a probability measure on a finite set quantifies one notion of the complexity of the measure. For a finite relational language $L$, and a measure $\mu$ on $L$-structures with underlying set the natural numbers, if $\mu$ is $S_\infty$-invariant then it is determined by its restriction to $L$-structures of the form $\{0, \ldots , n-1\}$. We can therefore canonically assign to $\mu$ its \emph{entropy function}, $En_\mu$, which sends each natural number $n$ to the entropy of the restriction of $\mu$ to $L$-structures with underlying set $\{0, \ldots , n-1\}$. In this talk I will discuss the relationship between the growth rate of $En_\mu$ and the language $L$. If the largest arity of a relation in $L$ is $k$, then $En_\mu$ grows as $O(n^k)$. I will give a precise expression for the coefficient of $n^k$ based on the hypergraphon representation of $\mu$, and show how these notions generalize what is often called the \emph{entropy of a graphon}. When $\mu$ comes from sampling a Borel structure we will show that the growth rate of the entropy function is $o(n^k)$. We will also discuss lower bounds on the possible growth rates of the entropy function in this case. This generalizes work of Hatami-Norine from graphons to hypergraphons. Joint work with Cameron Freer and Rehana Patel" |
February 25, 2019, 5:40 PM at Science Center 507 |
| OPEN NEIGHBORHOOD SEMINAR |
Joe Harris (HARVARD UNIVERSITY) |
Poncelet's theorem and the birth of modern algebraic geometry |
In the early 19th century, Poncelet asked a simple question: given two ellipses in the plane, one inside the other, does there exist a polygon inscribed in the outer one and circumscribed about the inner? In this talk, I ll describe the (somewhat surprising) answer, and also describe how consideration of this simple problem led to two major changes in how we do algebraic geometry: the introduction of projective space, and the use of complex numbers. (This talk will be accessible to members of the department at all levels." |
February 25, 2019, 4:30 PM at Science Center 507 |
| CMSA MATH PHYSICS SEMINAR |
Hossein Movasati (IMPA) |
Modular vector fields |
Using the notion of infinitesimal variation of Hodge structures I will define an R-variety which generalizes Calabi-Yau and abelian varieties, cubic four, seven and ten folds, etc. Then I will prove a theorem concerning the existence of certain vector fields in the moduli of enhanced R-varieties. These are algebraic incarnation of differential equations of the generating functions of GW invariants (Lian-Yau 1995), Ramanujan s differential equation between Eisenstein series (Darboux 1887, Halphen 1886, Ramanujan 1911), differential equations of Siegel modular forms (Resnikoff 1970, Bertrand-Zudilin 2005)" |
February 25, 2019, 12:00 - 1:00 PM at CMSA, 20 Garden St, G10 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
John Baldwin (BOSTON COLLEGE) |
Instanton L-space knots |
A 3-manifold is said to be SU(2)-abelian if all homomorphisms from its fundamental group to SU(2) factor through the first homology of the manifold. Understanding which manifolds are SU(2)-abelian is a difficult and wide open problem, even in the case of 3-manifolds arising from surgery on a knot in the 3-sphere. Kronheimer and Mrowka showed, for instance, that n-surgery on a nontrivial knot is not SU(2)-abelian for n = 1 or 2, but it isn t even known whether the same is true for n = 3 or 4 (the same isn t true for n = 5 as 5-surgery on the right-handed trefoil is a lens space, which has abelian fundamental group). We approach this question by trying to understand which knots have instanton L-space surgeries. A rational homology sphere is said to be an instanton L-space if its framed instanton homology has the smallest rank possible, in analogy with Heegaard Floer homology; familiar examples include lens spaces and branched double covers of alternating knots. Moreover, it is generally the case that SU(2)-abelian manifolds are instanton L-spaces. We conjecture that if surgery on a knot K in the 3-sphere results in an instanton L-space then K is fibered and its Seifert genus equals its smooth slice genus, and we discuss a strategy for proving this" |
February 22, 2019, 3:30 PM at Science Center 507 |
| SOCIAL SCIENCE APPLICATIONS FORUM |
Bobby Pakzad-Hurson (BROWN UNIVERSITY) |
Crowdsourcing and Optimal Market Design |
" |
February 22, 2019, 3:00 PM at CMSA Building, 20 Garden St, G02 |
| CMSA GENERAL RELATIVITY SEMINAR |
Hsin-Yu Chen (BLACK HOLE INITIATIVE) |
Measuring the Hubble Constant with Gravitational Waves |
The first detection of binary neutron star merger by Advanced LIGO-Virgo and the discovery of the optical counterpart allowed for the first independent measurement of Hubble constant with gravitational waves. In this talk, I will summarize latest cosmological measurements with gravitational waves, and discuss the future aspects of them. I will then talk about the potential challenges and how we improve the measurements" |
February 21, 2019, 3:00 -4:00 PM at Sci Center 411 |
| COLLOQUIUM |
June Huh (PRINCETON UNIVERSITY) |
Lorentzian polynomials |
I will give a gentle overview of my ongoing work with Petter BrÀndén on Lorentzian polynomials. The class contains homogeneous stable polynomials as well as volume polynomials of convex bodies and projective varieties. Lorentzian polynomials link continuous convex analysis and discrete convex analysis via tropical geometry. The tropical connection is used to produce Lorentzian polynomials from discrete convex functions. I will give two applications of the general theory. First, it will be shown that the multivariate Tutte polynomial of a graph is Lorentzian whenever the parameter q satisfies 0 < q < 1. Consequences are proofs of the strongest Mason s conjecture from 1972 and negative dependence properties for the random cluster model in statistical physics. Second, it will be shown that the multivariate characteristic polynomial of an M-matrix is Lorentzian. This refines a result of Holtz who proved that the coefficients of the characteristic polynomial of an M-matrix form an ultra log-concave sequence. No specific background will be needed to enjoy the talk." |
February 21, 2019, 3:00 PM at Science Center 507 |
| JOINT CMSA AND DEPARTMENT OF MATHEMATICS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Michael Loss (GEORGIA TECH) |
Some results for functionals of Aharonov-Bohm type |
In this talk I present some variational problems of Aharonov-Bohm type, i.e., they include a magnetic flux that is entirely concentrated at a point. This is maybe the simplest example of a variational problems for systems, the wave function being necessarily complex. The functional is rotationally invariant and the issue to be discussed is whether the optimizer have this symmetry or whether it is broken" |
February 21, 2019, 4:30 pm at CMSA, 20 Garden St, G10 |
| THURSDAY SEMINAR |
Morgan Opie (HARVARD UNIVERSITY) |
Hopf algebras, Witt vectors, and Brown-Gitler spectra, ctd |
" |
February 21, 2019, 3:00 -5:00 PM at Sci Center Hall E |
| CMSA COLLOQUIUM |
Michael Woodford (COLUMBIA UNIVERSITY) |
Optimally Imprecise Memory and Biased Forecasts |
We propose a model of optimal decision making subject to a memory constraint. The constraint is a limit on the complexity of memory measured using Shannonâs mutual information, as in models of rational inattention; the structure of the imprecise memory is optimized (for a given decision problem and noisy environment) subject to this constraint. We characterize the form of the optimally imprecise memory, and show that the model implies that both forecasts and actions will exhibit idiosyncratic random variation; that beliefs will fluctuate forever around the rational-expectations (perfect-memory) beliefs with a variance that does not fall to zero; and that more recent news will be given disproportionate weight. The model provides a simple explanation for a number of features of observed forecast bias in laboratory and field settings. [Joint work with Rava Azeredo da Silveira and Yeji Sung" |
February 20, 2019, 4:30 pm at CMSA, 20 Garden St, G10 |
| CMSA SPECIAL SEMINAR |
Quan Wen (HEFEI NATIONAL LABORATORY FOR PHYSICAL SCIENCES AT THE MICROSCOPE) |
Motor Systems: Searching for Principles |
I will discuss our recent progress towards an algorithmic understanding of the neural mechanisms underlying stereotyped and flexible motor behaviors. We are paying special attention to a one millimeter long roundworm C. elegans, a unique systems neuroscience model to test computational theories via a combination of genetic and imaging methods" |
February 20, 2019, 1:15 PM at CMSA, 20 Garden St, G10 |
| CMSA FLUID DYNAMICS SEMINAR |
Xiaolin Wang (SEAS, HARVARD) |
The effect of piezoelectric material on the stability of flexible flags |
Piezoelectric material has drawn enormous attention in recent decades due to its ability to convert mechanical deformation energy into electrical potential energy, and vice versa. It has been applied to both energy harvesting and passive vibration control applications. In this talk, we will discuss the effect of piezoelectric material on the stability of a flexible flag using a fully coupled fluid-solid-electric model. An inviscid vortex-sheet model and a linear electro-mechanical model are combined to describe the problem. We find that the critical flutter speed is increased due to the extra damping effect of piezoelectric material, and can also be altered by tuning the output inductance-resistance circuit. Optimal resistances and inductances are found that either maximize or minimize the flutter speed. The former application is useful for vibration control while the latter is important for energy harvesting." |
February 20, 2019, 3:00-4:00 PM at CMSA, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Lillian Pierce (DUKE UNIVERSITY) |
Recent progress on understanding class groups of number fields |
It is natural to think of number fields in families---for example, all number fields of a fixed degree. Correspondingly, we can ask about the distribution of the class number, or of the class group, as the field varies over a family. We will describe a diverse array of recent work that studies for a fixed prime p the size of the p-torsion subgroup of the class group, as the number field varies over a family." |
February 20, 2019, 3:00 PM at Science Center 507 |
| CMSA SPECIAL SEMINAR |
Xu Xu (WUHAN UNIVERSITY) |
Rigidity of sphere packing on triangulated 3-manifolds |
Sphere packing on triangulated 3-manifolds is a generalization of circle packing on triangulated surfaces. In this talk, we will describe some rigidity results of sphere packings on 3-manifolds. Part of the talk is based on recent joint work with Xiaokai He" |
February 19, 2019, 11:15 am - 12:00 pm at CMSA, 20 Garden St, G02 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Maksym Fedorchuk (BOSTON COLLEGE) |
Standard models of low degree del Pezzo fibrations |
A del Pezzo fibration is one of the natural outputs of the Minimal Model Program for threefolds. At the same time, geometry of an arbitrary del Pezzo fibration can be unsatisfying due to the presence of non-integral fibers and terminal singularities of an arbitrarily large index. In 1996, Corti developed a program of constructing `standard models of del Pezzo fibrations within a fixed birational equivalence class. Standard models enjoy a variety of desired properties, one of which is that all of their fibers are Q-Gorenstein integral del Pezzo surfaces. Corti proved the existence of standard models for del Pezzo fibrations of degree d\geq 2, with the case of d=2 being the most difficult. The case of d=1 remained a conjecture. In 1997, KollĂĄr recast and improved the Cortiâs result in degree d=3 using ideas from the Geometric Invariant Theory for cubic surfaces. I will present a generalization of KollĂĄrâs approach in which we develop notions of stability for families of low degree (d\leq 2) del Pezzo fibrations in terms of their Hilbert points (i.e., low degree equations cutting out del Pezzos). A correct choice of stability and a bit of enumerative geometry then leads to (very good) standard models in the sense of Corti. This is a joint work with Hamid Ahmadinezhad and Igor Krylov" |
February 19, 2019, 3:00 pm at MIT 2-147 |
| CMSA SPECIAL SEMINAR |
Feng Luo (RUTGERS UNIVERSITY) |
Volume and rigidity of hyperbolic polyhedral 3-manifolds |
We investigate the rigidity of hyperbolic cone metrics on 3-manifolds based on triangulations. The key tools used are the discrete Einstein-Hilbert functional (Schlaefli formula), hyperbolic volume and Legendre transformation of them. This is a join work with Tian Yang" |
February 19, 2019, 10:30 - 11:15 am at CMSA, 20 Garden St, G02 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Valentino Tosatti (NORTHWESTERN UNIVERSITY) |
Ricci-flat metrics and dynamics on K3 surfaces |
Holomorphic automorphisms of complex K3 surfaces with interesting dynamical behavior are relatively easy to come by. I will describe how Ricci-flat Kahler metrics on K3 surfaces can be used to prove a rigidity statement in holomorphic dynamics, conjectured by McMullen and Cantat, characterizing Kummer examples by the absolute continuity of their measure of maximal entropy with respect to Lebesgue, a result first proved by Cantat-Dupont in the projective case with a more complicated argument. Joint work with Simion Filip" |
February 19, 2019, 4:00 pm at Science Center 507 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Cagatay Kutluhan (BUFFALO) |
Can Floer-theoretic invariants detect overtwisted contact structures? |
In joint work with Matic, Van Horn-Morris, and Wand, we seek an answer to this question. We define a refinement of the contact invariant in Heegaard Floer homology that takes values in $\mathbb{Z}_{\geq 0}\cup\{\infty\}$, called (spectral) order. Among other things, we prove that overtwisted contact structures have zero order, whereas Stein fillable contact structures have infinite order. Furthermore, we show that a strictly increasing sequence of positive integers is realized as the order of a family of contact structures with vanishing Heegaard Floor contact invariant. After defining our contact invariant and discussing some of its key properties, I will talk about its computability and some problems that are content of work in progress" |
February 15, 2019, 3:30 pm at Science Center 507 |
| CMSA SPECIAL ALGEBRAIC GEOMETRY SEMINAR |
Jin Cao (TSINGHUA UNIVERSITY) |
Elliptic motives and related topics |
In this talk, we will describe elliptic motives from the commutative differential algebras point view and explain the idea behind the construction which is closely related with the relative completion" |
February 15, 2019, 3:00 pm at CMSA, 20 Garden St, G10 |
| HARVARD-MIT-MSR COMBINATORICS SEMINAR |
Sylvie Corteel (CNRS/UC BERKELEY) |
Arctic curves for bounded Lecture Hall Tableaux |
Lecture Hall partitions were introduced at the end of the 90s by Bousquet-Melou and Erickson as the inversion vectors of elements of the parabolic quotient tilde{C}_n/C_n. Lecture Hall partitions and compositions are also the combinatorial interpretation of the coefficients of Little q-Little Jacobi polynomials and their moments. This approach coming from orthogonal polynomials guided us to define a new family of tableaux called Lecture Hall Tableaux. These give the combinatorial interpretation of the expansion the multivariate Little q-Laguerre polynomials in the Schur basis and of their moments. If time permits I will present also the asymptotics of bounded Lecture Hall tableaux of a given shape. These tableaux can be seen as non intersecting paths on a strip of the lecture hall lattice and also as a dimer model on the lecture hall honeycomb lattice. Thanks to these two points of view, we can compute the arctic curves of their limit shapes using dimers or the tangent method due to Colomo and Sportiello. This is joint work with Jang Soo Kim (SKKU), David Keating (Berkeley) and Matthew Nicoletti (Berkeley)" |
February 15, 2019, 3:30 pm at Science Center 530 (SC 232 - backup location) |
| CMSA GENERAL RELATIVITY SEMINAR |
Charles Marteau (ECOLE POLYTECHNIQUE) |
Null hypersurfaces and ultra-relativistic physics in gravity |
I will explain how the induced geometry on a null hypersurface gives rise to a particular type of structure called Carrollian geometry. The latter emerges when taking the ultra-relativistic limit of the usual pseudo-Riemannian metric. This property has strong consequences on the gravitational dynamics satisfied by the extrinsic geometry of the null hypersurface and on its symmetry group. We will see how the first one can be interpreted as ultra-relativistic conservation laws while the second corresponds to the isometries of the induced Carrollian geometry. These are very general statements for any null hypersurface but I will focus all along on a physically interesting case: the null infinity of an asymptotically flat spacetime" |
February 14, 2019, 3:00 pm at Science Center 411 |
| THURSDAY SEMINAR |
Morgan Opie (HARVARD UNIVERSITY) |
Hopf algebras, Witt vectors, and Brown-Gitler spectra |
" |
February 14, 2019, 3:00 - 4:30 pm at Science Center 507 |
| BRANDEIS-HARVARD-MIT-NORTHEASTERN JOINT COLLOQUIUM |
Allen Knutson (CORNELL UNIVERSITY) |
Schubert calculus and quiver varieties |
Schubert calculus, the intersection theory of homogeneous spaces such as Grassmannians (or 1-step flag manifolds), is famously a problem for which we have easy alternating-sum formulae but know in advance that the intersection numbers will be nonnegative. We ve had positive rules (i.e. counting a set such as Young tableaux) for the Grassmannian case since 1934, but 2-step and 3-step rules only came in 2009 and 2017. I ll explain how connecting these puzzle rules to quantum integrable systems made them easy to derive and prove, and how further connection to quiver varieties has brought about several more advances. This work is joint with Paul Zinn-Justin and Iva Halacheva" |
February 14, 2019, Tea at 4:00 pm; Talk at 4:30 pm at Science Center Hall A |
| JOINT CMSA AND DEPARTMENT OF MATHEMATICS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Nike Sun (MIT) |
Capacity lower bound for the Ising perceptron |
The perceptron is a toy model of a simple neural network that stores a collection of given patterns. Its analysis reduces to a simple problem in high-dimensional geometry, namely, understanding the intersection of the cube (or sphere) with a collection of random half-spaces. Despite the simplicity of this model, its high-dimensional asymptotics are not well understood. I will describe what is known and present recent results" |
February 14, 2019, 4:30 pm at CMSA, 20 Garden St, G10 |
| CMSA COLLOQUIUM |
Christian Santangelo (UNIVERSITY OF MASSACHUSETTS AT AMHERST) |
4D printing with folding forms |
4D printing is the name given to a set of advanced manufacturing techniques for designing flat materials that, upon application of a stimulus, fold and deform into a target three-dimensional shapes. The successful design of such structures requires an understanding of geometry as it applies to the mechanics of thin, elastic sheets. Thus, 4D printing provides a playground for both the development of new theoretical tools as well as old tools applied to new problems and experimental challenges in soft materials. I will describe our groupâs efforts to understand and design structures that can fold from an initially flat sheet to target three-dimensional shapes. After reviewing the state-of-the-art in the theory of 4D printing, I will describe recent results on the folding and misfolding of flat structures and highlight the challenges remaining to be overcome" |
February 13, 2019, 4:30 pm at CMSA, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Preston Wake (INSTITUTE FOR ADVANCED STUDY) |
Variation of Iwasawa invariants in residually reducible Hida families |
We ll discuss a work in progress describing properties of p-adic L-functions of a modular form whose Galois representation is residually reducible. As an application, we prove cases of a conjecture of Greenberg about mu-invariants of Selmer groups of elliptic curves, paying particular attention to the case of X_0(11) with p=5. This is joint work with Rob Pollack" |
February 13, 2019, 3:00 pm at Science Center 507 |
| CMSA SPECIAL ALGEBRAIC GEOMETRY SEMINAR |
Qingyuan Jiang (IAS) |
Categorical duality between joins and intersections |
In this talk, I will discuss some recent progress in the program of homological projective geometry, a program proposed by KuznetsovâPerry based on the framework of homological projective duality (HPD). In classical projective geometry, there are two important monoidal operations on all subvarieties of a given projective space: joins of varieties, and intersections of varieties. These two operations are only projective dual to each other in good cases. However, categorically, in the framework HPD, the duality between joins and intersections holds in great generality. This result has many applications as well as its own theoretical importance. The talk is based on recent joint works with Conan Leung." |
February 13, 2019, 3:00 pm at CMSA Building, 20 Garden St, G10 |
| CMSA HODGE AND NOETHER-LEFSCHETZ LOCI SEMINAR |
Hossein Movasati (IMPA) |
Foliations and Hodge loci |
In this talk I will introduce a holomorphic foliation in a larger parameter space attached to families of enhanced projective varieties. Irreducible components of the Hodge locus with constant periods are algebraic leaves of such a foliation. Under the hypothesis that these are all the algebraic leaves, we get the fact that such algebraic leaves are defined over the algebraic closure of the base field and that Hodge classes are weak absolute in the sense of C. Voisin" |
February 13, 2019, 1:30 - 3:00 pm at CMSA, 20 Garden St, G10 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Liang Kong (SHENZHEN INSTITUTE FOR QUANTUM SCIENCE AND ENGINEERING AND SOUTHERN UNIVERSITY OF SCIENCE AND TECHNOLOGY) |
A unified mathematical theory of gapped and gapless boundaries of 2d topological orders |
A 2d topological order can be described by a unitary modular tensor category (UMTC) of anyons and a chiral central charge. The mathematical theory for gapped boundaries of 2d topological orders has been established a few years ago. A gapped boundary is described by a unitary fusion category whose Drinfeld center gives precisely the UMTC associated to the bulk. The mathematical theory for gapless boundaries is not known, but it was long believed that a chiral gapless boundary should be described by a âchiral conformal field theory,â the precise meaning of which was not known. In this talk, I will establish this missing theory and show that observables on the 1+1D world sheet of such a boundary form an enriched monoidal category, whose Drinfeld center is again precisely the UMTC associated to the bulk. This is joint work with Hao Zheng" |
February 12, 2019, 3:00 pm at Jefferson 356 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Dan Abramovich (BROWN UNIVERSITY) |
Moduli technique in resolution of singularities |
" |
February 12, 2019, 3:00 pm at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Mitchell Faulk (COLUMBIA UNIVERSITY) |
Yau's theorem on Asymptotically Conical manifolds with prescribed decay rates |
We discuss a variant of Yau s theorem on a certain class of non-compact manifolds that are asymptotically conical. It is natural to require the prescribed Ricci form to decay with a certain rate, and following Conlon-Hein, one obtains different existence/uniqueness results for each interval of decay rates where the Fredholm index of the Laplacian is constant. We focus on a small improvement of precision with regard to the left-hand endpoint of a certain interval of decay rates corresponding to the interval where the Fredholm index of the Laplacian is the first negative value" |
February 12, 2019, 4:00 pm at Science Center 507 |
| CMSA SPECIAL LECTURE SERIES ON DERIVED ALGEBRAIC/DIFFERENTIAL GEOMETRY: TUESDAYS & THURSDAYS BEGINNING FEBRUARY 5, 2019 |
Artan Sheshmani (CMSA) |
Lecture 3: Derived Artin stacks |
Derived algebraic geometry is a branch of mathematics whose aim is to extend algebraic geometry to study of spaces which are locally defined over topological ring spectra (rather than commutative rings of polynomials) and hence they can come equipped with higher homotopical structure. An object in derived geometry comes with an infinity groupoid of internal symmetries as well as infinity algebra of functions (which we will define in detail during the course). One main application of study of derived algebraic spaces (derived schemes or stacks) has been to provide an algebraic description of configuration spaces in gauge theory. Take for instance the so-called BV-BRST complex which encodes the function algebra on the homological resolution of a locus of solutions to differential equation which encodes movement of particles in certain gauge theoretic mechanical system. The derived (or higher) differential geometry is also similar to differential geometry in higher homotopical setting. In derived differential geometry smooth manifolds are replaced with smooth infinity-stacks or (infinity, 1)-sheaves which live over their site. The course discusses both derived algebraic and derived differential geometries and aims to eventually study application of these two constructions in enumerative geometry of moduli stack of algebraic objects on Calabi-Yau or Fano manifolds (for instance Donaldson-Thomas theory of sheaves on Calabi-Yau 4 folds which have a priori ill-behaved non-perfect deformation-obstruction theories). Some of the main topics covered in the course are: Derived Artin Stacks and their cotangent complexes, De Rham complexes and S1 equivariant schemes (loop spaces), Cyclic homology, Shifted symplectic structures, Lagrangians and Lagrangian fibrations, Derived intersection theory and finally a derived analog of Uhlenbeck-Yau correspondences. The detail syllabus of the course and schedule is provided at: http://cmsa.fas.harvard.edu/derived-geometry" |
February 12, 2019, 3:00 - 4:30 pm at CMSA Building, 20 Garden St, G10 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Tristan Collins (MIT) |
Stability and Nonlinear PDE in mirror symmetry |
A longstanding problem in mirror symmetry has been to understand the relationship between the existence of solutions to certain geometric nonlinear PDES (the special Lagrangian equation, and the deformed Hermitian-Yang-Mills equation) and algebraic notions of stability, mainly in the sense of Bridgeland. I will discuss progress in this direction through ideas originating in infinite dimensional GIT. This is joint work with S.-T. Yau" |
February 11, 2019, 12:00 - 1:00 pm at CMSA, 20 Garden St, G10 |
| COLLOQUIUM |
Hector Pasten (PONTIFICIA UNIVERSIDAD CATOLICA DE CHILE) |
Modular forms and the ABC conjecture |
The ABC conjecture concerns a surprising relation between addition and factorization of integers, and it is well-known for having a number of unexpected consequences. The problem remains open and most of the literature around it is focused on conditional applications, but nonetheless there are some unconditional results. In this talk I will give an overview of the available unconditional progress on the ABC conjecture and the relevant techniques, with particular attention to its connection with modular forms" |
February 11, 2019, 3:00 pm at Science Center 507 |
| CMSA SPECIAL LECTURE SERIES ON DERIVED ALGEBRAIC/DIFFERENTIAL GEOMETRY: TUESDAYS & THURSDAYS BEGINNING FEBRUARY 5, 2019 |
Artan Sheshmani (CMSA) |
Lecture 2: Grothendieck topologies and homotopy descent |
Derived algebraic geometry is a branch of mathematics whose aim is to extend algebraic geometry to study of spaces which are locally defined over topological ring spectra (rather than commutative rings of polynomials) and hence they can come equipped with higher homotopical structure. An object in derived geometry comes with an infinity groupoid of internal symmetries as well as infinity algebra of functions (which we will define in detail during the course). One main application of study of derived algebraic spaces (derived schemes or stacks) has been to provide an algebraic description of configuration spaces in gauge theory. Take for instance the so-called BV-BRST complex which encodes the function algebra on the homological resolution of a locus of solutions to differential equation which encodes movement of particles in certain gauge theoretic mechanical system. The derived (or higher) differential geometry is also similar to differential geometry in higher homotopical setting. In derived differential geometry smooth manifolds are replaced with smooth infinity-stacks or (infinity, 1)-sheaves which live over their site. The course discusses both derived algebraic and derived differential geometries and aims to eventually study application of these two constructions in enumerative geometry of moduli stack of algebraic objects on Calabi-Yau or Fano manifolds (for instance Donaldson-Thomas theory of sheaves on Calabi-Yau 4 folds which have a priori ill-behaved non-perfect deformation-obstruction theories). Some of the main topics covered in the course are: Derived Artin Stacks and their cotangent complexes, De Rham complexes and S1 equivariant schemes (loop spaces), Cyclic homology, Shifted symplectic structures, Lagrangians and Lagrangian fibrations, Derived intersection theory and finally a derived analog of Uhlenbeck-Yau correspondences. The detail syllabus of the course and schedule is provided at: http://cmsa.fas.harvard.edu/derived-geometry" |
February 07, 2019, 3:00 - 4:30 pm at CMSA Building, 20 Garden St, G10 |
| JOINT CMSA AND DEPARTMENT OF MATHEMATICS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Ramis Movassagh (IBM RESARCH) |
Generic Gaplessness, and Hamiltonian density of states from free probability theory |
Quantum many-body systems usually reside in their lowest energy states. This among other things, motives understanding the gap, which is generally an undecidable problem. Nevertheless, we prove that generically local quantum Hamiltonians are gapless in any dimension and on any graph with bounded maximum degree. We then provide an applied and approximate answer to an old problem in pure mathematics. Suppose the eigenvalue distributions of two matrices M_1 and M_2 are known. What is the eigenvalue distribution of the sum M_1+M_2? This problem has a rich pure mathematics history dating back to H. Weyl (1912) with many applications in various fields. Free probability theory (FPT) answers this question under certain conditions. We will describe FPT and show examples of its powers for approximating physical quantities such as the density of states of the Anderson model, quantum spin chains, and gapped vs. gapless phases of some Floquet systems. These physical quantities are often hard to compute exactly (provably NP-hard). Nevertheless, using FPT and other ideas from random matrix theory excellent approximations can be obtained. Besides the applications presented, we believe the techniques will find new applications in fresh new contexts" |
February 07, 2019, 4:30 pm at Science Center 530 |
| CMSA COLLOQUIUM |
Ulrich Mueller (PRINCETON UNIVERSITY) |
Inference for the Mean |
Consider inference about the mean of a population with finite variance, based on an i.i.d. sample. The usual t-statistic yields correct inference in large samples, but heavy tails induce poor small sample behavior. This paper combines extreme value theory for the smallest and largest observations with a normal approximation for the t-statistic of a truncated sample to obtain more accurate inference. This alternative approximation is shown to provide a refinement over the standard normal approximation to the full sample t-statistic under more than two but less than three moments, while the bootstrap does not. Small sample simulations suggest substantial size improvements over the bootstrap" |
February 07, 2019, 4:30 pm at CMSA Building, 20 Garden St, G10 |
| CMSA GENERAL RELATIVITY SEMINAR |
Pei-Ken Hung (MIT) |
The linear stability of the Schwarzschild spacetime in the harmonic gauge: even part |
We study the even solution of the linearlized Einstein equation on the Schwarzschild background and in the harmonic gauge. With the aid of the Zerilli equation, we estimate the even part of Lichnerowicz d Alembertian equation. In particular, we show that up to a one dimensional stationary mode, the solution decays to a linearlized Kerr solution. This is ongoing joint work with S. Brendle" |
February 07, 2019, 3:00 pm at Science Center 411 |
| CMSA HODGE AND NOETHER-LEFSCHETZ LOCI SEMINAR |
Hossein Movasati (IMPA) |
Integrality properties of CY modular forms |
The integrality of the coefficients of the mirror map is a central problem in the arithmetic of Calabi-Yau varieties and it has been investigated by Lian-Yau (1996, 1998), Hosono-Lian-Yau (1996), Zudilin (2002), Kontsevich-Schwarz-Vologodsky (2006) Krattenthaler-Rivoal (2010). The central tool in most of these works has been the so called Dwork method. In this talk we use this method and classify all hypergeometric differential equations with a maximal unipotent monodromy whose mirror map has integral coefficients. We also give a computable condition on the parameters of a hypergeometric function which conjecturally computes all the primes which appear in the denominators of the coefficients of the mirror map. This is a joint work with Kh. Shokri." |
February 06, 2019, 1:30 - 3:00 pm at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Rong Zhou (IAS) |
Motivic cohomology of quaternionic Shimura varieties and level raising |
For a smooth scheme of finite type over a field its motivic cohomology groups generalize the usual Chow groups and are an important algebraic invariant. In this talk we will explain how, for the special fibers of certain quaternionic Shimura varieties, its motivic cohomology can encode very rich arithmetic information. More precisely we will show that the cycle class map from motivic cohomology to Ă©tale cohomology gives a geometric realization of level raising between Hilbert modular forms. The main ingredient for this construction is a form of Ihara s Lemma for Shimura surfaces which we prove by generalizing a method of Diamond-Taylor." |
February 06, 2019, 3:00 pm at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Xin Zhou (UNIVERSITY OF CALIFORNIA AT SANTA BARBARA) |
Multiplicity One Conjecture in Min-max theory |
I will present a recent proof of the Multiplicity One Conjecture in Min-max theory. This conjecture was raised by Marques and Neves. It says that in a closed manifold of dimension between 3 and 7 with a bumpy metric, the min-max minimal hypersurfaces associated with the volume spectrum introduced by Gromov, Guth, Marques-Neves are all two-sided and have multiplicity one. As direct corollaries, it implies the generalized Yau s conjecture for such manifolds with positive Ricci curvature, which says that there exist infinitely many pairwise non-isometric minimal hypersurfaces, and the Weighted Morse Index Bound Conjecture by Marques and Neves" |
February 05, 2019, 4:00 pm at Science Center 507 |
| CMSA SPECIAL LECTURE SERIES ON DERIVED ALGEBRAIC/DIFFERENTIAL GEOMETRY: TUESDAYS & THURSDAYS BEGINNING FEBRUARY 5, 2019 |
Artan Sheshmani (CMSA) |
Lecture 1: Model and NA-categories |
Derived algebraic geometry is a branch of mathematics whose aim is to extend algebraic geometry to study of spaces which are locally defined over topological ring spectra (rather than commutative rings of polynomials) and hence they can come equipped with higher homotopical structure. An object in derived geometry comes with an infinity groupoid of internal symmetries as well as infinity algebra of functions (which we will define in detail during the course). One main application of study of derived algebraic spaces (derived schemes or stacks) has been to provide an algebraic description of configuration spaces in gauge theory. Take for instance the so-called BV-BRST complex which encodes the function algebra on the homological resolution of a locus of solutions to differential equation which encodes movement of particles in certain gauge theoretic mechanical system. The derived (or higher) differential geometry is also similar to differential geometry in higher homotopical setting. In derived differential geometry smooth manifolds are replaced with smooth infinity-stacks or (infinity, 1)-sheaves which live over their site. The course discusses both derived algebraic and derived differential geometries and aims to eventually study application of these two constructions in enumerative geometry of moduli stack of algebraic objects on Calabi-Yau or Fano manifolds (for instance Donaldson-Thomas theory of sheaves on Calabi-Yau 4 folds which have a priori ill-behaved non-perfect deformation-obstruction theories). Some of the main topics covered in the course are: Derived Artin Stacks and their cotangent complexes, De Rham complexes and S1 equivariant schemes (loop spaces), Cyclic homology, Shifted symplectic structures, Lagrangians and Lagrangian fibrations, Derived intersection theory and finally a derived analog of Uhlenbeck-Yau correspondences. The detail syllabus of the course and schedule is provided at: http://cmsa.fas.harvard.edu/derived-geometry" |
February 05, 2019, 3:00 - 4:30 pm at CMSA Building, 20 Garden St, G10 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Mihai Fulger (UNIVERSITY OF CONNECTICUT) |
Seshadri constants for bundles |
For line bundles, Seshadri constants are classical local positivity invariants at a point. They detect ampleness in several ways, and they measure jet separation at the point in an asymptotic sense. A generalization of Seshadri constants to higher rank was first studied explicitly by Hacon. In our work, we extend the classical rank one results. We also give three applications. First, we offer a Seshadri characterization of projective space as the only Fano manifold whose tangent bundle has positive Seshadri constant for at least one point. We conjecture that the Fano assumption can be removed, and offer the case of surfaces as evidence. Second, we make partial progress towards a conjecture on the shape of the nef cone of the self product of a very general curve of high genus. Third, we observe that Seshadri constants control jet separation for direct images of pluricanonical sheaves. This is all in joint work with Takumi Murayama" |
February 05, 2019, 3:00 pm at MIT 2-142 |
| COLLOQUIUM |
Dana Mendelson (UNIVERSITY OF CHICAGO) |
Probabilistic methods and long-time dynamics for nonlinear dispersive PDEs |
Nonlinear dispersive equations model wave propagation phenomena for many physical systems, from water waves to quantum gases. For the last few decades, research on these equations has centered around questions on the existence of solutions, their long time behavior, and the possibility of singularity formation. Fundamental progress has been made in many settings, yet in some regimes, the nonlinear interactions overwhelm the dispersion of the waves, and standard methods break down. In recent years, probabilistic tools have been instrumental in analyzing the behavior of these equations in previously inaccessible regimes. This approach, which goes back to the seminal work of Bourgain in the 90s on invariant Gibbs measures for Hamiltonian PDEs, has opened the door to new and exciting questions in a variety of settings. In this talk, we will describe some recent work and ongoing progress in this area" |
February 04, 2019, 3:00 pm at Science Center 507 |
| SNAPSHOTS OF MATH AT HARVARD |
Ben Knudsen, Alison Miller, Sebastien Picard, Bena Tshishiku (HARVARD UNIVERSITY) |
|
Sebastien Picard: Calabi-Yau manifolds with torsion and geometric flows Bena Tshishiku: Surface bundles, monodromy, and arithmetic groups Ben Knudsen: Configuration spaces of manifolds and graph Alison Miller: Asymptotics for Sp_2g-orbits of integer quadratic for" |
February 04, 2019, 4:30 pm at Science Center 507 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Netanel (Nati) Rubin-Blaier (HARVARD & BRANDEIS) |
Abelian cycles, and homology of symplectomorphism groups |
Based on work of Kawazumi-Morita, Church-Farb, and N. Salter in the classical case of Riemann surfaces, I will describe a technique which allows one to detect some higher homology classes in the symplectic Torelli group using parametrized Gromov-Witten theory. As an application, we will consider the complete intersection of two quadrics in $P^5$, and produce a non-trivial lower bound for the dimension of the 2nd group homology of the symplectic Torelli group (relative to a fixed line) with rational coefficients." |
February 04, 2019, 12:00 - 1:00 pm at CMSA Building, 20 Garden St, G10 |
| LOGIC SEMINAR |
Sebastien Vasey (HARVARD UNIVERSITY) |
On categoricity in successive cardinals |
The upward Löwenheim-Skolem theorem says that any first-order theory with an infinite model has arbitrarily large models. Such a result completely completely breaks down when we start looking at infinitary logics. In this case, one can still ask what properties of small models imply the existence of larger models. One of the simplest such property is categoricity (the existence of a unique model of a fixed cardinality). In that direction, Shelah proved the remarkable result that an L_{\omega_1, \omega} sentence categorical in aleph_0 and aleph_1 has a model of cardinality aleph_2. Generalizations of this result have been key motivating questions for the development of a classification theory of infinitary logics, and also have also yielded some interesting set theory. We will survey some old results as well as recent developments" |
February 04, 2019, 5:40 pm at Science Center 507 |
| HARVARD - MIT COMBINATORICS SEMINAR |
Michael Wheeler (THE UNIVERSITY OF MEBOURNE) |
Matrix product expressions for Macdonald polynomials and combinatorial applications |
The symmetric Macdonald polynomials admit a representation as the partition function of a certain higher-rank integrable lattice model. This expression is an inhomogeneous generalization of a matrix product formula for the steady state of the asymmetric simple exclusion process (ASEP) on a ring. I will review some of these facts, and focus in particular on the limit to TASEP (totally asymmetric case), which leads to an unexpected and elegant formula for the Kostka--Foulkes polynomials" |
February 01, 2019, 3:30 pm at Science Center 530 (SC 309a - backup location) |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
ZoltĂĄn SzabĂł (PRINCETON UNIVERSITY) |
Algebraic methods in knot Floer homology |
The aim of this talk is to present an algebraic description of knot Floer homology, discovered in a joint work with Peter OzsvĂĄth. Future schedule is found here: https://scholar.harvard.edu/gerig/semina" |
February 01, 2019, 3:30 pm at Science Center 507 |
| COLLOQUIUM |
Simion Filip (HARVARD AND IAS) |
Discrete groups, Lyapunov exponents, and Hodge theory |
Families of algebraic manifolds give interesting examples of discrete subgroups of Lie groups, via their monodromy. They also lead to differential equations, such as the hypergeometric ones, whose solutions have an arithmetic significance. After providing the necessary background I will explain a connection to dynamical invariants called Lyapunov exponents, which reveals special geometric features of the discrete groups and the corresponding differential equations" |
January 31, 2019, 4:00 pm at Science Center 507 |
| CMSA GENERAL RELATIVITY SEMINAR |
Shahar Hadar (HARVARD UNIVERSITY) |
Late-time behavior of near-extremal black holes from symmetry |
Linear perturbations of extremal black holes exhibit the Aretakis instability, in which higher derivatives of the fields grow polynomially with time along the event horizon. Near-extremal black holes display similar behavior for some time, and eventually decay exponentially through quasinormal modes. In the talk I will show that the above behaviors are dictated by the conformal symmetry of the near-horizon region of such black holes. I will then discuss the significance of backreaction in the problem, and show how it can be simply accounted for within the near-horizon picture" |
January 31, 2019, 3:00 - 4:00 pm at Science Center 232 *note different location* |
| CMSA HODGE AND NOETHER-LEFSCHETZ LOCI SEMINAR |
Hossein Movasati (IMPA) |
Constant Yukawa couplings |
In this talk I will first introduce algebraic Yukawa couplings for any moduli of enhanced Calabi-Yau n-folds. Then I will list many examples in support of the following conjecture. A moduli of Calabi-Yau n-folds is a quotient of a Hermitian symmetric domain (constructed from periods) by an arithmetic group if and only if the corresponding Yukawa couplings are constants" |
January 30, 2019, 1:30 - 3:00 pm at CMSA Building, 20 Garden St, G10 |
| CMSA COLLOQUIUM |
Richard B. Freeman (HARVARD UNIVERSITY AND NBER) |
Innovation in Cell Phones in the US and China: Who Improves Technology Faster? |
Cell phones are the archetypical modern consumer innovation, spreading around the world at an incredible pace, extensively used for connecting people with the Internet and diverse apps. Consumers report spending from 2-5 hours a day at their cell phones, with 44% of Americans saying âcouldnât go a day without their mobile devices.â Cell phone manufacturers introduce new models regularly, embodying additional features while other firms produce new applications that increase demand for the phones. Using newly developed data on the prices, attributes, and sales of different models in the US and China, this paper estimates the magnitude of technological change in the phones in the 2000s. It explores the problems of analyzing a product with many interactive attributes in the standard hedonic price regression model and uses Principal Components Regression to reduce dimensionality. The main finding is that technology improved the value of cell phones at comparable rates in the US and China, despite different market structures and different evaluations of some attributes and brands. The study concludes with a discussion of ways to evaluate the economic surplus created by the cell phones and their contribution to economic well-being" |
January 30, 2019, 4:30 pm at CMSA Building, 20 Garden St, G10 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Enno Kessler (HARVARD CMSA) |
Supergeometry, Super Riemann Surfaces and the Superconformal Action |
It is well-known that harmonic maps can be used to study Riemann surfaces and TeichmĂŒller space. A supersymmetric extension of the harmonic action, the two- dimensional non-linear supersymmetric sigma model or superconformal action, originates from string theory and supergravity. In this talk, I will show how this supersymmetric extension can be understood as a supergeometric analogue of the harmonic action on super Riemann surfaces. Using maps from Riemann surfaces to super Riemann surfaces one can describe precisely how super Riemann surfaces extend the notion of Riemann surfaces and how supergeometry leads to supersymmetry of this model. Finally, I will indicate why this superconformal action might be a good tool to study the super moduli space" |
January 29, 2019, 4:00 pm at Science Center 507 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Per Berglund (UNIVERSITY OF NEW HAMPSHIRE) |
A Generalized Construction of Calabi-Yau Manifolds and Mirror Symmetry |
We extend the construction of Calabi-Yau manifolds to hypersurfaces in non-Fano toric varieties. This provides a generalization of Batyrevâs original work, allowing us to construct new pairs of mirror manifolds. In particular, we find novel K3-fibered Calabi-Yau manifolds, relevant for type IIA/heterotic duality in d=4, N=2, string compactifications. We also calculate the three-point functions in the A-model following Morrison-Plesser, and find perfect agreement with the B-model result using the Picard-Fuchs equations on the mirror manifold" |
January 28, 2019, 12:00 - 1:00 pm at CMSA Building, 20 Garden St, G10 |
| CMSA HODGE AND NOETHER-LEFSCHETZ LOCI SEMINAR |
Hossein Movasati (IMPA) |
A new model for modular curves |
One of the non-trivial examples of a Hodge locus is the modular curve X_0(N), which is due to isogeny of elliptic curves (a Hodge/algebraic cycle in the product of two elliptic curves). After introducing the notion of enhanced moduli of elliptic curves, I will describe a new model for X_0(N) in the weighted projective space of dimension 4 and with weights (2,3,2,3,1). I will also introduce some elements in the defining ideal of such a model. The talk is based on the article arXiv:1808.01689" |
January 23, 2019, 1:30 - 3:00 pm at CMSA Building, 20 Garden St, G10 |
| CMSA HODGE AND NOETHER-LEFSCHETZ LOCI SEMINAR |
Hossein Movasati (IMPA) |
Algebraic BCOV anomaly equation |
We introduce the moduli space T of non-rigid compact Calabi-Yau threefolds enhanced with differential forms and a Lie algebra of vector fields in T. This will be used in order to give a purely algebraic interpretation of topological string partition functions and the Bershadsky-Cecotti-Ooguri-Vafa holomorphic anomaly equation (joint work with M. Alim, E. Scheidegger, S.-T. Yau). We will also define similar moduli spaces for even dimensional Calabi-Yau varieties, where we have the notion of Hodge locus" |
January 16, 2019, 1:30 - 3:00 pm at CMSA Building, 20 Garden St, G10 |
| CMSA TOPOLOGICAL ASPECTS OF CONDENSED MATTER SEMINAR |
Lukasz Fidkowski (UNIVERSITY OF WASHINGTON) |
Non-trivial quantum cellular automata in 3 dimensions |
Motivated by studying the entanglement structure of certain symmetry protected topological phases, we construct a non-trivial quantum cellular automaton in a Hilbert space for a 3d lattice of spin 1/2 degrees of freedom. This is an operator which takes local operators to nearby local operators, but is not locally generated. We discuss implications for the classification of SPT phases in equilibrium and Floquet settings" |
January 08, 2019, 2:00 PM at CMSA Building, 20 Garden St, G10 |
| STUDENT/POSTDOC SYMPLECTIC GEOMETRY SEMINAR |
Fenglong You (UNIVERSITY OF ALBERTA) |
Mirror theorems for orbifold and relative Gromov-Witten invariants |
Enumerative mirror symmetry can be stated as the relation between generating functions(J-functions) of Gromov--Witten invariants and period integrals(or the I-functions). Such relations are called mirror theorems. We obtained a mirror theorem for orbifold Gromov-Witten invariants of root stacks. Using the relation between relative and orbifold Gromov-Witten invariants, we also obtain a mirror theorem for relative Gromov-Witten invariants. This is joint work with Honglu Fan and Hsian-Hua Tseng" |
December 14, 2018, 2:00 - 3:15 pm at Science Center 507 |
| CMSA HODGE AND NOETHER-LEFSCHETZ LOCI SEMINAR |
Hossein Movasati (IMPA) |
A conjectural Hodge locus for cubic tenfold |
In this talk we will consider the difference of two linear algebraic cycles of dimension 5 inside a smooth cubic tenfold and such that the dimension of their intersection is 3. We will show some computer assisted evidences to the fact that the corresponding Hodge locus is bigger than the expected locus of algebraic deformations of the cubic tenfold together with its linear cycles. A similar discussion will be also presented for cubic six and eightfold, for which we will prove that the corresponding second and third order infinitesimal Hodge loci are smooth. The main ingredient is a computer implementation of power series of periods of hypersurfaces" |
December 12, 2018, 1:30 - 3:00 pm at CMSA Building, 20 Garden St, G10 |
| CMSA COLLOQUIUM |
Zhiwei Yun (MIT) |
Shtukas: what and why |
This talk is of expository nature. Drinfeld introduced the notion of Shtukas and the moduli space of them. I will review how Shtukas compare to more familiar objects in geometry, how they are used in the Langlands program, and what remains to be done about them" |
December 12, 2018, 4:30 pm at CMSA Building, 20 Garden St, G10 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Lino Amorim (KANSAS STATE) |
Mirror symmetry for an orbifold sphere |
In this talk, I will construct a Landau-Ginzburg mirror for a sphere with three orbifold points using the Lagrangian Floer theory of an immersed circle. I will then prove closed mirror symmetry for this space: more precisely I will define an isomorphism between the big quantum cohomology ring of the orbifold and the Jacobian ring of the mirror potential" |
December 11, 2018, 4:00 pm at Science Center 507 |
| CMSA TOPOLOGICAL ASPECTS OF CONDENSED MATTER SEMINAR |
Anders Sandvik (BOSTON UNIVERSITY AND INSTITUTE OF PHYSICS, CAS, BEIJING) |
Quantum Monte Carlo simulations of exotic states in 2D quantum magnets |
Some exotic ground states of 2D quantum magnets can be accessed through sign-free quantum Monte Carlo simulations of certain ``designer Hamiltonians . I will discuss recent examples within the J-Q family of models, where the standard Heisenberg exchange J on the square lattice is supplemented by multi-spin terms Q projecting correlated singlets, such that dimer (columnar valence-bond) order is favored. In addition to a possible deconfined quantum critical point separating the Neel and dimer phases, I will discuss recent work on a modified model where a rather strongly first-order transition between the Neel state and a plaquette-singlet-solid is associated with emergent O(4) symmetry up to length scales of at least 100 lattice spacings. This type of transition may be realized in SrCu2(BO3)2 under pressure. I will also discuss a random-singlet state obtained when randomness is introduced in a system with dimerized ground state. This type of state may be realized in some frustrated disordered quantum magnets" |
December 10, 2018, 10:00 - 11:30 am at CMSA Building, 20 Garden St, G02 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Fenglong You (UNIVERSITY OF ALBERTA) |
Relative and orbifold Gromov-Witten theory |
Given a smooth projective variety X and a smooth divisor D \subset X, one can study the enumerative geometry of counting curves in X with tangency conditions along D. There are two theories associated to it: relative Gromov-Witten invariants of (X,D) and orbifold Gromov-Witten invariants of the r-th root stack X_{D,r}. For sufficiently large r, Abramovich-Cadman-Wise proved that genus zero relative invariants are equal to the genus zero orbifold invariants of root stacks (with a counterexample in genus 1). We prove that higher genus orbifold Gromov-Witten invariants of X_{D,r} are polynomials in r and the constant terms are exactly higher genus relative Gromov-Witten invariants of (X,D). If time permits, I will also talk about further results in genus zero which allows us to study structures of genus zero relative Gromov-Witten theory. This is based on joint work with Hisan-Hua Tseng, Honglu Fan and Longting Wu" |
December 10, 2018, 12:00 - 1:00 pm at CMSA Building, 20 Garden St, G10 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Raphael Zentner (REGENSBURG) |
Irreducible SL(2,C)-representations of homology-3-spheres |
We prove that the splicing of any two non-trivial knots in the 3-sphere admits an irreducible SU(2)-representation of its fundamental group. This uses instanton gauge theory, and in particular a non-vanishing result of Kronheimer-Mrowka and some new results that we establish for holonomy perturbations of the ASD equation. Using a result of Boileau, Rubinstein, and Wang (which builds on the geometrization theorem of 3-manifolds), it follows that the fundamental group of any integer homology 3-sphere different from the 3-sphere admits irreducible representations of its fundamental group in SL(2,C)" |
December 07, 2018, 3:30 pm at Science Center 507 |
| STUDENT/POSTDOC SYMPLECTIC GEOMETRY SEMINAR |
Patrick Clarke (DREXEL UNIVERSITY AND CMSA) |
Homological mirror symmetry for toric Landau-Ginzburg models: dual pairs, T-duality, and curved A-infinity categories |
Three aspects of the dual-fan mirror construction for Landau-Ginzburg models make it a particularly promising framework for homological mirror symmetry: 1) the manner in which dual fans reproduce, provide insight into, and generalize familiar mirror constructions, 2) a natural T-duality that exists between dual-fan Landau-Ginzburg models and the resulting SYZ-type approach to HMS, and 3) the burgeoning homotopy theory for curved A-infinity algebras. We will describe the basic constructions in these three areas, and illustrate how they weave together to form an elegant and geometrically appealing form of homological mirror symmetry" |
December 07, 2018, 2:00 - 3:15 pm at Science Center 507 |
| CMSA SPECIAL MATHEMATICAL PHYSICS SEMINAR |
Qintao Chen () |
Recent progress of various Volume Conjectures for links as well as 3-manifolds |
The original Volume Conjecture of Kashaev-Murakami-Murakami predicts a precise relation between the asymptotics of the colored Jones polynomials of a knot in S^3 and the hyperbolic volume of its complement. I will discuss two different directions that lead to generalizations of this conjecture. The first direction concerns different quantum invariants of knots, arising from the colored SU(n) (with the colored Jones polynomial corresponding to the case n= 2). I will first display subtle relations between congruence relations, cyclotomic expansions and the original Volume Conjecture for colored Jones polynomials of knots. I will then generalize this point of view to the colored SU(n) invariant of knots. Certain congruence relations for colored SU(n) invariants, discovered in joint work with K. Liu, P. Peng and S. Zhu, lead us to formulate cyclotomic expansions and a Volume Conjecture for these colored SU(n) invariants. I will also discuss similar ideas for the superpolynomials that arise in HOMFLY-PT homology. In fact, I proposed cyclotomic expansion conjectures and Volume conjectures for superpolynomials. Another direction for generalization involves the Witten-Reshetikhin-Turaev and (modified) Turaev-Viro quantum invariants of 3-manifolds. In a joint work with T. Yang, we formulated a new Volume Conjecture for the asymptotics of these 3-manifolds invariants evaluated at certain roots of unit, and numerically checked it for many examples. Interestingly, this conjecture uses roots of unity that are different from the one usually considered in literature. This may indicate that the understanding of this new phenomenon requires new physical and geometric interpretations that go beyond the usual quantum Chern-Simons theory. I will also introduce a work on Krillov-Reshetikhin quantum 6j-symbols done by J. Murakami & me" |
December 06, 2018, 3:30 - 4:30 pm at Science Center 530 |
| THURSDAY SEMINAR |
Tomer Schlank (HEBREW UNIVERSITY OF JERUSALEM) |
Ambidexterity in localizations of spectra |
" |
December 06, 2018, 3:00 - 4:00 pm *note earlier ending time* at Science Center 507 |
| CMSA GENERAL RELATIVITY SEMINAR |
Pengzi Miao (UNIVERSITY OF MIAMI) |
Localization of the Penrose inequality and variation of quasi-local mass |
In the study of manifolds with nonnegative scalar curvature, a fundamental result is the Riemannian Positive mass theorem. If the manifold has horizon boundary, one has the Riemannian Penrose inequality. Given a compact region with boundary in these manifolds, one wants to understand how much mass or energy is localized in such a region. This question is usually referred to as the quasi-local mass problem. In this talk, we discuss an inequality on a compact manifold with nonnegative scalar curvature, which can be thought as a body surrounding horizons. Our discussion of the rigidity case of this inequality reveals an intriguing relation between two of the most important notions of quasi-local mass, the Bartnik mass and the Wang-Yau mass. The talk is based on joint work with Siyuan Lu. " |
December 05, 2018, 11:00 am - 12:00 pm at CMSA Building, 20 Garden St, G02 |
| INFORMAL GEOMETRY AND DYNAMICS SEMINAR |
Curtis McMullen (HARVARD UNIVERSITY) |
The failure of Ratnerâs theorem for moduli spaces |
" |
December 05, 2018, 4:00 pm at Science Center 530 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Omer Angel (UNIVERSITY OF BRITISH COLUMBIA) |
Balanced excited random walks |
I will present results on the scaling limit and asymptotics of the balanced excited random walk and related processes. This is a walk the that moves vertically on the first visit to a vertex, and horizontally on every subsequent visit. We also analyze certain versions of clairvoyant scheduling of random walks. Joint work with Mark Holmes and Alejandro Ramirez" |
December 05, 2018, 3:00 - 4:00 pm at CMSA Building, 20 Garden St, G02 |
| NUMBER THEORY SEMINAR |
Sol Friedberg (BOSTON COLLEGE) |
Langlands functoriality, the converse theorem, and integral representations of L-functions |
Langlands functoriality predicts maps between automorphic forms on different groups, dictated by a map of L-groups. One important class of such maps are endoscopic liftings, established by Arthur using the trace formula. In this talk I describe an approach to endoscopic lifting that does not use the trace formula. Instead it relies on the converse theorem of Cogdell and Piatetski-Shapiro and on new integral representations of L-functions of Cai, Friedberg, Ginzburg and Kaplan." |
December 05, 2018, 3:00 pm at Science Center 507 |
| CMSA COLLOQUIUM |
Robert McCann (UNIVERSITY OF TORONTO) |
Displacement convexity of Boltzmann's entropy characterizes positive energy in general relativity |
Einstein s theory of gravity is based on assuming that the fluxes of a energy and momentum in a physical system are proportional to a certain variant of the Ricci curvature tensor on a smooth 3+1 dimensional spacetime. The fact that gravity is attractive rather than repulsive is encoded in the positivity properties which this tensor is assumed to satisfy. Hawking and Penrose (1971) used this positivity of energy to give conditions under which smooth spacetimes must develop singularities. By lifting fractional powers of the Lorentz distance between points on a globally hyperbolic spacetime to probability measures on spacetime events, we show that the strong energy condition of Hawking and Penrose is equivalent to convexity of the Boltzmann-Shannon entropy along the resulting geodesics of probability measures. This new characterization of the strong energy condition on globally hyperbolic manifolds also makes sense in (non-smooth) metric measure settings, where it has the potential to provide a framework for developing a theory of gravity which admits certain singularities and can be continued beyond them. It provides a Lorentzian analog of Lott, Villani and Sturm s metric-measure theory of lower Ricci bounds, and hints at new connections linking gravity to the second law of thermodynamics. Preprint available at http://www.math.toronto.edu/mccann/papers/GRO.pdf " |
December 05, 2018, 4:30 pm at CMSA Building, 20 Garden St, G10 |
| CMSA HODGE AND NOETHER-LEFSCHETZ LOCI SEMINAR |
Hossein Movasati (IMPA) |
Some explicit Hodge cycles |
Explicit examples of Hodge cycles are due to D. Mumford and A. Weil in the case of CM abelian varieties. In this talk, I will describe few other examples for the Fermat variety. Effective verification of the Hodge conjecture for these cycles is not known" |
December 05, 2018, 1:30 - 3:00 pm at CMSA Building, 20 Garden St, G02 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Beomjun Choi (COLUMBIA UNIVERSITY) |
Evolution of Non-Compact Hypersurface By Inverse Mean Curvature |
In this talk, we give an existence theorem of the inverse mean curvature flow for convex non-compact hypersurfaces in Euclidean space. The key ingredient of the proof is an a priori estimate of the weighted speed $(H|F|)^{-1}$ which does not depend on its initial bound. The maximal time of existence is explicitly given by the area of initial tangent cone at infinity and the solution becomes flat as time approaches to it. This is a joint work with P. Daskalopoulos and I will also briefly mention the recent work with P.K. Hung where we treat the evolution of Lipschitz convex hypsersurfaces" |
December 04, 2018, 4:00 pm at Science Center 507 |
| LOGIC SEMINAR |
Tibor Beke (UNIVERSITY OF MASSACHUSETTS - LOWELL) |
Schanuel functors and the Grothendieck (semi)ring of some theories |
In a little known article, Schanuel defines a functor from semirings to idempotent semirings and a notion of dimension that is not linearly ordered. He uses it to give an elegant presentation of the Grothendieck semiring of semi-algebraic sets, from which the (much better known) structure of the Grothendieck ring of semi-algebraic sets easily follows. I will review his work and related results on the Grothendieck semiring of algebraically closed fields and similar geometric structures" |
December 03, 2018, 5:40 pm at Science Center 507 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Monica Pate (HARVARD UNIVERSITY) |
Gravitational Memory in Higher Dimensions |
A precise equivalence among Weinberg s soft graviton theorem, supertranslation conservation laws and the gravitational memory effect was previously established in theories of asymptotically flat gravity in four dimensions. Moreover, this triangle of equivalence was proposed to be a universal feature of generic theories of gauge and gravity. In theories of gravity in even dimensions greater than four, I will show that there exists a universal gravitational memory effect which is precisely equivalent to the soft graviton theorem in higher dimensions and a set of conservation laws associated to infinite-dimensional asymptotic symmetries" |
December 03, 2018, 12:00 - 1:00 pm at CMSA Building, 20 Garden St, G02 |
| CMSA TOPOLOGICAL ASPECTS OF CONDENSED MATTER SEMINAR |
Claudio Chamon (BOSTON UNIVERSITY) |
Many-body scar states with topological properties in 1D, 2D, and 3D |
We construct (some) exact excited states of a class of non-integrable quantum many-body Hamiltonians in 1D, 2D and 3D. These high energy many-body scar states have area law entanglement entropy, and display properties usually associated to gapped ground states of symmetry protected topological phases or topologically ordered phases of matter, including topological degeneracies" |
December 03, 2018, 10:00 - 11:30 am at CMSA Building, 20 Garden St, G02 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
John Pardon (PRINCETON UNIVERSITY) |
Structural results in wrapped Floer theory |
I will discuss results relating different partially wrapped Fukaya categories. These include a Kunneth formula, a stop removal result relating partially wrapped Fukaya categories relative to different stops, and a gluing formula for wrapped Fukaya categories. The techniques also lead to generation results for Weinstein manifolds and for Lefschetz fibrations. The methods are mainly geometric, and the key underlying Floer theoretic fact is an exact triangle in the Fukaya category associated to Lagrangian surgery along a short Reeb chord at infinity. This is joint work with Sheel Ganatra and Vivek Shende" |
November 30, 2018, 3:30 pm at Science Center 507 |
| STUDENT/POSTDOC SYMPLECTIC GEOMETRY SEMINAR |
Daniel Pomerleano (UNIVERSITY OF MASSACHUSETTS - BOSTON) |
Degenerations from Floer cohomology |
I will explain how, under suitable hypotheses, one can construct a flat degeneration from the symplectic cohomology of log Calabi-Yau varieties to the Stanley-Reisner ring of the dual intersection complex of a compactifying divisor and how this result relates to recent mirror constructions of Gross-Hacking-Keel and Gross-Siebert. Along the way, I will hopefully explain various techniques for understanding symplectic cohomology of affine varieties which apply beyond the log Calabi-Yau setting. Parts of this are based on joint work with Sheel Ganatra" |
November 30, 2018, 2:00 - 3:15 pm at Science Center 507 |
| THURSDAY SEMINAR |
Sanath Devalapurkar () |
Stable splittings for classifying spaces of compact Lie groups |
" |
November 29, 2018, 3:00 pm - 5:00 pm at Science Center 507 |
| LOGIC COLLOQUIUM |
Charles Parsons (HARVARD UNIVERSITY) |
Kreisel and Gödel |
We present a narrative of Georg Kreiselâs relation to Kurt Gšdel, based on their correspondence. What appears to have been their first contact was Kreiselâs application in 1955 for a yearâs membership at the Institute for Advanced Study. This was granted and extended for a second year. Then Kreisel returned to his position at the University of Reading in England. But he began a wandering life, spending time at Reading, Stanford University, the University of Paris, and the IAS. In 1964 he achieved a permanent position at Stanford, with the understanding that his presence would be less than full time. The correspondence continued until 1972. Matters discussed were developments in mathematical logic, the health of both, plans for Kreisel to visit the IAS, and the careers of some other logicians. In a letter of 1972, which ended their correspondence, Kreisel broke off the relationship" |
November 28, 2018, 3:00 - 4:00 pm at Logic Center, 2 Arrow St, Rm 420 |
| CMSA COLLOQUIUM |
Robert Haslhofer (UNIVERSITY OF TORONTO) |
Recent progress on mean curvature flow |
A family of surfaces moves by mean curvature flow if the velocity at each point is given by the mean curvature vector. Mean curvature flow is the most natural evolution in extrinsic geometry and shares many features with Hamiltonâs Ricci flow from intrinsic geometry. In the first half of the talk, I will give an overview of the well developed theory in the mean convex case, i.e. when the mean curvature vector everywhere on the surface points inwards. Mean convex mean curvature flow can be continued through all singularities either via surgery or as level set solution, with a precise structure theory for the singular set. In the second half of the talk, I will report on recent progress in the general case without any curvature assumptions. Namely, I will describe our solution of the mean convex neighborhood conjecture and the nonfattening conjecture, as well as a general classification result for all possible blowup limits near spherical or cylindrical singularities. In particular, assuming Ilmanenâs multiplicity one conjecture, we conclude that for embedded two-spheres the mean curvature flow through singularities is well-posed. This is joint work with Kyeongsu Choi and Or Hershkovits" |
November 28, 2018, 4:30 pm at CMSA Building, 20 Garden St, G10 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Sean O'Rourke () |
Universality and least singular values of random matrix products |
We consider the product of m independent iid random matrices as m is fixed and the sizes of the matrices tend to infinity. In the case when the factor matrices are drawn from the complex Ginibre ensemble, Akemann and Burda computed the limiting microscopic correlation functions. In particular, away from the origin, they showed that the limiting correlation functions do not depend on m, the number of factor matrices. We show that this behavior is universal for products of iid random matrices under a moment matching hypothesis. In addition, we establish universality results for the linear statistics for these product models, which show that the limiting variance does not depend on the number of factor matrices either. The proofs of these universality results require a near-optimal lower bound on the least singular value for these product ensembles." |
November 28, 2018, 3:00 - 4:00 pm at CMSA Building, 20 Garden St, G10 |
| CMSA HODGE AND NOETHER-LEFSCHETZ LOCI SEMINAR |
Roberto Villaflor () |
Periods of Complete Intersection Algebraic Cycles |
In order to compute periods of algebraic cycles inside even dimensional smooth degree d hypersurfaces of the projective space, we restrict ourselves to cycles supported in a complete intersection subvariety. When the description of the complete intersection is explicit, we can compute its periods, and furthermore its cohomological class. As an application, we can use this data to describe the Zariski tangent space of the corresponding Hodge locus, as the degree d part of some Artinian Gorenstein ideal of the homogeneous coordinate ring of the projective space. Using this description, we can show that for d>5, the locus of hypersurfaces containing two linear cycles, is a reduced component of the Hodge locus in the underlying parameter space" |
November 28, 2018, 1:30 - 3:00 pm at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
John Bergdall (BRYN MAWR COLLEGE) |
Upper bounds for constant slope p-adic families of modular forms |
This talk is concerned with the radius of convergence of p-adic families of modular forms --- q-series over a p-adic disc whose specialization to certain integer points is the q-expansion of a classical Hecke eigenform of level p. Numerical experiments by GouvĂȘa and Mazur in the nineties predicted the general existence of such families but also suggested, in spirit, the radius of convergence in terms of an initial member. Buzzard and Calegari showed, ten years later, that the GouvĂȘa--Mazur prediction was false. It has since remained open question how to salvage it. Here we will present some recent theoretical results towards such a salvage, backed up by numerical data." |
November 28, 2018, 3:00 pm at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Aaron Bertram (UTAH) |
Stability for Regular Coherent Sheaves |
The Gieseker slope of a coherent sheaf on projective space is the ratio: m(t) = Hilbert polynomial/Leading coefficient. This is a polynomial that is used to define an open stability condition with (quasi)-projective moduli. If, however, we consider the rational function n(t) = Hilbert polynomial/Derivative, then we get a one-parameter family of open stability conditions on sheaves (and complexes) of varying Castelnuovo-Mumford-regularity. This produces moduli that exhibit (GIT) wall-crossing and converge (conjecturally) to the moduli spaces of Gieseker-stable sheaves. This recovers, for example, the construction by Piene-Schlessinger of the Hilbert scheme of twisted cubics, as was shown by Schmidt and Xia. This is joint work with Altavilla, Mu and Petkovic" |
November 27, 2018, 3:00 pm at MIT 2-142 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Bin Guo (COLUMBIA UNIVERSITY) |
Geometric estimates for complex Monge-Ampere equations |
In the talk, we will present a recent result concerning the uniform gradient and diameter estimates for a family of geometric complex Monge-Ampere equations. Such estimates can be applied to study geometric regularity of singular solutions of complex Monge-Ampere equations. We will also discuss uniform diameter estimate for a collapsing family of twisted Kahler-Einstein metrics on Kahler manifolds of nonnegative Kodaira dimensions" |
November 27, 2018, 4:00 pm at Science Center 507 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Charles Doran (ALBERTA) |
Feynman Amplitudes from Calabi-Yau Fibrations |
After briefly reviewing the interpretation of Feynman amplitudes as periods of graph hypersurfaces, we will focus on a class of graphs called the n-loop sunset (or banana) graphs. For these graphs, the underlying geometry consists of very special families of (n-1)-dimensional Calabi-Yau hypersurfaces of degree n+1 in projective n-space. We will present a reformulation using fibrations induced from toric geometry, which implies a simple, iterative construction of the corresponding Feynman integrals to all loop orders. We will then reinterpret the mass-parameter dependence in the case of the 3-loop sunset in terms of moduli of lattice-polarized elliptic fibered K3 surfaces, and describe a method to construct their Picard-Fuchs equations. (As it turns out, the 3-loop sunset K3 surfaces are all specializations of those constructed by Clingher-Malmendier in the originally scheduled talk!) This is joint work with Andrey Novoseltsev and Pierre Vanhove" |
November 26, 2018, 12:00 - 1:00 pm at CMSA Building, 20 Garden St, G10 |
| CMSA HODGE AND NOETHER-LEFSCHETZ LOCI SEMINAR |
Hossein Movasati (IMPA) |
Periods of algebraic cycles |
The tangent space of the Hodge locus at a point can be described by the so called infinitesimal variation of Hodge structures and the cohomology class of Hodge cycles. For hypersurfaces of dimension $n$ and degree $d$ it turns out that one can describe it without any knowledge of cohomology theories and in a fashion which E. Picard in 1900âs wanted to study integrals/periods. The data of cohomology class is replaced with periods of Hodge cycles, and explicit computations of these periods, will give us a computer implementable description of the tangent space. As an application of this we show that for examples of $n$ and $d$, the locus of hypersurfaces containing two linear cycles whose intersection is of low dimension, is a reduced component of the Hodge locus in the underlying parameter space" |
November 21, 2018, 1:30 - 3:00 pm at CMSA Building, 20 Garden St, G10 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Vaughan Jones (VANDERBILT UNIVERSITY) |
A stroll around the subfactor zoo |
*note change in day and location** Intimately related to quantum field theory, both topological and conformal, subfactors come in all shapes and sizes. I will give some idea of the state of the art of the subject starting with the definition of the index dating back to 1980, up to the full list of subfactors of index less than about 5.5. A subfactor comes with a graph which may be finite or infinite and the question of which graphs appear is quite fascinating" |
November 19, 2018, 2:00 pm at CMSA Building, 20 Garden St, G10 **note change in day and location** |
| CMSA COLLOQUIUM |
Xiaoqin Wang (JOHNS HOPKINS UNIVERSITY) |
Computational Principles of Auditory Cortex |
Auditory cortex is located at the top of a hierarchical processing pathway in the brain that encodes acoustic information. This brain region is crucial for speech and music perception and vocal production. Auditory cortex has long been considered a difficult brain region to study and remained one of less understood sensory cortices. Studies have shown that neural computation in auditory cortex is highly nonlinear. In contrast to other sensory systems, the auditory system has a longer pathway between sensory receptors and the cerebral cortex. This unique organization reflects the needs of the auditory system to process time-varying and spectrally overlapping acoustic signals entering the ears from all spatial directions at any given time. Unlike visual or somatosensory cortices, auditory cortex must also process and differentiate sounds that are externally generated or self-produced (during speaking). Neural representations of acoustic information in auditory cortex are shaped by auditory feedback and vocal control signals during speaking. Our laboratory has developed a unique and highly vocal non-human primate model (the common marmoset) and quantitative tools to study neural mechanisms underlying audition and vocal communication." |
November 19, 2018, 3:00 pm *note special day and time* at CMSA Building, 20 Garden St, G10 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Yusuf Baris Kartal (MIT) |
Distinguishing symplectic fillings using dynamics of Fukaya categories |
The purpose of this talk is to produce examples of symplectic fillings that cannot be distinguished by the dynamical invariants at a geometric level, but that can be distinguished by the dynamics and deformation theory of (wrapped) Fukaya categories. More precisely, given a Weinstein domain $M$ and a compactly supported symplectomorphism $\phi$, one can produce another Weinstein domain $T_\phi$-\textbf{the open symplectic maping torus}. Its contact boundary is independent of $\phi$ and it is the same as the boundary of $T_0\times M$, where $T_0$ is the once punctured torus. We will outline a method to distinguish $T_\phi$ from $T_0\times M$. This will involve the construction of a mirror symmetry inspired algebro-geometric model related to Tate curve for the Fukaya category of $T_\phi$ and exploitation of dynamics on these models to distinguish them" |
November 19, 2018, 12:00 - 1:00 pm at CMSA Building, 20 Garden St, G10 |
| CMSA TOPOLOGICAL ASPECTS OF CONDENSED MATTER SEMINAR |
Xiao-Gang Wen (MIT) |
A classification of 3+1D topological orders |
I will discuss a classification of 3+1D topological orders in terms of fusion 2-category. The 3+1D topological orders can be divided into two classes: the ones without emergent fermions and the ones with emergent fermions. The 3+1D topological orders with emergent fermions can be further divided into two classes: the ones without emergent Majorana zero mode and the ones with emergent Majorana zero mode. I will present pictures to understand those 3+1D topological orders" |
November 19, 2018, 10:00 - 11:30 am at CMSA Building, 20 Garden St, G10 |
| BRANDEIS - HARVARD - MIT - NORTHEASTERN JOINT COLLOQUIUM |
Andrei Okounkov (COLUMBIA UNIVERSITY) |
New worlds for Lie theory |
Lie groups are one of the cornerstones of modern mathematics and mathematical physics. Throughout its history, boundaries of Lie theory have been constantly expanding to include new important structures and cover new important applications. My goal in this talk is to give a sense of what is being currently explored in the context of 3-dimensional supersymmetric QFTs, in particular, K-theoretic counting of curves in certain algebraic varieties." |
November 15, 2018, Tea at 4:00 pm, Talk at 4:30 pm at Science Center Hall A |
| NUMBER THEORY SEMINAR |
Eric Urban (COLUMBIA UNIVERSITY) |
Eisenstein congruences and Euler systems |
It is now well-known since the work of Mazur-Wiles that one can find lower bound for the size of Selmer groups by studying ordinary Eisenstein congruences. On the other hand, upper bound have been mainly obtained thanks to the use of Euler systems constructed from special units (cyclotomic, elliptic or Siegel units) or Heegner points. In this talk, I will present a general and new construction of Euler systems using Eisenstein congruences. I will stress on the key aspects of the construction and as an example, I will show that this method recovers the Euler system of cyclotomic units." |
November 14, 2018, 3:00 pm at Science Center 507 |
| CMSA GENERAL RELATIVITY SEMINAR |
Niky Kamran (MCGILL UNIVERSITY) |
Lorentzian Einstein metrics with prescribed conformal infinity |
We prove a local well-posedness theorem for the $(n+1)$-dimensional Einstein equations in Lorentzian signature, with initial data whose asymptotic geometry at infinity is similar to that anti-de Sitter (AdS) space and compatible boundary data prescribed at the time-like conformal boundary of space-time. This extends the fundamental result of Friedrich on the existence of anti-de Sitter space-times in 3+1 dimensions to arbitrary space-time dimensions, by a different approach that allows for generic smoothness and polyhomogeneity assumptions on the initial data. This is joint work with Alberto Enciso (ICMAT, Madrid)" |
November 14, 2018, 11:00 am at CMSA Building, 20 Garden St, G10 |
| CMSA HODGE AND NOETHER-LEFSCHETZ LOCI SEMINAR |
Hossein Movasati (IMPA) |
Integral Hodge conjecture for Fermat varieties |
We describe an algorithm which verifies whether linear algebraic cycles of the Fermat variety generate the lattice of Hodge cycles. A computer implementation of this confirms the integral Hodge conjecture for quartic and quintic Fermat fourfolds. Our algorithm is based on computation of the list of elementary divisors of both the lattice of linear algebraic cycles, and the lattice of Hodge cycles written in terms of vanishing cycles, and observing that these two lists are the same. This is a joint work with E. Aljovin and R. Villaflor" |
November 14, 2018, 1:30 - 3:00 pm at CMSA Building, 20 Garden St, G10 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
David Gamarnik (MIT AND HARVARD) |
Two Algorithmic Hardness Results in Spin Glasses and Compressive Sensing |
I will discuss two computational problems in the area of random combinatorial structures. The first one is the problem of computing the partition function of a Sherrington-Kirkpatrick spin glass model. While the the problem of computing the partition functions associated with arbitrary instances is known to belong to the #P complexity class, the complexity of the problem for random instances is open. We show that the problem of computing the partition function exactly (in an appropriate sense) for the case of instances involving Gaussian couplings is #P-hard on average. The proof uses Lipton s trick of computation modulo large prime number, reduction of the average case to the worst case instances, and the near uniformity of the stretched log-normal distribution. In the second part we will discuss the problem of explicit construction of matrices satisfying the Restricted Isometry Property (RIP). This challenge arises in the field of compressive sensing. While random matrices are known to satisfy the RIP with high probability, the problem of explicit (deterministic) construction of RIP matrices eluded efforts and hits the so-called square root barrier which I will discuss in the talk. Overcoming this barrier is an open problem explored widely in the literature. We essentially resolve this problem by showing that an explicit construction of RIP matrices implies an explicit construction of graphs satisfying a very strong form of Ramsey property, which has been open since the seminal work of Erdos in 1947" |
November 14, 2018, 3:00 - 4:00 pm at CMSA Building, 20 Garden St, G10 |
| CMSA COLLOQUIUM |
Dusa McDuff (COLUMBIA UNIVERSITY) |
The virtual fundamental class in symplectic geometry |
Essential to many constructions and applications of symplectic geometry is the ability to count J-holomorphic curves. The moduli spaces of such curves have well understood compactifications, and if cut out transversally are oriented manifolds of dimension equal to the index of the problem, so that they a fundamental class that can be used to count curves. In the general case, when the defining equation is not transverse, there are various different approaches to constructing a representative for this class, We will discuss and compare different approaches to such a construction e.g. using polyfolds or various kinds of finite dimensional reduction. Most of this is joint work with Katrin Wehrheim." |
November 14, 2018, 4:00 pm at CMSA Building, 20 Garden St, G10 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
William Norledge (PENN STATE) |
The adjoint braid arrangement as a free Lie algebra in species via the Steinmann relations |
We describe a discrete derivative of piecewise constant functions on the adjoint braid arrangement with respect to binary layered trees. We show that this derivative is the cobracket of a Lie coalgebra internal to the category of linear species precisely when one restricts to functions which satisfy the so-called Steinmann relations. We prove that this restriction coincides with the span of characteristic functions of permutohedral cones, and that the kernel of the cobracket is spanned by characteristic functions of complete fans over systems of affine roots. This is joint work with Zhengwei Liu and Adrian Ocneanu." |
November 13, 2018, 4:00 pm at Jefferson 356 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Siyuan Lu (RUTGERS UNIVERSITY) |
On a localized Riemannian Penrose inequality |
For a bounded manifold with nonnegative scalar curvature, the Brown-York quasi-local mass is nonnegative and equals to 0 iff it s a domain in Euclidean space by fundamental results of Shi and Tam. Moreover, it is shown that the inequality is equivalent to Positive mass theorem. We consider the general setting that the bounded manifold allows a horizon. We establish a localized Riemannian Penrose inequality and prove that the equality holds iff it s a domain in Schwarzschild manifold. Similar to the Shi-Tam case, the inequality is equivalent to Riemannian Penrose inequality. This is based on joint works with P. Miao" |
November 13, 2018, 4:00 pm at Science Center 507 |
| LOGIC SEMINAR |
Rehana Patel (HARVARD UNIVERSITY) |
Around Cherlin's question on countable universal $H$-free graphs |
A longstanding open problem of Cherlin asks: Is there an algorithm that decides, given as input a finite connected constraint graph H, whether there exists a countable universal H-free graph? I will describe what is known about this decision problem, including old and new results, and discuss some further model-theoretic questions generated by these results" |
November 12, 2018, 5:40 pm at Science Center 507 |
| OPEN NEIGHBORHOOD SEMINAR |
Laure Flapan (NORTHEASTERN UNIVERSITY) |
The Luroth problem: algebraic curves, field extensions, and beyond |
The Luroth theorem describes when a complex algebraic curve, meaning a real surface given by polynomial equations, is topologically a sphere. In this talk we will discuss how this problem may be translated into a seemingly completely different problem about algebra. In this talk weâll discuss the proof of theorem, some generalizations to higher dimensions, and some related long-standing open questions in algebraic geometry. (This talk will be accessible to members of the department at all levels, including undergraduates." |
November 12, 2018, 4:30 pm at Science Center 507 |
| SPECIAL DIFFERENTIAL GEOMETRY SEMINAR |
Simon Donaldson (STONY BROOK UNIVERSITY) |
Multi-valued harmonic functions and Nash-Moser theory |
In this lecture we will consider a model problem involving branched, or 2-valued, harmonic functions on a Riemannian manifold, with branch set a codimension 2 submanifold. The problem is to deform the branch set to remove the leading term in the asymptotic expansion of the function. This can be seen as a variant of a free boundary-value problem and leads to an interesting pseudo-differential operator on the branch set. We will spend some time to explain motivations for this model problem from the adiabatic limit of $G_{2}$ structures with K3 fibrations and from other questions in differential geometry, including connections with work of Taubes, Takahashi, Walpuski , Haydys and Doan. We will explain how an extension by Hamilton and Zehnder of the Nash-Moser implicit function theorem can be applied to study the model problem" |
November 09, 2018, 2:00 pm at Science Center 507 |
| CMSA SPECIAL SEMINAR |
Nima Arkani-Hamed (INSTITUTE FOR ADVANCED STUDY) |
Spacetime, Quantum Mechanics and Positive Geometry |
Spacetime and Quantum Mechanics form the pillars of our understanding of modern physics, but there are several indications that these concepts are approximate and must emerge from deeper principles, undoubtedly involving new mathematics. In this talk I will describe some emerging ideas along these lines, and present a new formulation of some very basic physics-- fundamental to particle scattering and to cosmology--not following from quantum evolution in space-time, but associated with simple new mathematical structures in positive geometry. In these examples we can concretely see how the usual rules of space-time and quantum mechanics can arise, joined at the hip, from primitive geometric and combinatorial origins" |
November 09, 2018, 12:00 - 1:30 pm at Science Center 507 |
| CMSA SPECIAL SEMINAR |
Yang-Hui He (UNIVERSITY OF OXFORD) |
Deep-learning the Landscape |
We propose a paradigm to deep-learn the ever-expanding databases which have emerged in mathematical physics and particle phenomenology, as diverse as the statistics of string vacua or combinatorial and algebraic geometry. As concrete examples, we establish multi-layer neural networks as both classifiers and predictors and train them with a host of available data ranging from Calabi-Yau manifolds and vector bundles, to quiver representations for gauge theories. We find that even a relatively simple neural network can achieve astounding accuracy in a matter of minutes. This paradigm should prove useful in various investigations in landscapes in physics as well as pure mathematics" |
November 09, 2018, 10:30 am - 12:00 pm at Science Center 530 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Xun Gao (HARVARD AND MAX PLANCK INSTITUTE) |
Pictorial language in quantum computation |
Quantum circuits are a standard and powerful tool to describe the process of quantum computation. It is important to simplify or to simulate quantum circuits classically. Here we report the recent progress on the representation of a quantum circuit using the pictorial language called quon. This gives a new way to understand topological complexity in quantum computing" |
November 09, 2018, 3:30 pm at Jefferson 256 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Mohammed Abouzaid (COLUMBIA UNIVERSITY) |
A formalism for Floer theory with coefficients |
I will discuss a formalism for defining (Lagrangian) Floer homology with coefficients which is a little more abstract than has been used so far in the literature, and is designed to generalise a recent construction of Rezchikov, in the exact setting, to the case of Lagrangians which may bound holomorphic discs. Various parts of this talk will report on joint work with Pardon, and with Blumberg and Kragh. Future schedule is found here: https://scholar.harvard.edu/gerig/semina" |
November 09, 2018, 3:30 pm at Science Center 507 |
| BRANDEIS - HARVARD - MIT - NORTHEASTERN JOINT COLLOQUIUM |
Steven Gubser (PRINCETON UNIVERSITY) |
Number theory and spacetime |
Our description of spacetime relies on the real numbers and hence is wedded to arbitrarily small intervals of length and time. But quantum theory hints at the existence of a smallest possible length, the Planck length. Number theory provides an alternative to the real numbers known as the p-adic numbers. Recent work has argued that quantum field theory defined over the p-adic numbers is holographically dual to a discrete spacetime. Constructions related to p-adic numbers also have a surprisingly prominent role in the early development of the renormalization group. I will explain what the p-adic numbers are and provide some intuition for what they are good for in string theory and beyond. The ultimate aim of using them to understand quantum gravity is ambitious indeed, but I will explain some first steps that give hope for the future" |
November 08, 2018, Tea at 4:00 pm, Talk at 4:30 pm at Tea: 100 Goldsmith; Talk: 317 Goldsmith |
| THURSDAY SEMINAR |
Jeremy Hahn (HARVARD UNIVERSITY) |
The construction of BO/I_n |
" |
November 08, 2018, 3:00 pm - 5:00 pm at Science Center 507 |
| CMSA GENERAL RELATIVITY SEMINAR |
Jordan Keller (HARVARD UNIVERSITY) |
Linear Stability of Higher Dimensional Schwarzschild Black Holes |
The Schwarzschild-Tangherlini black holes are higher-dimensional generalizations of the Schwarzschild spacetimes, comprising a static, spherically symmetric family of black hole solutions to higher-dimensional vacuum gravity. The physical relevance of such solutions is intimately related to their stability under gravitational perturbations. This talk will address results on the linear stability of the Schwarzschild-Tangherlini black holes, part of ongoing joint work with Pei-Ken Hung and Mu-Tao Wang" |
November 07, 2018, 11:00 am at CMSA Building, 20 Garden St, G10 |
| INFORMAL GEOMETRY AND DYNAMICS SEMINAR |
Curtis McMullen (HARVARD UNIVERSITY) |
A Panorama of Teichmueller Curves |
" |
November 07, 2018, 4:00 pm at Science Center 530 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Wilhelm Schlag (YALE UNIVERSITY) |
On the Bourgain-Dyatlov fractal uncertainty principle |
We will present the Bourgain-Dyatlov theorem on the line, it s connection with other uncertainty principles in harmonic analysis, and my recent partial progress with Rui Han on the problem of higher dimensions." |
November 07, 2018, 3:00 - 4:00 pm at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Florian Herzig (UNIVERSITY OF TORONTO) |
Ordinary representations and locally analytic vectors for GL_n(Q_p) |
Suppose that rho is an irreducible automorphic n-dimensional global p-adic Galois representation that is upper-triangular locally at p. In previous work with Breuil we constructed a unitary representation of GL_n(Q_p) on a p-adic Banach space (depending only on rho locally at p) that is an extension of finitely many principal series, and we conjectured that this representation occurs globally in a space of p-adic automorphic forms cut out by rho. Together with C. Breuil we prove many new cases of this conjecture, assuming that rho is moreover crystalline. If time permits, I ll also discuss how we can construct certain amalgams inside the locally analytic vectors cut out by rho (even when rho is not ordinary)." |
November 07, 2018, 3:00 pm at Science Center 507 |
| CMSA SPECIAL LECTURE SERIES |
Hossein Movasati (IMPA) |
Hodge and Noether-Lefschetz Loci Seminar |
Wednesdays, November 17, 2018 through January 30, 2019.Hodge cycles are topological cycles which are conjecturally (the millennium Hodge conjecture) supported in algebraic cycles of a given smooth projective complex manifold. Their study in families leads to the notion of Hodge locus, which is also known as Noether-Lefschetz locus in the case of surfaces. The main aim of this mini course is to introduce a computational approach to the study of Hodge loci for hypersurfaces and near the Fermat hypersurface. This will ultimately lead to the verification of the variational Hodge conjecture for explicit examples of algebraic cycles inside hypersurfaces and also the verification of integral Hodge conjecture for examples of Fermat hypersurfaces. Both applications highly depend on computer calculations of rank of huge matrices. We also aim to review some classical results on this topic, such as Cattani-Deligne-Kaplan theorem on the algebraicity of the components of the hodge loci, Deligneâs absolute Hodge cycle theorem for abelian varieties etc. In the theoretical side another aim is to use the available tools in algebraic geometry and construct the moduli space of projective varieties enhanced with elements in their algebraic de Rham cohomology ring. These kind of moduli spaces have been useful in mathematical physics in order to describe the generating function of higher genus Gromov-Witten invariants, and it turns out that the Hodge loci in such moduli spaces are well-behaved, for instance, they are algebraic leaves of certain holomorphic foliations. Such foliations are constructed from the underlying Gauss-Manin connection. This lectures series involves many reading activities on related topics, and contributions by participants are most welcome" |
November 07, 2018, 1:30 - 3:00 pm at CMSA Building, 20 Garden St, G10 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Alex Perry (COLUMBIA UNIVERSITY) |
Stability conditions and cubic fourfolds |
Kuznetsov showed the derived category of a cubic fourfold contains a special subcategory which can be thought of as a noncommutative K3 surface. The goal of this talk is to describe the structure of moduli spaces of Bridgeland stable objects on this noncommuative K3 surface, together with several applications. This is joint work with Bayer, Lahoz, Macri, Nuer, and Stellari" |
November 06, 2018, 3:00 pm at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Pengfei Guan (MCGILL UNIVERSITY) |
Interior curvature estimates for immersed hypersurfaces in R^{n+1} |
We discuss pure interior curvature estimates for immersed hypersurface in R^{n+1} with positive scalar curvature. The result is an extension of Heintz s classical estimate for immersed surfaces with positive Gauss curvature in R^3. In the case in n=2, this type of curvature estimate is a consequence of interior estimate for Monge-Ampere equation in dimension 2. Such interior estimate is false if n>2 by counter-examples of Pogorelov. It is also false for convex solutions of k-mean curvature equations when k>2 in general. We will present a recent result jointly with Guohuan Qiu, interior curvature estimate for immersed hypersurfaces by maximum principle directly. The argument also yields interior curvature estimate for convex solutions of prescribing scalar curvature equation in any dimension" |
November 06, 2018, 4:00 pm at Science Center 507 |
| CMSA MATH PHYSICS SEMINAR |
Siqi He (SIMONS CENTER) |
The Kapustin-Witten Equations, Opers and Khovanov Homology |
We will discuss a Witten s gauge theory program to define Jones polynomial and Khovanov homology for knots inside of general 3-manifolds by counting singular solutions to the Kapustin-Witten or Haydys-Witten equations. We will prove that the dimension reduction of the solutions moduli space to the Kapustin-Witten equations can be identified with Beilinson-Drinfeld Opers moduli space. We will also discuss the relationship between the Opers and a symplectic geometry approach to define the Khovanov homology for 3-manifolds. This is joint work with Rafe Mazzeo" |
November 05, 2018, 12:00 - 1:00 PM at CMSA Building, 20 Garden St, G10 |
| LOGIC SEMINAR |
Gabriel Goldberg (HARVARD UNIVERSITY) |
Descending sequences in the Mitchell order |
The axiom I2 is a large cardinal axiom just short of the Kunen inconsistency which implies that the (generalized) Mitchell order is illfounded. We will sketch a proof of a conjecture of Steel that constrains how illfoundedness can occur" |
November 05, 2018, 5:40 pm at Science Center 507 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Laure Flapan (NORTHEASTERN UNIVERSITY) |
Monodromy of Kodaira fibrations |
A long-standing question in studying the topology of complex algebraic varieties is the question of what groups can occur as the fundamental group of a smooth projective variety. One approximation of this question in the case of fibered varieties is to ask what groups can occur as the monodromy group of such a fibration. We use Hodge theory to investigate this question in the case of fibered algebraic surfaces, called Kodaira fibrations, whose fibers are all smooth and draw connections with questions about Shimura varieties and the moduli space of smooth algebraic curves. Future schedule is found here: https://scholar.harvard.edu/gerig/semina" |
November 02, 2018, 3:30 pm at Science Center 507 |
| STUDENT/POSTDOC SYMPLECTIC GEOMETRY SEMINAR |
Jingyu Zhao (HARVARD CMSA) |
A connection on symplectic cohomology |
The recent work by P. Seidel (arXiv:1608.04012) defines a connection on symplectic cohomology of Lefschetz fibrations. When the Kodaira-Spencer class of the mirror family vanishes, one can derive a second order ODE from the enumerative geometry of certain Borman-Sheridan classes defined in symplectic cohomology. In this talk, I will explain this construction and its analogue on S^1-equivariant symplectic cohomology if time permits" |
November 02, 2018, 2:00 - 3:15 pm at Science Center 507 |
| THURSDAY SEMINAR |
Robert Burklund (MIT) |
Properties of Brown-Gitler spectra |
" |
November 01, 2018, 3:00 pm - 5:00 pm at Science Center 507 |
| NUMBER THEORY SEMINAR |
Chris Skinner (PRINCETON) |
Some recent results on Euler systems |
Euler systems remain one of the best tools for relating Selmer groups to L-values and especially for making progress on special value formulas, at least whenever a related Euler system exists. In this talk we describe some recent work on Euler systems, which includes some new results in the anticyclotomic setting as well as some new constructions of Euler systems in the cyclotomic setting" |
October 31, 2018, 3:00 pm at Science Center 507 |
| INFORMAL GEOMETRY AND DYNAMICS SEMINAR |
Ronen Mukamel (RICE UNIVERSITY) |
Teichmueller curves: Theory and exploration |
We will discuss the remarkable phenomena of totally geodesic curves V = H/\Gamma in M_g, and the challenge of explicitly determining the lattice Gamma in SL_2(R)" |
October 31, 2018, 4:00 pm at Science Center 530 |
| CMSA GENERAL RELATIVITY SEMINAR |
Alex Lupsasca (HARVARD UNIVERSITY) |
Polarization Whorls from M87 at the Event Horizon Telescope |
The Event Horizon Telescope (EHT) is expected to soon produce polarimetric images of the supermassive black hole at the center of the neighboring galaxy M87. This black hole is believed to be very rapidly spinning, within 2% of extremality. General relativity predicts that such a high-spin black hole has an emergent conformal symmetry near its event horizon. In this talk, I will briefly review this symmetry and use it to derive an analytic prediction for the polarized near-horizon emissions to be seen at the EHT. The resulting pattern is very distinctive and consists of whorls aligned with the spin" |
October 31, 2018, 11:00 am at CMSA Building, 20 Garden St, G10 |
| CMSA COLLOQUIUM |
Moon Duchin (TUFTS) |
Exploring the (massive) space of graph partitions |
The problem of electoral redistricting can be set up as a search of the space of partitions of a graph (representing the units of a state or other jurisdiction) subject to constraints (state and federal rules about the properties of districts). I ll survey the problem and some approaches to studying it, with an emphasis on the deep mathematical questions it raises, from combinatorial enumeration to discrete differential geometry to dynamics" |
October 31, 2018, 4:30 PM- 5:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Lauren Williams (HARVARD UNIVERSITY) |
Introduction to the asymmetric simple exclusion process (from a combinatorialist's point of view) |
The asymmetric simple exclusion process (ASEP) is a model of particles hopping on a one-dimensional lattice, subject to the condition that there is at most one particle per site. This model was introduced in 1970 by biologists (as a model for translation in protein synthesis) but has since been shown to display a rich mathematical structure. There are many variants of the model -- e.g. the lattice could be a ring, or a line with open boundaries. One can also allow multiple species of particles with different weights. I will explain how one can give combinatorial formulas for the stationary distribution using various kinds of tableaux. I will also explain how the ASEP is related to interesting families of orthogonal polynomials, including Askey-Wilson polynomials, Koornwinder polynomials, and Macdonald polynomials" |
October 30, 2018, 10:30 am at Science Center 507 -*note special day, time & location* |
| DIFFERENTIAL GEOMETRY SEMINAR |
Sebastien Picard (HARVARD UNIVERSITY) |
Anomaly Flows and Calabi-Yau Manifolds with Torsion |
We will describe recent results on the Anomaly flow, which is a geometric flow on complex manifolds with trivial canonical bundle which admit balanced metrics. The Anomaly flow is inspired by the Hull-Strominger system of theoretical physics. We hope to use this flow to study the underlying geometry of these non-Kahler Calabi-Yau manifolds. This is joint work with D.H. Phong and X.-W. Zhang" |
October 30, 2018, 4:00 pm at Science Center 507 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Chunlan Jiang (HEBEI NORMAL UNIVERSITY) |
Similarity Invariants of Geometric Operators |
In 1978, I.M.Cowen and R.G .Douglas introduced a class of geometric operators in a Grassmann manifold. In their influential paper they give a unitary invariant involving geometric ideas, such as curvature, that completely classifies these operators. At the same time, they ask: Can one use geometric ideas to characterize completely the similarity invariants of geometric operators? We give a partial answer to this question. We show that the curvature and second fundamental form completely characterize the similarity invariants for a norm dense class of all geometric operators" |
October 30, 2018, 4:00 pm at Jefferson 453 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Francois Greer (SIMONS CENTER) |
Rigid Varieties with Lagrangian Spheres |
Let X be a smooth complex projective variety with its induced Kahler structure. If X admits an algebraic degeneration to a nodal variety, then X contains a Lagrangian sphere as the vanishing cycle. Donaldson asked whether the converse holds. We answer this question in the negative by constructing rigid complex threefolds with Lagrangian spheres using Teichmuller curves in genus 2" |
October 29, 2018, 12:00 - 1:00 pm at CMSA Building, 20 Garden St, G10 |
| CMSA TOPOLOGICAL ASPECTS OF CONDENSED MATTER SEMINAR |
Dominic Williamson (YALE UNIVERSITY) |
Symmetry and topological order in tensor networks |
I will present an overview of how topological states of matter with global symmetries can be described using tensor networks. First reviewing the classification of 1D symmetry-protected topological phases with matrix product states, before moving on to the description of 2D symmetry-enriched topological phases with projected-entangled pair states" |
October 29, 2018, 10:00 am at CMSA Building, 20 Garden St, G10 |
| LOGIC SEMINAR |
Doug Blue (HARVARD UNIVERSITY) |
Sacks' embedding problem |
Sacks (1963) conjectured that in ZFC the Turing degrees are universal in the sense that any locally countable partial order of size at most continuum is isomorphic to a subordering of the degrees. This conjecture remains unresolved. Sacks proved it assuming CH, but his method depends on maximal independent sets of degrees being of size continuum. Groszek and Slaman showed that this is independent, indicating the need for a new method. We will review these results and sketch a proof that the arithmetic degrees are universal for continuum sized, locally countable partial orders" |
October 29, 2018, 5:40 pm at Science Center 507 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Michael Hutchings (UC BERKELEY) |
Equivariant symplectic capacities |
We define a sequence of symplectic capacities using positive S^1-equivariant symplectic homology. These capacities are conjecturally equal to the Ekeland-Hofer capacities. However they satisfy axioms which allow them to be computed for many examples, such as convex toric domains. They also give sharp obstructions to symplectic embeddings of cubes into convex toric domains. The asymptotics of these capacities are conjecturally related to Lagrangian embeddings. This is a joint work with Jean Gutt. Future schedule is found here: https://scholar.harvard.edu/gerig/semina" |
October 26, 2018, 3:30 pm at Science Center 507 |
| STUDENT/POSTDOC SYMPLECTIC GEOMETRY SEMINAR |
**Canceled** Patrick Clarke (DREXEL UNIVERSITY AND CMSA) |
**Canceled** Homological mirror symmetry for toric Landau-Ginzburg models: dual pairs, T-duality, and curved A-infinity categories |
**Canceled**Three aspects of the dual-fan mirror construction for Landau-Ginzburg models make it a particularly promising framework for homological mirror symmetry: 1) the manner in which dual fans reproduce, provide insight into, and generalize familiar mirror constructions, 2) a natural T-duality that exists between dual-fan Landau-Ginzburg models and the resulting SYZ-type approach to HMS, and 3) the burgeoning homotopy theory for curved A-infinity algebras. We will describe the basic constructions in these three areas, and illustrate how they weave together to form an elegant and geometrically appealing form of homological mirror symmetry" |
October 26, 2018, 2:00 - 3:15 pm at Science Center 507 |
| CMSA SPECIAL SEMINAR |
John Loftin (RUTGERS UNIVERSITY) |
Equivariant minimal surfaces in real hyperbolic 3- and 4-spaces |
We use Higgs bundle techniques to describe the moduli space of equivariant minimal surfaces into hyperbolic 3 and 4 space, in terms of the data of a holomorphic bundle over Teichmuller space. To be more specific, consider a closed oriented surface $\Sigma$ of genus at least 2, and a pair $(\rho,f)$ of a representation $\rho$ of $\pi_1\Sigma$ into the group of hyperbolic isometries, and a minimal immersion $f$ from the universal cover to the hyperbolic space which is equivariant with respect to $\rho$. As the minimal immersion can be considered an equivariant harmonic map, we may use the nonlinear Hodge correspondence of Donaldson, Corlette, Hitchin and Simpson to describe such pairs in terms of holomorphic data (stable Higgs bundles) over a Riemann surface structure on $\Sigma$. We describe the moduli space in terms of holomorphic bundles over Teichm\uller space. " |
October 26, 2018, 1:30 pm at CMSA Building, 20 Garden St, G10 |
| CMSA SOCIAL SCIENCE APPLICATIONS FORUM SPECIAL EDITION |
Daniel Marszalec (UNIVERSITY OF TOKYO) |
Auctions for complements: theories vs experiments |
We evaluate four auctions for complements in an experimental setting with one global and two local bidders. Using between-subject design, we also vary the degree of correlation between local biddersâ values. The experiment covers two standard auctions (Vickrey and fist-price), and two sealed-bid core-selecting designs (Nearest-Bid and Reference Rule). At the auction level, we find the first-price auction revenue-dominant, and most efficient, across for all correlation parameters. At the bidder level, Bayesian-Nash predictions are rejected, and bidders do not account for the effects of correlation. Furthermore, under full correlation, bidders are also not best-responding to their expectations of their rivalsâ play. Though a small degree of free-riding is observed between local bidders in the first-price auction, we reject level-K type bounded rationality as likely explanation of bidder behaviour. Using numerically calculated best-response functions, we propose risk aversion as the best fit to the data, which can also explain the strong performance of the first-price auction. Joint work with Alexander Levkun (UCSD) and Alex Teytelboym (University of Oxford" |
October 26, 2018, 3:00 pm at CMSA Building, 20 Garden St, G02 |
| THURSDAY SEMINAR |
Ben Knudsen (HARVARD UNIVERSITY) |
Braid groups and braid Thom spectra |
" |
October 25, 2018, 3:00 pm - 5:00 pm at Science Center 507 |
| BRANDEIS - HARVARD - MIT - NORTHEASTERN JOINT COLLOQUIUM |
Gabor Szekelyhidi (UNIVERSITY OF NOTRE DAME) |
Gromov-Hausdorff limits of Kahler manifolds |
Through the work of Cheeger, Colding, Naber and others we have a deep understanding of the structure of Gromov-Hausdorff limits of Riemannian manifolds with Ricci curvature lower bounds. For polarized Kahler manifolds, this was taken further by Donaldson-Sun, who showed that under two-sided Ricci curvature bounds, non-collapsed limit spaces are projective varieties, leading to major progress in Kahler geometry. I will discuss joint work with Gang Liu giving an extension of this result to the case when the Ricci curvature is only bounded from below." |
October 25, 2018, Tea at 4:00 pm, Talk at 4:30 pm at Science Center Hall A |
| HARVARD-MIT COMBINATORICS SEMINAR |
Bernd Sturmfels (MPI LEIPZIG AND UC BERKELEY) |
Moment varieties of measures on polytopes |
The uniform probability measure on a convex polytope induces piecewise polynomial densities on the projections of that polytope. For a fixed combinatorial type, the moments of these measures are rational functions in the vertex coordinates. We study projective varieties that are parametrized by such rational functions, with focus on the ideals defining these moment varieties. Special cases include Hankel determinantal ideals for polytopal splines, and relations among multisymmetric functions given by cumulants of a simplex. In general, our moment varieties are quite complicated, and they offer nice challenges, also for combinatorialists. This is joint work with Kathlen Kohn and Boris Shapiro" |
October 24, 2018, 4:15 - 5:15 pm at Science Center Hall E |
| NUMBER THEORY SEMINAR |
Wei Ho (UNIVERSITY OF MICHIGAN) |
Integral points on elliptic curves |
We show that the second moment for the number of integral points on elliptic curves over Q is bounded. The main new ingredient in our proof is an upper bound on the number of integral points on an affine integral Weierstrass model of an elliptic curve depending only on the rank of the curve and the square divisors of the discriminant. We obtain the bound by studying a bijection first observed by Mordell between integral points on these curves and certain types of binary quartic forms. The results on moments then follow from Holderâs inequality, analytic techniques, and results on bounds on the average sizes of Selmer groups in the families. This is joint work with Levent Alpoge" |
October 24, 2018, 3:00 pm at Science Center 507 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Tselil Schramm (HARVARD UNIVERSITY AND MIT) |
(Nearly) Efficient Algorithms for the Graph Matching Problem in Correlated Random Graphs |
The Graph Matching problem is a robust version of the Graph Isomorphism problem: given two not-necessarily-isomorphic graphs, the goal is to find a permutation of the vertices which maximizes the number of common edges. We study a popular average-case variant; we deviate from the common heuristic strategy and give the first quasi-polynomial time algorithm, where previously only sub-exponential time algorithms were known. Based on joint work with Boaz Barak, Chi-Ning Chou, Zhixian Lei, and Yueqi Sheng" |
October 24, 2018, 3:00 - 4:00 pm at CMSA Building, 20 Garden St, G02 *note different location* |
| LOGIC COLLOQUIUM |
Sam Buss (UC SAN DIEGO) |
Bounded Arithmetic, Expanders, and Monotone Propositional Proofs |
This talk discusses a new combinatorial proof of the existence of expander graphs, which can be carried out in the bounded arithmetic theory VNC1 corresponding to alternating linear time. As an application, we prove that the monotone propositional sequent calculus polynomially simulates the full propositional sequent calculus. Prior to this, only a quasipolynomial simulation was known. Joint work with Valentine Kabanets, Antonina Kolokolova, and Michal Koucky" |
October 24, 2018, 3:00 - 4:00 pm at Logic Center, 2 Arrow St, Rm 420 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Tim Magee (INSTITUTO DE MATHEMĂĄTICAS, UNAM) |
Toric degenerations of cluster varieties |
Cluster varieties are a particularly nice class of log Calabi-Yau varieties-- the non-compact analogue of usual Calabi-Yaus. They come in pairs (A,X), with A and X built from dual tori. The punchline of this talk will be that compactified cluster varieties are a natural progression from toric varieties. Essentially all features of toric geometry generalize to this setting in some form, and the objects studied remain simple enough to get a hold of and do calculations. And examples are abundant, with many applications in representation theory and TeichmĂŒller theory. Compactifications of A and their toric degenerations were studied extensively by Gross, Hacking, Keel, and Kontsevich. These compactifications generalize the polytope construction of toric varieties-- a construction which is recovered in the central fiber of the degeneration. Compactifications of X were introduced by Fock and Goncharov and generalize the fan construction of toric varieties. Recently, Lara Bossinger, Juan Bosco FrĂas Medina, Alfredo NĂĄjera ChĂĄvez, and I introduced the notion of an X-variety with coefficients, expanded upon the notion of compactified X-varieties, and for each torus in the atlas gave a toric degeneration where each fiber is a compactified X-variety with coefficients. We showed that these fibers are stratified, and each stratum is a union of compactified X-varieties with coefficients. In the central fiber, we recover the toric variety associated to the fan in question, and we show that strata of the fibers degenerate to toric strata. This talk is based on arXiv:1809.08369 [math.AG]" |
October 23, 2018, 3:00 pm at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Mark Stern (DUKE UNIVERSITY) |
Monotonicity and Betti Number Bounds |
In this talk I will discuss the application of techniques initially developed to study singularities of Yang Mill s fields and harmonic maps to obtain Betti number bounds, especially for negatively curved manifolds" |
October 23, 2018, 4:00 pm at Science Center 507 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Shamil Shakirov (HARVARD UNIVERSITY) |
Rational integrable systems associated with higher genus surfaces |
We construct some systems of commuting difference operators associated with higher genus surfaces" |
October 23, 2018, 4:00 pm at Jefferson 356 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Sze Ning Mak (Hazel) (BROWN UNIVERSITY) |
Tetrahedral geometry in holoraumy spaces of 4D, $\mathcal{N}=1$ and $\mathcal{N}=2$ minimal supermultiplets |
In this talk, I will review the supersymmetry algebra. For Lie algebras, the concepts of weights and roots play an important role in the classification of representations. The lack of linear eigen-equations in supersymmetry leads to the failure to realize the Jordan-Chevalley decomposition of ordinary Lie algebras on the supersymmetry algebra. Therefore, we introduce the concept holoraumy for the 4D, $\mathcal{N}$-extended supersymmetry algebras, which allows us to explore the possible representations of supersymmetric systems of a specified size. The coefficients of the holoraumy tensors for different representations of the same size form a lattice space. For 4D, $\mathcal{N}=1$ minimal supermultiplets (4 bosons + 4 fermions), a tetrahedron is found in a 3D subspace of the 4D lattice parameter space. For 4D, $\mathcal{N}=2$ minimal supermultiplets (8 bosons + 8 fermions), 4 tetrahedrons are found in 4 different 3D subspaces of a 16D lattice parameter space" |
October 22, 2018, 12:00 - 1:00 pm at CMSA Building, 20 Garden St, G02 |
| CMSA TOPOLOGICAL ASPECTS OF CONDENSED MATTER SEMINAR |
Yin-Chen He (PERIMETER INSTITUTE) |
Emergent QED3 and QCD3 in condensed matter system |
QED3-Chern-Simons and QCD3-Chern-Simons theories are interesting critical theories in the 2+1 dimension. These theories are described by gapless Dirac fermions interacting with dynamical gauge fields (U(1), SU(N), U(N), etc.) with a possible Chern-Simon term. These theories have fundamental importance as it will flow to the 3D conformal field theories and have interesting dualities in the infrared. Various of condensed matter system are described by these critical theories. I will introduce several examples including the Dirac spin liquid in the frustrated magnets (kagome, triangular lattice), quantum phase transitions in the fractional quantum Hall systems and Kitaev materials." |
October 22, 2018, 10:00 - 11:30 am at CMSA Building, 20 Garden St, G02 |
| CMSA MIRROR SYMMETRY SEMINAR |
Jingyu Zhao (CMSA) |
Big quantum period theorem for the bulk-deformed potentials of toric surfaces |
In this talk, we provide an inductive algorithm to compute the bulk-deformed potentials for toric Fano surfaces via wall-crossing. This recovers the work of M. Gross in the case of P^2. We also prove a big quantum period theorem which relates descendant Gromov-Witten invariants with the oscillatory integrals of their Landau-Ginzburg mirrors" |
October 19, 2018, 11:00 am - 12:00 pm at Science Center 530 |
| HARVARD-MIT COMBINATORICS SEMINAR |
Bruno Benedetti (UNIVERSITY OF MIAMI) |
Local constructions of manifolds |
Starting with a tree of tetrahedra, suppose that you are allowed to recursively glue together two boundary triangles that have nonempty intersection. You may perform this type of move as many times you want. Let us call Mogami manifolds the triangulated 3-manifolds (with or without boundary) that can be obtained this way. Mogami, a quantum physicist, conjectured in 1995 that all triangulated 3-balls are Mogami. This conjecture implies an important one in discrete quantum gravity (namely, that there are exponentially many triangulations of the 3-ball.) Using a topological trick, we show that Mogami s conjecture is false" |
October 19, 2018, 4:15 - 5:15 pm at MIT 2-147 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Aleksander Doan (STONY BROOK UNIVERSITY) |
Harmonic Z/2 spinors and wall-crossing in Seiberg-Witten theory |
The notion of a harmonic Z/2 spinor was introduced by Taubes as an abstraction of various limiting objects appearing in compactifications of gauge-theoretic moduli spaces. I will explain this notion and discuss an existence result for harmonic Z/2 spinors on three-manifolds. The proof uses a wall-crossing formula for solutions of generalized Seiberg-Witten equations in dimension three, a result itself motivated by Yang-Mills theory on Riemannian manifolds with special holonomy G_2. The talk is based on joint work with Thomas Walpuski. Future schedule is found here: https://scholar.harvard.edu/gerig/semina" |
October 19, 2018, 3:30 pm at Science Center 507 |
| STUDENT/POSTDOC SYMPLECTIC GEOMETRY SEMINAR |
Yu-Wei Fan (HARVARD UNIVERSITY) |
Bridgeland stability conditions and mirror symmetry |
We will introduce the notion of Bridgeland stability conditions, and discuss conjectural descriptions of stability conditions on Fukaya category and derived category of coherent sheaves. If time permits, we will also discuss the space of stability conditions on quiver/local Calabi-Yau category, and some geometric properties on the space" |
October 19, 2018, 2:00 - 3:15 pm at Science Center 507 |
| THURSDAY SEMINAR |
Daniel Ălvarez-Gavela (INSTITUTE FOR ADVANCED STUDY) |
Smale-Hirsch inmersion theory via holonomic approximation |
" |
October 18, 2018, 3:00 pm - 5:00 pm at Science Center 507 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Thomas Chen (UNIVERSITY OF TEXAS AT AUSTIN) |
Dynamics of a heavy quantum tracer particle in a Bose gas |
We consider the dynamics of a heavy quantum tracer particle coupled to a non-relativistic boson field in R^3. The pair interactions of the bosons are of mean-field type, with coupling strength proportional to 1/N where N is the expected particle number. Assuming that the mass of the tracer particle is proportional to N, we derive generalized Hartree equations in the limit where N tends to infinity. Moreover, we prove the global well-posedness of the associated Cauchy problem for sufficiently weak interaction potentials. This is joint work with Avy Soffer (Rutgers University)" |
October 17, 2018, 3:30 - 4:30 pm * please note change in time* at CMSA Building, 20 Garden St, G10 |
| CMSA COLLOQUIUM |
Jeremy England (MIT) |
Wisdom of the Jumble |
There are certain, specific behaviors that are particularly distinctive of life. For example, living things self-replicate, harvest energy from challenging environmental sources, and translate experiences of past and present into actions that accurately anticipate the predictable parts of their future. What all of these activities have in common from a physics standpoint is that they generally take place under conditions where the pronounced flow of heat sharpens the arrow of time. We have therefore sought to use thermodynamics to understand the emergence and persistence of life-like phenomena in a wide range of messy systems made of many interacting components. In this talk I will discuss some of the recent insights we have gleaned from studying emergent fine-tuning in disordered collections of matter exposed to complexly patterned environments. I will also point towards future possible applications in the design of new, more life-like ways of computing that have the potential to either be cheaper or more powerful than existing means" |
October 17, 2018, 4:30 - 5:30 pm at CMSA Building, 20 Garden St, G10 |
| CMSA GENERAL RELATIVITY SEMINAR |
SĂ©bastien Picard (HARVARD UNIVERSITY) |
The Anomaly flow over Riemann surfaces |
The Anomaly flow is a geometric flow on Calabi-Yau threefolds which is motivated by string theory. We will study the flow on certain fibrationswhere it reduces to a scalar evolution equation on a Riemann surface. This is joint work with T. Fei and Z. Huang" |
October 17, 2018, 11:00 am at CMSA Building, 20 Garden St, G02 |
| NUMBER THEORY SEMINAR |
Sean Howe (STANFORD UNIVERSITY) |
A unipotent circle action on p-adic modular forms |
The horizontal translation action of the real line on the complex upper half plane descends to an action of the circle group S^1 on the unstable locus, or image of Im \tau > 1, in the complex modular curve. In this talk, we explain an analogous action of the p-adic formal multiplicative group on the Katz moduli problem over the p-adic ordinary locus, whose ring of functions is the ring of p-adic modular forms. The analogy is richer than one might expect, and leads to new perspectives on classical notions in the p-adic theory of modular curves and modular forms such as Dwork s equation \tau=\log q and Hida s space of ordinary p-adic modular forms." |
October 17, 2018, 3:00 pm at Science Center 507 |
| INFORMAL GEOMETRY AND DYNAMICS SEMINAR |
Curtis McMullen (HARVARD UNIVERSITY) |
Ergodic theory of foliations of surfaces |
" |
October 17, 2018, 4:00 pm at Science Center 530 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Dori Bejleri (MIT) |
Compact moduli of elliptic fibrations and degree one del Pezzo surfaces |
A degree one del Pezzo surface is the blowup of P^2 at 8 general points. By the classical Cayley-Bacharach Theorem, there is a unique 9th point whose blowup produces a rational elliptic surface with a section. Via this relationship, we can construct a stable pair compactification of the moduli space of anti-canonically polarized degree one del Pezzo surfaces. The KSBA theory of stable pairs (X,D) is the natural extension to dimension 2 of the Deligne-Mumford-Knudsen theory of stable curves. I will discuss the construction of the space of interest as a limit of spaces of weighted stable elliptic surface pairs and explain how it relates to some previous compactifications of the space of degree one del Pezzo surfaces. This is joint work with Kenny Ascher" |
October 16, 2018, 3:00 pm at MIT 2-142 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Teng Fei (COLUMBIA UNIVERSITY) |
cscK metrics and the coupled flow of Li-Yuan-Zhang |
Y. Li, Y. Yuan, and Y.-G. Zhang introduced a coupled 2nd order parabolic flow of a Kahler metric and a closed 2-form to study cscK metrics. We introduce a one-parameter family of coupled-flows depending on a parameter \kappa>0 which reduces to the LYZ flow when \kappa=1. We show that estimates for derivatives of all orders would follow from C0 estimates. Together with the monotonicity of suitably adapted energy functionals, this can be applied to establish the convergence of the flow on negatively curved Riemann surfaces" |
October 16, 2018, 4:00 pm at Science Center 507 |
| CMSA SPECIAL SEMINAR |
Artan Sheshmani (CMSA) |
Atiyah class and sheaf counting on local Calabi-Yau four folds |
We discuss Donaldson-Thomas (DT) invariants of torsion sheaves with 2 dimensional support on a smooth projective surface in an ambient non-compact Calabi Yau fourfold given by the total space of a rank 2 bundle on the surface. We prove that in certain cases, when the rank 2 bundle is chosen appropriately, the universal truncated Atiyah class of these codimension 2 sheaves reduces to one, defined over the moduli space of such sheaves realized as torsion codimension 1 sheaves in a noncompact divisor (threefold) embedded in the ambient fourfold. Such reduction property of universal Atiyah class enables us to relate our fourfold DT theory to a reduced DT theory of a threefold and subsequently then to the moduli spaces of sheaves on the base surface. We finally make predictions about modularity of such fourfold invariants when the base surface is an elliptic K3. This is joint work with Shing-Tung Yau and Emanuel Diaconescu" |
October 16, 2018, 2:30 pm at CMSA Building, 20 Garden St, G10 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Christoph Gorgulla (HARVARD MEDICAL SCHOOL AND THE MATHEMATICAL PICTURE LANGUAGE PROJECT) |
A quantum mechanical free energy method based on Feynman's path integral formulation |
One of the most promising potential applications of quantum information science can be found within the field of computer-aided drug discovery (CADD). Quantum computing can in principle be the key to finding cures for almost any type of disease. In between quantum information science and CADD lies computational chemistry, which is part of the bridge connecting these two fields and which provides many of the methods and tools already utilized in CADD. Among them are methods for estimating the free energy of binding, which is arguably the most important quantity in CADD. In the main part of this talk, a novel free energy method will be described which is based on the path integral formulation of quantum mechanics, and which allows taking nuclear quantum effects explicitly into account" |
October 16, 2018, 4:00 pm at Jefferson 356 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Chris Gerig (HARVARD UNIVERSITY) |
A geometric interpretation of the Seiberg-Witten invariants |
Whenever the Seiberg-Witten (SW) invariants of a 4-manifold X are defined, there exist certain 2-forms on X which are symplectic away from some circles. When there are no circles, i.e. X is symplectic, Taubesâ âSW=Grâ theorem asserts that the SW invariants are equal to well-defined counts of J-holomorphic curves (Taubesâ Gromov invariants). In this talk I will describe an extension of Taubesâ theorem to non-symplectic X: there are well-defined counts of J-holomorphic curves in the complement of these circles, which recover the SW invariants. This âGromov invariantâ interpretation was originally conjectured by Taubes in 1995. This talk will involve contact forms and spin-c structures" |
October 15, 2018, 12:00 - 1:00 pm at CMSA Building, 20 Garden St, G10 |
| CMSA TOPOLOGICAL ASPECTS OF CONDENSED MATTER SEMINAR |
Ethan Lake (MIT) |
A primer on higher symmetries |
The notion of a higher symmetry, namely a symmetry whose charged objects have a dimension greater than zero, is proving to be very useful for organizing our understanding of gauge theories and topological phases of matter. Just like regular symmetries, higher symmetries can be gauged, spontaneously broken, and can have anomalies. I will review these aspects of higher symmetries and motivate why beyond their conceptual utility, they are often an indispensable tool for making statements about dualities and phase diagrams of theories with gauge fields." |
October 15, 2018, 10:00 - 11:30 am at CMSA Building, 20 Garden St, G10 |
| OPEN NEIGHBORHOOD SEMINAR |
Bena Tshishiku (HARVARD UNIVERSITY) |
The odd thing about can sunshades |
There s something magical about the Magic Shade (https://www.youtube.com/watch?v=LN65aQsKnMo). It has to do with topology, group theory, and the mathematics of braids and links. (This talk will be accessible to members of the department at all levels." |
October 15, 2018, 4:30 pm at Science Center 507 |
| LOGIC SEMINAR |
Will Boney (HARVARD UNIVERSITY) |
ErdĆ`s-Rado Classes |
Ramsey classes are used to construct generalized indiscernibles in models of first-order theories. However, the lack of compactness means that Ramsey s theorem (and its generalizations) are not enough to build indiscernibles in nonelementary classes. Instead, order indiscernibles are built with the Erdos-Rado Theorem. We present a framework for building indiscernibles in (many) nonelementary classes: Erdos-Rado classes (and some variants). The combinatorial definition of these classes is that they satisfy a certain partition relation for building large homogeneous sets when given many colors. We connect this to building indiscernibles, present several examples (some independent of ZFC), and provide some applications" |
October 15, 2018, 5:40 pm at Science Center 507 |
| CMSA SPECIAL SEMINAR |
Xin Wang (COLUMBIA UNIVERSITY) |
Quasi-modularity and holomorphic anomaly equation for GW invariants of elliptic curve |
In this talk, I will first prove the quasi-modularity and holomorphic anomaly equation for the twisted theory O(3) over P^2. Then I will talk about how to get quasi-modularity and holomorphic anomaly equation for elliptic curve from the twisted theory. If time permit, we will sketch some recent progress towards the holomorphic anomaly equation for elliptic fibrations conjectured by Oberdieck and Pixton. This is based on joint work with Felix Janda" |
October 15, 2018, 3:00 pm at CMSA Building, 20 Garden St, G10 |
| STUDENT/POSTDOC SYMPLECTIC GEOMETRY SEMINAR |
Yusuf Baris Kartal (MIT) |
Distinguishing open symplectic mapping tori via the dynamics of Fukaya categories |
Given a Weinstein domain M and a compactly supported exact symplectomorphism Ï, one can construct a Weinstein domain TÏ - the open symplectic mapping torus of Ï. The boundary of TÏ is independent of Ï and it is equal to that of T_0ĂM, where T_0 is the punctured two torus. In this talk, we will outline a method to distinguish fillings TÏ and T_0ĂM using the dynamics and deformation theory of their (wrapped) Fukaya categories" |
October 12, 2018, 2:00 - 3:15 pm at Science Center 507 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Paul Feehan (RUTGERS UNIVERSITY) |
Lojasiewicz inequalities and Morse-Bott functions |
The Lojasiewicz gradient and distance inequalities for real analytic functions on Euclidean space were first proved by Stanislaw Lojasiewicz (1965) using methods of semianalytic and subanalytic sets, arguments later simplified by Bierstone and Milman. We shall first describe a more direct proof of the Lojasiewicz gradient inequality that uses resolution of singularities for real analytic varieties to reduce to the case of functions with simple normal crossings, where the Lojasiewicz exponent may be computed explicitly â thus giving insight into its geometric meaning. It is well-known and easy to prove that if a function on a Banach space is Morse-Bott, then its Lojasiewicz exponent is 1/2. We show that the less obvious converse is also true: if the Lojasiewicz exponent of an analytic function on a Banach space is 1/2 at a critical point, then the function is Morse-Bott on a neighborhood of that point. We illustrate these phenomena with applications of Lojasiewicz inequalities to the Yang-Mills energy function near the critical set of flat connections on a principal G-bundle over a closed Riemannian manifold" |
October 12, 2018, 3:30 PM at Science Center 507 |
| BRANDEIS - HARVARD - MIT - NORTHEASTERN JOINT COLLOQUIUM |
Zhiwei Yun (MIT) |
From Kloosterman sums to exceptional groups |
I will give a survey on the construction of rigid local systems with monodromy in a general reductive group. The construction uses automorphic representation theory and geometric Langlands theory. The emphasis will be on what kind of input data one needs, and how to exhibit the resulting local system in a motivic fashion" |
October 11, 2018, Tea at 4:00 pm, Talk at 4:30 pm at Brandeis - 317 Goldsmith |
| THURSDAY SEMINAR |
Emily Saunders (HARVARD UNIVERSITY) |
The Hirsch-Smale theorem |
" |
October 11, 2018, 3:00 pm - 5:00 pm at Science Center 507 |
| INFORMAL GEOMETRY AND DYNAMICS SEMINAR |
Curtis McMullen (HARVARD UNIVERSITY) |
Ergodic theory of foliations of surfaces |
" |
October 10, 2018, 4:00 pm at Science Center 530 |
| CMSA GENERAL RELATIVITY SEMINAR |
Salem Al Mosleh (CMSA) |
Thin elastic shells and isometric embedding of surfaces in three-dimensional Euclidean space |
We will first discuss the reduction of theories describing elastic bodies in three-dimensions to effective descriptions defined on embedded surfaces. Then, we describe the isometric deformations of surfaces and the key role of played by asymptotic curves, curves with zero normal curvature, in determining the local mechanical behavior of thin shells. This was joint work with C. Santangelo" |
October 10, 2018, 11:00 am at CMSA Building, 20 Garden St, G02 |
| NUMBER THEORY SEMINAR |
Max Menzies (HARVARD UNIVERSITY) |
The p-curvature and Bost's Conjecture for the Gauss-Manin connection on non-abelian cohomology |
I ll begin with Bost s generalization of the p-curvature conjecture, and describe the classical geometric concepts at play such as the horizontal subbundle corresponding to a connection and parallel transport. This naturally motivates the discovery of the Gauss-Manin connection on algebraic de Rham cohomology, and its non-abelian analogue due to Simpson. I ll state Katz s theorem that the p-curvature conjecture (equivalently Bost) holds for the abelian Gauss-Manin connection, and the ingredients to even make that statement, such as the Hodge filtration, conjugate filtration, and Kodaira-Spencer map. I ll then define non-abelian analogues of these objects, and state a theorem which suitably equates them. This is the non-abelian analogue of part 1 of Katz s theorem, and is progress towards proving Bost for the non-abelian Gauss-Manin connection" |
October 10, 2018, 3:00 pm at Science Center 507 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Alfonso Bandeira (NEW YORK UNIVERSITY) |
Statistical estimation under group actions: The Sample Complexity of Multi-Reference Alignment |
Many problems in signal/image processing, and computer vision amount to estimating a signal, image, or tri-dimensional structure/scene from corrupted measurements. A particularly challenging form of measurement corruption are latent transformations of the underlying signal to be recovered. Many such transformations can be described as a group acting on the object to be recovered. Examples include the Simulatenous Localization and Mapping (SLaM) problem in Robotics and Computer Vision, where pictures of a scene are obtained from different positions and orientations; Cryo-Electron Microscopy (Cryo-EM) imaging where projections of a molecule density are taken from unknown rotations, and several others. One fundamental example of this type of problems is Multi-Reference Alignment: Given a group acting in a space, the goal is to estimate an orbit of the group action from noisy samples. For example, in one of its simplest forms, one is tasked with estimating a signal from noisy cyclically shifted copies. We will show that the number of observations needed by any method has a surprising dependency on the signal-to-noise ratio (SNR), and algebraic properties of the underlying group action. Remarkably, in some important cases, this sample complexity is achieved with computationally efficient methods based on computing invariants under the group of transformation" |
October 10, 2018, 3:00 - 4:00 pm at CMSA Building, 20 Garden St, G10 |
| CMSA COLLOQUIUM |
Justin Solomon (MIT) |
Correspondence and Optimal Transport for Geometric Data Processing |
Correspondence problems involving matching of two or more geometric domains find application across disciplines, from machine learning to computer vision. A basic theoretical framework involving correspondence along geometric domains is optimal transport (OT). Dating back to early economic applications, the OT problem has received renewed interest thanks to its applicability to problems in machine learning, computer graphics, geometry, and other disciplines. The main barrier to wide adoption of OT as a modeling tool is the expense of optimization in OT problems. In this talk, I will summarize efforts in my group to make large-scale transport tractable over a variety of domains and in a variety of application scenarios, helping transition OT from theory to practice. In addition, I will show how OT can be used as a unit in algorithms for solving a variety of problems involving the processing of geometrically-structured dat" |
October 10, 2018, 4:30 pm at CMSA Building, 20 Garden St, G10 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Jean-Bernard Zuber (SORBONNE UNIVERSITĂ©) |
ADE and all that, 30 years after |
In the late 80âs, some unexpected occurrences of the well known ADE classification of simply laced Lie algebras and Dynkin diagrams were found in the two contexts of Conformal Field Theories and Integrable Lattice Models. Soon after, some generalizations involving new diagrams and possibly generalized root systems were introduced. In this talk, personal recollections will be given of the developments of that period and of the following decade. The material of this talk is to a large extent covered by the review article in http://www.scholarpedia.org/article/A-D-E_Classification_of_Conformal_Field_Theorie" |
October 09, 2018, 4:00 pm at Jefferson 356 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Semyon Alesker (TEL AVIV UNIVERSITY) |
Quaternionic Monge-Ampere equations on HKT manifolds |
Real and complex Monge-Ampere equations play a central role in several areas of geometry and analysis. We introduce a quaternionic version of the Calabi problem for Kahler manifolds (proved by Yau). It is a non-linear elliptic equation of second order on so called HyperKahler with Torsion (HKT) manifolds (such manifolds were introduced by physicists in 1990 s). While in full generality the problem is unsolved, we will describe in the talk its solution in a special case and a few partial results towards its solution in the general case. Part of the results are joint with E. Shelukhin and M. Verbitsky" |
October 09, 2018, 4:00 pm at Science Center 507 |
| CMSA TOPOLOGICAL ASPECTS OF CONDENSED MATTER SEMINAR |
Sagar Vijay (HARVARD UNIVERSITY) |
Fracton Phases of Matter |
**SPECIAL DAY** Fracton phases are new kinds of highly-entangled quantum matter in three spatial dimensions that are characterized by gapped, point-like excitations " |
October 09, 2018, 3:00 PM - 4:30 PM at CMSA Building, 20 Garden St, G10 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Ignacio Barros (NORTHEASTERN UNIVERSITY) |
Uniruledness of strata of holomorphic differentials in small genus |
We address the question concerning the birational geometry of the strata of holomorphic and quadratic differentials. We show strata of holomorphic and quadratic differentials to be uniruled in small genus by constructing rational curves via pencils on K3 and del Pezzo surfaces respectively. Of special interest is the case of genus ten where uniruledness is obtained via the study of the Severi variety of nodal curves on K3 surfaces. We also construct projective bundles over rational varieties that dominate the holomorphic strata with length at most g - 1, hence showing in addition that these strata are unirational" |
October 09, 2018, 3:00 pm at Science Center 507 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Pei-Ken Hung (MIT) |
The linear stability of the Schwarzschild spacetime in the harmonic gauge: odd part |
We study the odd solution of the linearlized Einstein equation on the Schwarzschild background and in the harmonic gauge. With the aid of Regge-Wheeler quantities, we are able to estimate the odd part of Lichnerowicz d Alembertian equation. In particular, we prove the solution decays at rate $\tau^{-1+\delta}$ to a linearlized Kerr solution" |
October 08, 2018, 12:00 - 1:00 pm at CMSA Building, 20 Garden St, G10 |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Anar Akhmedov (UNIVERSITY OF MINNESOTA AND HARVARD UNIVERSITY) |
Construction of symplectic 4-manifolds and Lefschetz fibrations via Luttinger surgery |
Luttinger surgery is a certain type of Dehn surgery along a Lagrangian torus in a symplectic 4-manifold. The surgery was introduced by Karl Luttinger in 1995, who used it to study Lagrangian tori in R^4. Luttinger s surgery has been very effective tool recently for constructing exotic smooth and symplectic structures on 4-manifolds. In this talk, using Luttinger surgery, I will present the constructions of smallest known closed exotic simply connected symplectic 4-manifolds and exotic Lefschetz fibrations over 2-sphere whose total spaces have arbitrary finitely presented group G as the fundamental group. If time permits, we will also discuss some applications to the geography of symplectic 4-manifolds and Lefschetz fibrations. Part of these are (separate) joint works with B. Doug Park, Burak Ozbagci, and Naoyuki Monden" |
October 05, 2018, 3:30 pm at Science Center 507 |
| **CANCELED** STUDENT/POSTDOC SYMPLECTIC GEOMETRY SEMINAR |
Yu-Wei Fan (HARVARD UNIVERSITY) |
**CANCELED**Bridgeland stability conditions and mirror symmetry |
**CANCELED** We will introduce the notion of Bridgeland stability conditions, and discuss conjectural descriptions of stability conditions on Fukaya category and derived category of coherent sheaves. If time permits, we will also discuss the space of stability conditions on quiver/local Calabi-Yau category, and some geometric properties on the space" |
October 05, 2018, 2:00 - 3:15 pm at Science Center 507 **CANCELED** |
| CMSA SPECIAL SEMINAR |
Xiao-Gang Wen (MIT) |
Classification of topological orders in 2+1D and 3+1D |
I will present some recent results on the classification of topological orders in 2+1D using tensor categories, and in 3+1D using fusion 2-categories" |
October 05, 2018, 11:00 am - 12:00 pm at Science Center 530 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Semyon Dyatlov (UC BERKELEY AND MIT) |
Fractal Uncertainty Principle and Quantum Chaos |
Fractal uncertainty principle states that no function can be localized close to a fractal set simultaneously in position and momentum. The strongest version so far has been obtained in one dimension by Bourgain and the speaker with recent higher dimensional advances by Han and Schlag. It has applications to spectral gaps in chaotic scattering and to localization and control of high energy eigenfunctions. More precisely, using the work with Bourgain and earlier work with Zahl, Jin and the speaker proved that on hyperbolic surfaces, the mass of an eigenfunction on an open set is bounded from below independently of the energy. As shown by Jin, these results lead to observability and control for the Schrödinger equation. Another application is the existence of a spectral gap for every convex co-compact hyperbolic surface, which implies local energy decay of waves at high frequency" |
October 05, 2018, 4:30 pm at Jefferson 453 |
| BRANDEIS - HARVARD - MIT - NORTHEASTERN JOINT COLLOQUIUM |
Semyon Dyatlov (MIT) |
Fractal uncertainty principle and quantum chaos |
Fractal uncertainty principle states that no function can be localized to a fractal set simultaneously in position and in frequency. The strongest version so far has been obtained in one dimension by Bourgain and the speaker with recent higher dimensional advances by Han and Schlag. I will present two applications of the fractal uncertainty principle. The first one (joint with Jin) is a frequency-independent lower bound on mass of eigenfunctions on compact hyperbolic surfaces, which in particular implies control for the Schrödinger equation by any nonempty open set. In work in progress with Jin and Nonnenmacher we handle surfaces of variable negative curvature which present serious new challenges. The second application (joint with Zahl) is an essential spectral gap for convex co-compact hyperbolic surfaces, which implies exponential energy decay of high frequency waves." |
October 04, 2018, Tea at 4:00 pm, Talk at 4:30 pm at MIT 2-190 |
| OPEN NEIGHBORHOOD SEMINAR |
Matt Parker (STANDUP MATHS AND QUEEN MARY UNIVERSITY OF LONDON) |
Stand-up Maths: using performance to engage people with mathematics |
(This talk will be accessible to members of the department at all levels." |
October 04, 2018, 5:00 pm at Science Center 507 |
| THURSDAY SEMINAR |
Bena Tshishiku (HARVARD UNIVERSITY) |
Relations among Stiefel-Whitney classes of manifolds |
" |
October 04, 2018, 3:00 pm - 5:00 pm at Science Center 507 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Ian Jauslin (INSTITUTE FOR ADVANCED STUDY) |
Liquid Crystals and the Heilmann-Lieb model |
In 1979, O.Heilmann and E.H. Lieb introduced an interacting dimer model with the goal of proving the emergence of a nematic liquid crystal phase in it. In such a phase, dimers spontaneously align, but there is no long range translational order. Heilmann and Lieb proved that dimers do, indeed, align, and conjectured that there is no translational order. I will discuss a recent proof of this conjecture. This is joint work with Elliott H. Lieb" |
October 03, 2018, 3:00 pm at CMSA Building, 20 Garden St, G10 |
| CMSA COLLOQUIUM |
Richard Schoen (UC IRVINE) |
Perspectives on the scalar curvature |
This will be a general talk concerning the role that the scalar curvature plays in Riemannian geometry and general relativity. We will describe recent work on extending the known results to all dimensions, and other issues which are being actively studied" |
October 03, 2018, 4:30 - 5:30 pm at CMSA Building, 20 Garden St, G10 |
| CMSA GENERAL RELATIVITY SEMINAR |
Christos Mantoulidis (MIT) |
The Bartnik mass of apparent horizons |
We will discuss a spectral characterization of apparent horizons in three-dimensional time-symmetric initial data sets. Then, for a dense class of nondegenerate apparent horizons, we will construct sharp asymptotically flat extensions to conclude that their Bartnik mass equals their Hawking mass. This is joint work with R. Schoen" |
October 03, 2018, 11:00 am at CMSA Building, 20 Garden St, G02 |
| NUMBER THEORY SEMINAR |
Lynnelle Ye (HARVARD UNIVERSITY) |
Geometry of eigenvarieties for definite unitary groups over the boundary of weight space |
The study of eigenvarieties began with Coleman and Mazur, who constructed the first eigencurve, a rigid space whose points are in bijection with $p$-adic modular Hecke eigenforms. Since then various authors have constructed eigenvarieties for automorphic forms on many other groups. We will state a structure theorem about Chenevier s eigenvarieties for definite unitary groups which generalizes slope bounds of Liu-Wan-Xiao for dimension $2$ to all dimensions, and discuss, time permitting, the ideas of the proof and a geometric consequence" |
October 03, 2018, 3:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Tom Bachmann (MIT) |
Affine Grassmannians in motivic homotopy theory |
Motivic homotopy theory was invented by Morel-Voevodsky in order to rigorously apply homotopy theoretical ideas to the study of schemes. In particular, for every field k they construct a closed symmetric monoidal category H(k)_* called the homotopy category of pointed motivic spaces over k, and every pointed smooth k-variety X has a homotopy type t(X) in H(k)_*. On the other hand if G is a group scheme over k, then the affine Grassmannian Gr(G) is an ind-scheme devised as an algebraic analog of the loop space of G and of importance in geometric representation theory. It is possible to make sense of t(Gr(G)) in H(k)_*. I will explain the following result: t(Gr(G)) is obtained from t(G) by applying the functor Hom(t(Gm), -), where Hom means internal hom and Gm denotes the pointed scheme (A^1 - 0, 1). In other words in motivic homotopy theory, affine grassmannians really are honest loop spaces" |
October 02, 2018, 3:00 pm at MIT 2-2142 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Hansol Hong (CMSA & BRANDEIS UNIVERSITY) |
Mirror construction via Lagrangian deformation |
Mirror symmetry predicts a duality between symplectic and complex geometries for a pair of (Kahler) manifolds. In this talk, I will explain a way to construct a mirror space of a symplectic manifold by studying Floer theoretical deformation theory of its Lagrangian submanifolds" |
October 02, 2018, 4:00 pm at Science Center 507 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Victor Kac (MIT) |
Multiplicative Poisson vertex algebras and differential-difference Hamiltonian equations |
It has been demonstrated in the past few years that Poisson vertex algebras (quasiclassical limits of vertex=chiral algebras) is the adequate framework for the theory of Hamiltonian PDE. After explaining this, I will demonstrate that likewise the multiplicative Poisson vertex algebras is the adequate framework for the theory of Hamiltonian differential-difference equations" |
October 02, 2018, 5:00 pm at Jefferson 356 |
| SPECIAL SEMINAR |
Andre Neves (UNIVERSITY OF CHICAGO) |
Abundance of minimal surfaces |
Minimal surfaces are ubiquitous in Geometry and in recent years their existence theory has enjoyed a dramatic progress. I will survey the main results. --Organized by Shing-Tung Ya" |
October 01, 2018, 3:00 - 4:00 pm at Science Center 507 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Dori Bejleri (MIT) |
Stable pair compactifications of the moduli space of degree one del Pezzo surfaces via elliptic fibrations |
A degree one del Pezzo surface is the blowup of P^2 at 8 general points. By the classical Cayley-Bacharach Theorem, there is a unique 9th point whose blowup produces a rational elliptic surface with a section. Via this relationship, we can construct a stable pair compactification of the moduli space of anti-canonically polarized degree one del Pezzo surfaces. The KSBA theory of stable pairs (X,D) is the natural extension to dimension 2 of the Deligne-Mumford-Knudsen theory of stable curves. I will discuss the construction of the space of interest as a limit of a space of weighted stable elliptic surface pairs and explain how it relates to some previous compactifications of the space of degree one del Pezzo surfaces. This is joint work with Kenny Ascher" |
October 01, 2018, 12:00 - 1:00 pm at CMSA Building, 20 Garden St, G10 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Yash Deshpande (MIT) |
Estimating low-rank matrices in noise: phase transitions from spin glass theory |
Estimating low-rank matrices from noisy observations is a common task in statistical and engineering applications. Following the seminal work of Johnstone, Baik, Ben-Arous and Peche, versions of this problem have been extensively studied using random matrix theory. In this talk, we will consider an alternative viewpoint based on tools from mean field spin glasses. We will present two examples that illustrate how these tools yield information beyond those from classical random matrix theory. The first example is the two-groups stochastic block model (SBM), where we will obtain a full information-theoretic understanding of the estimation phase transition. In the second example, we will augment the SBM with covariate information at nodes, and obtain results on the altered phase transition. This is based on joint works with Emmanuel Abbe, Andrea Montanari, Elchanan Mossel and Subhabrata Sen" |
September 28, 2018, 3:00 pm at CMSA Building, 20 Garden St, G10 |
| STUDENT/POSTDOC SYMPLECTIC GEOMETRY SEMINAR |
Yoosik Kim (BOSTON UNIVERSITY) |
Gelfand-Cetlin systems and their applications |
The Gelfand-Cetlin system is a completely integrable system on a partial flag manifold. We will discuss a combinatorial way of understanding the fibers of the Gelfand-Cetlin systems. If time permits, we will discuss some applications to symplectic geometry and mirror symmetry" |
September 28, 2018, 2:00 - 3:15 pm at Science Center 507 |
| BRANDEIS - HARVARD - MIT - NORTHEASTERN JOINT COLLOQUIUM |
Peter Bubenik (UNIVERSITY OF FLORIDA) |
Mathematical Aspects of Topological Data Analysis |
Topological Data Analysis (TDA) is a new approach to analyzing complicated geometric and/or high dimensional data. The central mathematical object of TDA is the persistence module, which can be understood using the language of a number of different branches of mathematics. It turns out that taking an applied viewpoint on this algebraic object leads us to new mathematics. I will give an introduction to TDA focusing on its mathematical foundations, describing the pipeline of turning input data into persistence modules and then mapping to a Hilbert space, allowing one to use tools from statistics and machine learning. I will end with some generalizations and open problems" |
September 27, 2018, 4:30 pm at Northeastern - 509 Lake Hall |
| THURSDAY SEMINAR |
Jun Hou Fung (HARVARD UNIVERSITY) |
Immersions up to cobordism |
" |
September 27, 2018, 3:00 pm - 5:00 pm at Science Center 507 |
| INFORMAL GEOMETRY AND DYNAMICS SEMINAR |
Curtis McMullen (HARVARD UNIVERSITY) |
Moduli spaces and dynamical systems |
" |
September 26, 2018, 4:00 pm at Science Center 530 |
| NUMBER THEORY SEMINAR |
Frank Thorne (UNIVERSITY OF SOUTH CAROLINA & TUFTS UNIVERSITY) |
Error Terms in Arithmetic Statistics |
Recent years have seen tremendous advances in arithmetic statistics: counting results for number field discriminants, class group torsion, and other arithmetic objects. In many cases, these can be expressed in terms of lattice point counting problems, often in prehomogeneous or coregular vector spaces. I will give an overview of some work on the following question: how to obtain the best possible error terms, especially when local conditions are imposed? Although sieve methods lead to some interesting applications, in this talk I will concentrate on the algebraic side of the story. Aiming to prove optimal error terms has revealed some interesting structure in prehomogeneous vector spaces, and it has posed several questions which I will discuss. This is joint work with Takashi Taniguchi" |
September 26, 2018, 3:00 pm at Science Center 507 |
| CMSA COLLOQUIUM |
Xiao-Gang Wen (MIT) |
A classification of low dimensional topological orders and fully extended TQFTs |
In this talk, I will review the recent progress on classification of gapped phases of quantum matter (ie topological orders) in 1,2, and 3 spatial dimensions for boson systems. In 1-dimension, there is no non-trivial topological orders. In 2-dimensions, the topological orders are classified by modular tensor category theory. In 3-dimensions, the topological orders are classified by a simple class of braided fusion 2-categories. The classification of topological orders may correspond to a classification of fully extended unitary TQFTs" |
September 26, 2018, 4:30 - 5:30 pm at CMSA Building, 20 Garden St, G10 |
| CMSA GENERAL RELATIVITY SEMINAR |
Jordan Keller (BHI) |
Quasi-local Angular Momentum and Center-of-Mass at Future Null Infinity |
We calculate the limits of the quasi-local angular momentum and center-of-mass defined by Chen-Wang-Yau [3] for a family of spacelike two-spheres approaching future null infinity in an asymptotically flat spacetime admitting a Bondi-Sachs expansion. Our result complements earlier work of Chen-Wang-Yau [2], where the authors calculate the quasi-local energy and linear momentum at null infinity. Finiteness of the quasi-local center-of-mass requires that the spacetime be in the so-called center-of-mass frame, which amounts to a mild assumption on the mass aspect function corresponding to vanishing of the quasi-local linear momentum calculated in [2]. With this condition and the assumption that the mass aspect function is non-trivial, we obtain explicit expressions for the quasi-local angular momentum and center-of-mass at future null infinity in terms of the observables appearing in the Bondi-Sachs expansion of the spacetime metric. This is joint work with Ye-Kai Wang and Shing-Tung Yau" |
September 26, 2018, 11 AM at CMSA Building, 20 Garden St., G02 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Pei-Ken Hung (MIT) |
The smoothing time of convex inverse mean curvature flows |
By using a local estimate recently proved by B. Choi and P. Daskalopoulos, we show that the smoothing time of convex inverse mean curvature flows can be computed by the area of the tangent cones. As a corollary, convex inverse mean curvature flows on the sphere become smooth before the extinction time unless the corresponding cone splits a line. This is ongoing joint work with B. Choi" |
September 25, 2018, 4:00 - 5:00 pm at Science Center 507 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Yi Xie (SIMONS CENTER) |
sl(3) Khovanov module and the detection of planar theta-graph |
In this talk we will show that Khovanov s sl(3) link homology together with its module structure can be generalized for spatial webs (bipartite trivalent graphs). We will also introduce a variant called pointed sl(3) Khovanov homology. Those two combinatorial invariants are related to Kronheimer-Mrowkaâs instanton invariants $J^\sharp$ and $I^\sharp$ for spatial webs by two spectral sequences. As an application, we will prove that sl(3) Khovanov module and pointed sl(3) Khovanov homology both detect the planar theta graph" |
September 24, 2018, 12:00 - 1:00 pm at CMSA Building, 20 Garden St, G10 |
| CMSA TOPOLOGICAL ASPECTS OF CONDENSED MATTER SEMINAR |
Max Metlitski (MIT) |
Surface Topological Order and a new 't Hooft Anomaly of Interaction Enabled 3+1D Fermion SPTs |
Symmetry protected topological (SPT) phases have attracted a lot of attention in recent years. A key property of SPTs is the presence of non-trivial surface states. While for 1+1D and 2+1D SPTs the boundary must be either symmetry broken or gapless, some 3+1D SPTs admit symmetric gapped surface states that support anyon excitation (intrinsic topological order). In all cases, the boundary of an SPT is anomalous - it cannot be recreated without the bulk; furthermore, the anomaly must ``matc" |
September 24, 2018, 10:00 - 11:30 am at CMSA Building, 20 Garden St, G10 |
| STUDENT/POSTDOC SYMPLECTIC GEOMETRY SEMINAR |
Tim Large (MIT) |
Steenrod operations and the Floer homotopy type |
A natural question in symplectic geometry and gauge theory is whether one can construct a homotopy type underlying the Floer homology groups. There are usually topological obstructions to this, but if one could, the Z/p coefficient versions of the Floer groups would come with natural Steenrod operations. On the other hand, one could try construct these operations as equivariant refinements of the pair-of-pants product, analogously to the story for singular homology. In this talk, we will explain how these two approaches relate to each other" |
September 21, 2018, 2:00 - 3:15 pm at Science Center 507 |
| GAUGE - TOPOLOGY - SYMPLECTIC SEMINAR |
Weiyi Zhang (UNIVERSITY OF WARWICK) |
From smooth to almost complex |
An almost complex manifold is a smooth manifold equipped with a smooth linear complex structure on each tangent space. We will discuss differential topology of almost complex manifolds, explain how to use transversality statements for smooth manifolds to formulate and prove corresponding results for an arbitrary almost complex manifold. The examples include intersection of almost complex manifolds, structure of pseudoholomorphic maps and zero locus of certain harmonic forms. One of the main technical tools is Taubes notion of positive cohomology assignment, which plays the role of local intersection number. I will begin with explaining its motivation through multiplicities of zeros of a smooth function. Our results would lead to a notion of birational morphism between almost complex manifolds. Various birational invariants, including Kodaira dimension, for almost complex manifolds will be introduced and discussed (this part is joint with Haojie Chen)" |
September 21, 2018, 3:30 pm at Science Center 507 |
| THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
The Immersion Conjecture, an overview |
" |
September 20, 2018, 3:00 pm - 5:00 pm at Science Center 507 |
| CMSA GENERAL RELATIVITY SEMINAR |
Pei-Ken Hung (MIT) |
The linear stability of the Schwarzschild spacetime in the harmonic gauge: odd part |
We study the odd solution of the linearlized Einstein equation on the Schwarzschild background and in the harmonic gauge. With the aid of Regge-Wheeler quantities, we are able to estimate the odd part of Lichnerowicz d Alembertian equation. In particular, we prove the solution decays at rate $\tau^{-1+\delta}$ to a linearlized Kerr solution" |
September 19, 2018, 11:00 am at Science Center 530 |
| NUMBER THEORY SEMINAR |
Ben Howard (BOSTON COLLEGE) |
Moduli spaces of shtukas and a higher derivative Gross-Kohnen-Zagier formula |
The Gross-Zagier formula expresses the Neron-Tate height of a Heegner point as the derivative of an L-function, while the Gross-Kohnen-Zagier formula expresses the Neron-Tate pairing of two different Heegner points as the product of the derivative of an L-function and a period integral. Yun and Zhang have proved a higher derivative version of the Gross-Zagier theorem, but with Heeger points on modular curves replaced by Heegner-Drinfeld cycles on moduli spaces of PGL(2)-Shtukas. I will describe a higher derivative version of Gross-Kohnen-Zagier for these Heegner-Drinfeld cycles. This is joint work with A. Shnidman" |
September 19, 2018, 3:00 pm at Science Center 507 |
| INFORMAL GEOMETRY AND DYNAMICS SEMINAR |
Curtis McMullen (HARVARD UNIVERSITY) |
Moduli spaces and dynamical systems |
" |
September 19, 2018, 4:00 pm at Science Center 530 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Austin Conner (TEXAS A&M UNIVERSITY) |
New approaches to upper bounds on the complexity of matrix multiplication |
I will describe two new paths using algebraic geometry and representation theory to prove upper bounds on the exponent of matrix multiplication. The first approach aims to apply the laser method of Strassen to previously unstudied tensors which uniquely share certain geometric properties with the Coppersmith-Winograd tensor. The second approach for upper bounds transforms the problem into that of finding a certain sequence of finite groups and associated representations. The first approach is joint work with Fulvio Gesmundo, JM Landsberg, and Emanuele Ventura" |
September 18, 2018, 3:00 pm at MIT 4-153 |
| DIFFERENTIAL GEOMETRY SEMINAR |
William Minicozzi (MIT) |
Dynamics near singularities in mean curvature flow |
I will talk about the dynamics of mean curvature flow near a singularity, including generic properties, a local stable manifold theorem, and the long-time behavior of the flow. This is joint work with Toby Colding" |
September 18, 2018, 4:00 pm at Science Center 507 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Liming Ge (CHINESE ACADEMY OF SCIENCE AND UNIVERSITY OF NEW HAMPSHIRE) |
On Multiplicative Fourier Transforms |
A multiplicative Fourier transform is introduced. Some properties and applications are given" |
September 18, 2018, 4:00 pm at Jefferson 356 |
| CMSA TOPOLOGICAL ASPECTS OF CONDENSED MATTER SEMINAR |
Adrian Po (MIT) |
A modern solution to the old problem of symmetries in band theory |
There are 230 space groups and 1,651 magnetic space groups in three dimensions. Thankfully, these are finite numbers, and one might go about solving all the possible ways free electrons represent them. This is a central question in the nine-decade-old band theory, which is long-thought to be solvable if only one had the time and patience to crank through all the cases. In this talk, I would describe how this problem can be solved efficiently from the modern perspective of band topology. As a by-product, we will describe a simple method to detect topologically nontrivial band insulators using only symmetry eigenvalues, which offers great computational advantage compared to the traditional, wave-function-based definitions of topological band invariants" |
September 17, 2018, 10:30 am - 12:00 pm at CMSA Building, 20 Garden St, G10 |
| OPEN NEIGHBORHOOD SEMINAR |
Moon Duchin (TUFTS UNIVERSITY) |
Random Everything |
Random processes and random constructions are all over math, and have many applications as well. I ll give a tour of some highlights of randomness in math, from number theory to geometry, plus applications to politics if I have time.(This talk will be accessible to members of the department at all levels, including undergraduates." |
September 17, 2018, 4:30 pm at Science Center 507 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Gaetan Borot (MAX PLANCK INSTITUTE) |
A generalization of Mirzakhani's identity, and geometric recursion |
McShane obtained in 1991 an identity expressing the function 1 on the Teichmueller space of the once-punctured torus as a sum over simple closed curves. It was generalized to bordered surfaces of all topologies by Mirzakhani in 2005, from which she deduced a topological recursion for the Weil-Petersson volumes. I will present new identities which represent linear statistics of the simple length spectrum as a sum over homotopy class of pairs of pants in a hyperbolic surface, from which one can deduce a topological recursion for their average over the moduli space. This is an example of application of a geometric recursion developed with Andersen and Orantin" |
September 17, 2018, 12:00 - 1:00 pm at CMSA Building, 20 Garden St, G10 |
| STUDENT/POSTDOC SYMPLECTIC GEOMETRY SEMINAR |
Andrew Hanlon (UC BERKELEY AND HARVARD) |
A new perspective on homological mirror symmetry for toric varieties |
We will introduce a new model for the Fukaya-Seidel category of a Laurent polynomial and compare it with a more standard setup. Then, we will discuss Abouzaid s proof of HMS for toric varieties from this new point of view. Finally, we will see how interesting new functors and natural transformations arise in this setup" |
September 14, 2018, 1:30 - 3:00 pm at Science Center 507 |
| GAUGE - TOPOLOGY - SYMPLECTIC SEMINAR |
Denis Auroux (HARVARD UNIVERSITY) |
An invitation to homological mirror symmetry |
We will give a gentle introduction to some recent developments in the area of homological mirror symmetry. We will use simple examples to illustrate Kontsevich s conjecture and its extension beyond the Calabi-Yau setting in which it was first formulated. We will mostly focus on a one-dimensional example, the pair of pants, to give a flavor of the geometric concepts involved in a general formulation of homological mirror symmetry. If time permits, we will then describe a program to prove homological mirror symmetry for essentially arbitrary complete intersections in toric varieties (joint work in progress with Mohammed Abouzaid)" |
September 14, 2018, 3:30 pm at Science Center 507 |
| NUMBER THEORY SEMINAR |
Daniel Kriz (MIT) |
A new p-adic Maass-Shimura operator and supersingular Rankin-Selberg p-adic L-functions |
We introduce a new p-adic Maass-Shimura operator acting on a space of generalized p-adic modular forms (extending Katz s notion of p-adic modular forms), defined on the p-adic (preperfectoid) universal cover of a Shimura curve. Using this operator, we construct new p-adic L-functions in the style of Katz, Bertolini-Darmon-Prasanna and Liu-Zhang-Zhang for Rankin-Selberg families over imaginary quadratic fields K, in the case where p is inert or ramified in K. We also establish new p-adic Waldspurger formulas, relating p-adic logarithms of elliptic units and Heegner points to special values of these p-adic L-functions" |
September 12, 2018, 3:00 pm at Science Center 507 |
| INFORMAL GEOMETRY AND DYNAMICS SEMINAR |
Curtis McMullen (HARVARD UNIVERSITY) |
Moduli spaces and dynamical systems |
" |
September 12, 2018, 4:00 pm at Science Center 530 |
| CMSA GENERAL RELATIVITY SEMINAR |
Aghil Alaee (CMSA) |
Mass-angular momentum inequality for black holes |
In this talk, I will review the results of mass-angular momentum inequality for four-dimensional axisymmetric black holes. Then I will establish versions of this inequality for five-dimensional black holes and in particular black ring, which is the most intriguing asymptotically flat solution of vacuum Einstein equations. Moreover, I will show these inequalities are sharp if and only if the initial data sets are isometric to the canonical slices of known extreme stationary solutions. These results are joint work with Marcus Khuri and Hari Kunduri" |
September 12, 2018, 11:00 am at CMSA Building, 20 Garden St, G02 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Jack Huizenga (PENN STATE) |
Moduli of sheaves on Hirzebruch surfaces |
Let X be a Hirzebruch surface. Moduli spaces of semistable sheaves on X with fixed numerical invariants are always irreducible by a theorem of Walter. On the other hand, many other basic properties of sheaves on Hirzebruch surfaces are unknown. I will discuss two different problems on this topic. First, what is the cohomology of a general sheaf on X with fixed numerical invariants? Second, when is the moduli space actually nonempty? The latter question should have an answer reminiscient of the Drezet-Le Potier classification of semistable sheaves on the projective plane; in particular, there is a fractal-like hypersurface in the space of numerical invariants which bounds the invariants of semistable sheaves. This is joint work with Izzet Coskun" |
September 11, 2018, 3:00 pm at Science Center 507 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Xiaomeng Xu (MIT) |
Stokes phenomenon, Yang-Baxter equations and Gromov-Witten theory |
This talk will include a general introduction to a linear differential system with singularities, and its relation with symplectic geometry, Yang-Baxter equations, quantum groups and 2d topological field theories" |
September 10, 2018, 12:00 - 1:00 pm at CMSA Building, 20 Garden St, G10 |
| CMSA TOPOLOGICAL ASPECTS OF CONDENSED MATTER SEMINAR |
Dominic Else (MIT) |
Phases and topology in periodically driven (Floquet) systems |
I will give a pedagogical overview of new topological phenomena that occur in systems that are driven periodically in time (Floquet systems). As a warm-up, I will review new topological invariants in free-fermion Floquet systems. Then, I will discuss the richer physics that occurs in interacting Floquet phases, stabilized in systems with strong quenched disorder by many-body-localization (MBL). Finally, time permitting, I will explain how to realize interacting topological phenomena in a metastable (pre-thermal) regime of a clean system" |
September 10, 2018, 10:30 am - 12:00 pm at CMSA Building, 20 Garden St, G10 |
| STUDENT/POSTDOC SYMPLECTIC GEOMETRY SEMINAR |
Denis Auroux (HARVARD UNIVERSITY) |
An introduction to Fukaya categories and homological mirror symmetry |
In this expository talk, we will give a brief review of Lagrangian Floer homology and Fukaya categories, and introduce homological mirror symmetry by describing its statement for simple examples such as the cylinder and CP^1. This may serve (or not) as background material for further talks in the seminar, during which advanced PhD students and postdocs working in this area of mathematics will present their work or material related to it" |
September 07, 2018, 1:30 - 3:00 pm at Science Center 530 |
| CMSA GENERAL RELATIVITY SEMINAR |
Christos Mantoulidis (MIT) |
Capacity and quasi-local mass |
This talk is based on work with P. Miao and L.-F. Tam. We derive new inequalities between the boundary capacity of an asymptotically flat 3-manifold with nonnegative scalar curvature and boundary quantities that relate to quasi-local mass; one relates to Brown-York mass and the other is new. Among other things, our work yields new variational characterizations of Riemannian Schwarzschild manifolds and new comparison results for surfaces in them" |
September 07, 2018, 2:00 pm at CMSA Building, 20 Garden St, G02 |
| INFORMAL GEOMETRY AND DYNAMICS SEMINAR |
Curtis McMullen (HARVARD UNIVERSITY) |
Moduli spaces and dynamical systems |
Organizational Meetin" |
September 05, 2018, 4:00 pm at Science Center 530 |
| MATHEMATICAL PICTURE LANGUAGE SEMINAR |
Bohan Fang (PEKING UNIVERSITY) |
Mirror symmetry for toric Calabi-Yau 3-folds |
Mirror symmetry, from the mathematical perspective, is a duality relation between symplectic geometry and algebraic geometry. The combinatorial nature of toric geometry makes the mirror symmetry relation very explicit in examples. I will explain various aspects of mirror symmetry, both enumerative and homological, for toric varieties and especially toric Calabi-Yau 3-folds" |
September 04, 2018, 4:00 pm at Jefferson 356 |
| CMSA SPECIAL SEMINAR |
Zhengcheng Gu (THE CHINESE UNIVERSITY OF HONG KONG) |
Towards a complete classification of symmetry protected topological phases for interacting fermions in three dimensions and a general group supercohomology theory |
Classification and construction of symmetry protected topological (SPT) phases in interacting boson and fermion systems have become a fascinating theoretical direction in recent years. It has been shown that the (generalized) group cohomology theory or cobordism theory can give rise to a complete classification of SPT phases in interacting boson/spin systems. Nevertheless, the construction and classification of SPT phases in interacting fermion systems are much more complicated, especially in 3D. In this talk, I will revisit this problem based on the equivalent class of fermionic symmetric local unitary (FSLU) transformations. I will show how to construct very general fixed point SPT wavefunctions for interacting fermion systems. I will also discuss the procedure of deriving a general group super-cohomology theoy in arbitrary dimensions" |
August 29, 2018, 3:00 pm at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL ALGEBRAIC GEOMETRY SEMINAR |
Netanel Rubin-Blaier (CMSA, HARVARD) |
The Kontsevich compactification, Abel-Jacobi maps, and symplectomorphism of algebraic varieties |
I ll describe a way to prove the existence of non-trivial elements in the homology and homotopy groups of $Symp(X,\omega)$, where $(X,\omega)$ is a Fano variety. The approach is based on considering the geometry of Kontsevich moduli spaces of stable maps and comparing it with a family of intermediate Jacobians. We will consider a number of examples including cubic 3-folds, complete intersection of quadrics, and moduli spaces of rank 2 stable bundles over algebraic curves of genus $g$, $g \geq 2$." |
May 24, 2018, 3:00 - 4:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS HOMOLOGICAL MIRROR SYMMETRY 2-PART LECTURE SERIES |
Charles Doran (UNIVERSITY OF ALBERTA AND ICERM) |
Calabi-Yau fibrations: construction and classification |
Part 1: Codimension one Calabi-Yau submanifolds induce fibrations, with the periods of the total space relating to those of the fibers and the structure of the fibration. We describe a method of iteratively constructing Calabi-Yau manifolds in tandem with their Picard-Fuchs equations. Applications include the tower of mirrors to degree n+1 hypersurfaces in P^n and a tower of Calabi-Yau hypersurfaces encoding the n-sunset Feynman integrals. Part 2: We develop the necessary theory to both construct and classify threefolds fibered by lattice polarized K3 surfaces. The resulting theory is a complete generalization to threefolds of that of Kodaira for elliptic surfaces. When the total space of the fibration is a Calabi-Yau threefold, we conjecture a unification of CY/CY mirror symmetry and LG/Fano mirror symmetry by mirroring fibrations as Tyurin degenerations. The detailed classification of Calabi-Yau threefolds with certain rank 19 polarized fibrations provides strong evidence for this conjecture by matching geometric characteristics of the fibrations with features of smooth Fano threefolds of Picard rank 1" |
May 17, 2018, 1:00 - 3:00 PM at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS HOMOLOGICAL MIRROR SYMMETRY 2-PART LECTURE SERIES |
Charles Doran (UNIVERSITY OF ALBERTA AND ICERM) |
Picard-Fuchs uniformization and Calabi-Yau geometry |
Part 1: We introduce the notion of the Picard-Fuchs equations annihilating periods in families of varieties, with emphasis on Calabi-Yau manifolds. Specializing to the case of K3 surfaces, we explore general results on âPicard-Fuchs uniformizationâ of the moduli spaces of lattice-polarized K3 surfaces and the interplay with various algebro-geometric normal forms for these surfaces. As an application, we obtain a universal differential-algebraic characterization of Picard rank jump loci in these moduli spaces. Part 2: We next consider families with one natural complex structure modulus, (e.g., elliptic curves, rank 19 K3 surfaces, b_1=4 Calabi-Yau threefolds, âŠ), where the Picard-Fuchs equations are ODEs. What do the Picard-Fuchs ODEs for such families tell us about the geometry of their total spaces? Using Hodge theory and parabolic cohomology, we relate the monodromy of the Picard-Fuchs ODE to the Hodge numbers of the total space. In particular, we produce criteria for when the total space of a family of rank 19 polarized K3 surfaces can be Calabi-Yau" |
May 15, 2018, 1:00 - 3:00 PM at CMSA Building, 20 Garden St, G10 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Renzo Cavalieri (COLORADO STATE) |
Witten conjecture for Mumford's kappa classes |
Kappa classes were introduced by Mumford, as a tool to explore the intersection theory of the moduli space of curves. Iterated use of the projection formula shows there is a close connection between the intersection theory of kappa classes on the moduli space of unpointed curves, and the intersection theory of psi classes on all moduli spaces. In terms of generating functions, we show that the potential for kappa classes is related to the Gromov-Witten potential of a point via a change of variables essentially given by complete symmetric polynomials, rediscovering a theorem of Manin and Zokgraf from 99. Surprisingly, the starting point of our story is a combinatorial formula that relates intersections of kappa classes and psi classes via a graph theoretic algorithm (the relevant graphs being dual graphs to stable curves).This is joint work (in progress) with Vance Blankers" |
May 08, 2018, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Netanel Rubin-Blaier (CMSA, HARVARD) |
The Kontsevich compactification, Abel-Jacobi maps, and symplectomorphism of algebraic varieties |
I ll describe a way to prove the existence of non-trivial elements in the homology and homotopy groups of $Symp(X,\omega)$, where $(X,\omega)$ is a Fano variety. The approach is based on considering the geometry of Kontsevich moduli spaces of stable maps and comparing it with a family of intermediate Jacobians. We will consider a number of examples including cubic 3-folds, complete intersection of quadrics, and moduli spaces of rank 2 stable bundles over algebraic curves of genus $g$, $g \geq 2$" |
May 01, 2018, 4:15 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Dmitry Tonkong (UC BERKELEY) |
Geometry of symplectic flux |
Symplectic flux measures the areas of cylinders swept in the process of an isotopy of a Lagrangian submanifold. This is a classical invariant which captures quantitative aspects of symplectic manifolds. I will report on joint work with Egor Shelukhin and Renato Vianna in which we study the geometry of flux using a technique inspired by mirror symmetry" |
April 30, 2018, 12:00 - 1:00 pm at CMSA Building, 20 Garden Street, Room G10 |
| CMSA SPECIAL SEMINAR ON SYMPLECTIC GEOMETRY |
Weiwei Wu (UNIVERSITY OF GEORGIA) |
Lagrangian surgery formulae and applications |
I will explain two new proofs of Lagrangian surgery formulae in Lagrangian Floer theory. The first one deals with transversal intersections and is robust with respect to auxiliary data near the transversal intersection. Our main innovation is to count the holomorphic solution in a local problem similar to FOOO s original proof using Lefschetz fibration, which simplifies the problem. For Lagrangian surgery with general clean intersections, we prove a new compactness theorem for holomorphic curves with degenerate Lagrangian boundary. This compactness result potentially has applications to problems of understanding the behavior of holomorphic disks with other types of Lagrangian degenerations. This is a joint work with Cheuk-Yu Mak" |
April 30, 2018, 1:30 - 2:30 pm at CMSA Building, 20 Garden Street, Room G10 |
| BRANDEIS, HARVARD, MIT, NORTHEASTERN JOINT COLLOQUIUM AT HARVARD |
Paul Hacking (UNIVERSITY OF MASSACHUSETTS, AMHERST) |
Mirror Symmetry and Fano manifolds |
Roughly speaking, a Fano manifold is a complex manifold with positive Ricci curvature. The Riemann sphere is the unique Fano manifold in complex dimension 1, there are 10 topological types in dimension 2, and 105 in dimension 3. I will describe a project initiated by Coates, Corti, Galkin, Golyshev, and Kasprzyk to classify Fano manifolds using mirror symmetry. This is joint work with Alessio Corti, Mark Gross, and Andrea Petracci" |
April 26, 2018, Tea at 4 pm, Talk at 4:30 pm at Science Center Hall A |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Yongquan Zhang (HARVARD UNIVERSITY ) |
Andreev's theorem on hyperbolic polyhedra and Kleinian reflection groups |
One way to obtain a Kleinian group is to consider the group generated by reflections in the faces of a hyperbolic polyhedron with dihedral angles submultiples of \pi. Andreevâs theorem guarantees the existence of hyperbolic polyhedra with non-obtuse dihedral angles satisfying certain combinatorial conditions. In this talk, I will construct a one dimensional family of hyperbolic polyhedra with the help of Andreevâs theorem so that the Kleinian groups obtained from reflections in some of the faces realize a one dimensional deformation of a convex cocompact acylindrical hyperbolic 3-manifold" |
April 25, 2018, 4:00 pm at Science Center 530 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Xi Yin (HARVARD UNIVERSITY ) |
How we can learn what we want to know about M-theory |
M-theory is a quantum theory of gravity that admits an eleven dimensional Minkowskian vacuum with super-Poincare symmetry and no dimensionless coupling constant. I will review what was known about M-theory based on its relation to superstring theories, then comment on a number of open questions, and discuss how they can be addressed from holographic dualities. I will outline a strategy for extracting the S-matrix of M-theory from correlation functions of dual superconformal field theories, and in particular use it to recover the 11D R^4 coupling of M-theory from ABJM theory" |
April 25, 2018, 4:30 PM at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Ali Altug (BOSTON UNIVERSITY) |
Beyond endoscopy, the trace formula, and its relatives |
Since their introduction in 1967 the functoriality conjectures have been among the most central problems in modern number theory and the theory of automorphic forms. There have been lots of progress in the past 50 years however the conjectures in their general form are still wide open (even for GL(2)). Recently there have been various approaches to attack the functoriality conjectures in their general form. With a liberal use of terminology one may refer to these approaches with the umbrella name âbeyond endoscopyâ (the original paper of Langlands titled Beyond Endoscopy refers to a specific approach). In this talk I will start by describe the original approach of Langlands, where one would like to take the limit of an average of trace formulae over Hecke operators. I will discuss the small set of cases where we have proven results and talk about various intricate points about the internal structure of the trace formula and its interaction with the averages involved in beyond endoscopy. I will then talk about the interaction between the non-tempered terms in the spectral side and the geometric side of the trace formula, and a recent proposal of Arthurâs regarding this connection. Finally, if time permits, I would like to say a few words about the recent proposal of Sakellaridis regarding possible connections between the trace formula and relative trace formulae (specifically Kuznetsov formula) around beyond endoscopy, and some ongoing work related to it" |
April 25, 2018, 3:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Melody Chan (BROWN UNIVERSITY) |
Cohomology of M_g and the tropical moduli space of curves |
Joint work with SĂžren Galatius and Sam Payne. We study the rational cohomology of M_g in degree 4g-6, showing that it grows at least exponentially in g. I will explain the relationship with the tropical moduli space of curves, and the combinatorial topology behind our result" |
April 24, 2018, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Jiaping Wang (MINNESOTA) |
Structure at infinity for four dimensional shrinking Ricci Solitons |
Ricci solitons, as self-similar solutions to the Ricci flows, play a prominent role in the study of singularity formation of Ricci flows. In this talk, we are primarily concerned with four dimensional shrinking Ricci solitons and discuss joint work with Ovidiu Munteanu on their geometric structure at infinity" |
April 24, 2018, 2:00 - 3:00 PM at Science Center 232 |
| LOGIC SEMINAR |
Paul Baginski (FAIRFIELD UNIVERSITY ) |
Model Theoretic Advances for Groups With Bounded Chains of Centralizers |
A group G has bounded chains of centralizers (G is \M_C) if every chain of centralizers C_G(A_1) \leq C_G(A_2) \leq ... is finite. While this class of groups is interesting in its own right, within model theory MC groups have been examined because they strictly contain the class of stable groups. Stable groups robustly extend ideas from algebraic groups, such as dimension and independence, to a wider setting, including free groups. Stable groups gain much of their strength through a chain condition known as the Baldwin-Saxl chain condition, which implies the \M_C property as a special case. Several basic, but key, properties of stable groups have been observed by Wagner [4] and others to follow purely from the \M_C condition (this builds upon the work of Bludov [2], Khukhro [3], and others). These properties were, as one would expect, purely group-theoretic. From the perspective of logic, the class of \M_C groups should be unruly, since the MC condition is not first-order (unless one insists on a uniform bound to the lengths of the chains). Yet the speaker and Tuna Altınel [1] have uncovered that MC groups possess a logical property of stable groups as well, namely the abundance of definable nilpotent subgroups. We shall present this result and describe the current investigations for finding an analogue for solvable subgroups. (Joint work with Tuna Altınel, UniversitÂŽe Lyon 1) References [1] T. Altınel and P. Baginski, Definable envelopes of nilpotent subgroups of groups with chain conditions on centralizers, Proc. Amer. Math. Soc. 142 (2014), no. 5, 1497â1506. [2] V.V. Bludov, On locally nilpotent groups with the minimality condition for centralizers, Algebra Logika 37 (1998), 270â278. [3] E.I. Khukhro, On solubility of groups with bounded centralizer chains, Glasg. Math. J. 51 (2009), 49â54. [4] F.O. Wagner, Stable Groups, London Mathematical Society Lecture Note Series, 240. Cambridge University Press, 1997" |
April 24, 2018, 5:15 PM at Science Center 507 |
| CMSA MATHEMATICAL PHYSICS SEMINAR |
Baohua Fu (CHINESE ACADEMY OF SCIENCE) |
Equivariant compactifications of vector groups |
In 1954, Hirzebruch raised the problem to classify smooth compactifications of vector spaces with second Betti number 1, which is known till now up to dim 3. In 1999, Hassett-Tschinkel considered the equivariant version of this problem and obtained the classification up to dim. 3. I ll report recent progress on this (equivariant) problem. In particular, we obtain the classification up to dimension 5." |
April 23, 2018, 12:00 - 1:00 PM at CMSA Building, 20 garden St., G02 |
| CMSA MIRROR SYMMETRY SEMINAR |
Alan Thompson (CAMBRIDGE) |
Threefolds fibred by K3 surfaces and mirror symmetry |
I will present a number of results about the classification of threefolds fibred by K3 surfaces. These will start out very general but rapidly specialize, first to the case where the K3 surface fibres admit a certain class of lattice polarization, then further to the case where the threefold total space is Calabi-Yau. In the process, we will begin to notice links between this classification and the classification of Fano threefolds. This turns out not to be a coincidence, but a manifestation of mirror symmetry, relating Calabi-Yau threefolds fibred by K3 surfaces to Calabi-Yau threefolds constructed by gluing together Fanos and smoothing the result. This is joint work with C. Doran, A. Harder, R. Kooistra, and A. Novoseltsev" |
April 20, 2018, 10:45 AM - 12:00 PM at Sci Center 530 |
| RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Yas Despande (MIT) |
Phase transitions in estimating low-rank matrices |
Low-rank perturbations of Wigner matrices have been extensively studied in random matrix theory; much information about the corresponding spectral phase transition can be gleaned using these tools. In this talk, I will consider an alternative viewpoint based on tools from spin glass theory, and two examples that illustrate how these they yield information beyond traditional spectral tools. The first example is the stochastic block model, where we obtain a full information-theoretic picture of estimation. The second example demonstrates how side information alters the spectral threshold. It involves a new phase transition that interpolates between the Wigner and Wishart ensembles. This is based on joint works with Emmanuel Abbe, Andrea Montanari, Elchanan Mossel and Subhabrata Sen" |
April 20, 2018, 3:00 - 4:00 pm at CMSA Building, 20 Garden St, G02 |
| CMSA MIRROR SYMMETRY SEMINAR |
Xiaomeng Xu (MIT) |
Stokes phenomenon, quantum groups and 2d topological field theory |
This talk will include a general introduction to differential equations with singularities, and its relation with symplectic geometry and representation theory. In particular, we will focus on the Stokes phenomenon of linear systems of ordinary differential equations, and construct the braiding of Drinfeld-Jimbo quantum groups as quantum Stokes matrices. We then introduce an isomonodromic deformation of KnizhnikâZamolodchikov type equations, and relate its classical limit to the theory of Frobenius manifolds." |
April 20, 2018, 9:30 - 10:45 AM at Sci Center 530 |
| RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Carl Lucibello (MIT) |
The Random Perceptron Problem: thresholds, phase transitions, and geometry |
The perceptron is the simplest feedforward neural network model, the building block of the deep architectures used in modern machine learning practice. In this talk, I will review some old and new results, mostly focusing on the case of binary weights and random examples. Despite its simplicity, this model provides an extremely rich phenomenology: as the number of examples per synapses is increased, the system undergoes different phase transitions, which can be directly linked to solvers performances and to information theoretic bounds. A geometrical analysis of the solution space shows how two different types of solutions, akin to wide and sharp minima, have different generalization capabilities when presented with new examples. Solutions in dense clusters generalize remarkably better, partially closing the gap with Bayesian optimal estimators. Most of the results I will present were first obtained using non-rigorous techniques from spin glass theory and many of them haven t been rigorously established yet, although some big steps forward have been taken in recent years." |
April 20, 2018, 2:00 - 3:00 pm at CMSA Building, 20 Garden St, G02 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY ) |
Koszul Duality IV |
" |
April 19, 2018, 3:00 - 5:00 pm at Science Center 507 |
| HARVARD LOGIC COLLOQUIUM |
Alekos Kechris (CALTECH) |
Borel equivalence relations, cardinal algebras, and structurability |
The theory of Borel equivalence relations has been a very active area of research in descriptive set theory during the last 25 years. In this talk, I will give an introduction to this theory and then discuss how Tarskiâs concept of cardinal algebras, going back to the 1940âs, appears naturally in this theory. I will show how Tarskiâs theory can be used to discover new laws concerning the structure of Borel equivalence relations, which, rather surprisingly, have not been realized before. In addition, I will discuss the concept of structurability for equivalence relations and explain some of its implications concerning the algebraic structure of the reducibility order among such equivalence relations. (This is joint work with H. Macdonald and R. Chen." |
April 19, 2018, 4:00 â" 5:00 PM at Logic Center, Room 420, 2 Arrow Street |
| CMSA COLLOQUIUM |
Washington Taylor (MIT) |
On the fibration structure of known Calabi-Yau threefolds |
In recent years, there is increasing evidence from a variety of directions, including the physics of F-theory and new generalized CICY constructions, that a large fraction of known Calabi-Yau manifolds have a genus one or elliptic fibration. In this talk I will describe recent work with Yu-Chien Huang on a systematic analysis of the fibration structure of known toric hypersurface Calabi-Yau threefolds. Among other results, this analysis shows that every known Calabi-Yau threefold with either Hodge number exceeding 150 is genus one or elliptically fibered, and suggests that the fraction of Calabi-Yau threefolds that are not genus one or elliptically fibered decreases roughly exponentially with h_{11}. I will also make some comments on the connection with the structure of triple intersection numbers in Calabi-Yau threefolds" |
April 18, 2018, 4:30 PM at CMSA Building, 20 Garden St, G10 |
| INFORMAL GEOMETRY & DYNAMICS SEMINAR |
Kathryn Lindsey (BOSTON COLLEGE) |
Galois conjugates of PCF generalized beta-transformations |
The exponential of the topological entropy of any postcritically finite generalized beta-map of a real interval is an algebraic integer. Bill Thurston plotted all the Galois conjugates of a large set of âtent mapsâ (which are a type of generalized beta-map); the visually stunning resulting image showed a set with a rich and complicated geometric structure. A similar set exists for other types of generalized beta-maps. What can we prove about the structure of these sets? I will discuss the existence of holesâ in these sets and the continuity/dependence of the Galois conjugates on the topological entropy. In particular, I will focus on the persistenceâ of conjugates inside the unit disk as the entropy increases" |
April 18, 2018, 4:00 PM at Sci Center 530 |
| NUMBER THEORY SEMINAR |
John Voight (DARTMOUTH COLLEGE) |
On the paramodularity of typical abelian surfaces |
Generalizing the method of Faltings--Serre, we rigorously verify that certain abelian surfaces without extra endomorphisms are paramodular. To compute the required Hecke eigenvalues, we develop a method of specialization of Siegel paramodular forms to modular curves. This is joint work with Armand Brumer, Ariel Pacetti, Cris Poor, Gonzalo Tornaria, and David S. Yuen" |
April 18, 2018, 3:00 PM at Sci Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL ALGEBRAIC GEOMETRY SEMINAR |
Yefeng Shen (UNIVERSITY OF OREGON) |
LG/CY correspondence for Fermat elliptic curves |
We use holomorphic Cayley transformations of quasi-modular forms to realize a correspondence between Fan-Jarvis-Ruan-Witten invariants of the Fermat cubic polynomial and Gromov-Witten invariants of elliptic curves at all genus. Use tautological relations, we know the building blocks in both theories are just genus one invariants. The latter are governed by a Chazy equation, by using Belorousski-Pandharipandeâs relation on \bar{M}_{2,3}. The modular properties essentially follow from the Chazy equation and the initial values in FJRW theory can be calculated by Chang-Li-Li s cosection localization. This work is joint with J. Li and J. Zhou" |
April 17, 2018, 12:30 - 1:30 pm at CMSA Building, 20 Garden Street, G02 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
June Park (BROWN UNIVERSITY) |
Arithmetic of the moduli of quasimaps and the moduli of fibered algebraic surfaces with heuristics for counting curves over global fields |
We give enumerative study of the moduli of quasimaps in terms of the motive counts in Grothendieck ring of variety and relate it to the moduli of genus 0 twisted maps. As a corollary, we acquire the arithmetic of the moduli of elliptic surfaces over P^1. We also provide the family of asymptotics for the point counts of the moduli of genus g hyperelliptic fibrations over P^1 focusing upon the genus 2 case. In the end, we pass the acquired arithmetic invariants through the global fields analogy which renders new heuristics of Z_g(B) for counting the elliptic or hyperelliptic genus g curves over Q by the bounded height of discriminant. This is a report on work in progress with Kenneth Ascher, Dori Bejleri and Changho Han" |
April 17, 2018, 3:00 PM at MIT 4-153 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Yuan Gao (STONY BROOK UNIVERSITY) |
On the extension of the Viterbo functor |
In this talk I will describe deformations of wrapped Fukaya categories that arise from cobordisms, using which the Viterbo restriction functor can be extended to any exact cylindrical Lagrangian submanifold. I will also discuss how this extension can be viewed from the perspective of Lagrangian correspondences" |
April 16, 2018, 12:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MIRROR SYMMETRY SEMINAR |
Fabian Haiden (HARVARD UNIVERSITY ) |
Geometric flows, iterated logarithms, and balanced weight filtrations |
The long term behavior of certain gradient flows, both finite and infinite dimensional, is governed by an algebraically defined balanced weight-type filtration which provides a canonical refinement of the Harder-Narasimhan filtration. In recent joint work with Katzarkov, Kontsevich, and Pandit ( arXiv:1802.04123 ) we consider in detail the case of the Yang-Mills flow on the space of metrics on a holomorphic bundle over a Riemann surface, as well as a modified curve shortening flow on the cylinder. I will discuss these results and conjectural generalizations" |
April 13, 2018, 11:00am - 12:00pm at Science Center 530 |
| HARVARD LOGIC COLLOQUIUM |
Boris Zilber (UNIVERSITY OF OXFORD) |
Between Model Theory and Physics |
There are several important issues in physics which model theory have potential to help with. First of all, there is the issue of adequate language and formalism, and closely related to this there is a more specific problem of giving rigorous meanings to limits and integrals used by physicists. I will present a variation of âpositive model theoryâ which addresses these issues and discuss some progress in defining and calculating oscillating integrals of importance in quantum physics" |
April 12, 2018, 4:00 - 5:00 pm at Logic Center, 2 Arrow St, Rm 420 |
| CMSA HOMOLOGICAL MIRROR SYMMETRY FOCUSED LECTURE SERIES |
Mauricio Romo (INSTITUTE FOR ADVANCED STUDY) |
Gauged Linear Sigma Models, Supersymmetric Localization and Applications, Part 2 |
In this series of lectures I will review various results on connections between gauged linear sigma models (GLSM) and mathematics. I will start with a brief introduction on the basic concepts about GLSMs, and their connections to quantum geometry of Calabi-Yaus (CY). In the first lecture I will focus on nonperturbative results on GLSMs on closed 2-manifolds, which provide a way to extract enumerative invariants and the elliptic genus of some classes of CYs. In the second lecture I will move to nonperturbative results in the case where the worldsheet is a disk, in this case nonperturbative results provide interesting connections with derived categories and stability conditions. We will review those and provide applications to derived functors and local systems associated with CYs. If time allows we will also review some applications to non-CY cases (in physics terms, anomalous GLSMs). " |
April 12, 2018, 3:00 - 5:00 pm at CMSA Building, 20 Garden Street, G02 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS |
Pablo Parillo (MIT) |
Graph Structure in Polynomial Systems: Chordal Networks |
The sparsity structure of a system of polynomial equations or an optimization problem can be naturally described by a graph summarizing the interactions among the decision variables. It is natural to wonder whether the structure of this graph might help in computational algebraic geometry tasks (e.g., in solving the system). In this lecture we will provide a gentle introduction to this area, focused on the key notions of chordality and treewidth, which are of great importance in related areas such as numerical linear algebra, database theory, constraint satisfaction, and graphical models. In particular, we will discuss âchordal networksâ, a novel representation of structured polynomial systems that provides a computationally convenient decomposition of a polynomial ideal into simpler (triangular) polynomial sets, while maintaining its underlying graphical structure. As we will illustrate through examples from different application domains, algorithms based on chordal networks can significantly outperform existing techniques. Based on joint work with Diego Cifuentes (MIT)" |
April 11, 2018, 4:30 PM at CMSA building, 20 Garden St., G10 |
| NUMBER THEORY SEMINAR |
Dino J. Lorenzini (UNIVERSITY OF GEORGIA) |
Regular models of curves and wild quotient singularities |
The regular models of a curve are key objects in the study of the curve, as information about the special fiber of a regular model provides information about its generic fiber (such as rational points, index, Tamagawa number of the Jacobian, etc). Regular models can be constructed from normal models by resolving singularities. Every curve has a regular model obtained from the quotient of its semistable model by resolving only quotient singularities. The resolution of quotient singularities is well understood when the quotient is tame; in the context of models of curves, the quotient singularities are tame when the residue characteristic p is larger than 2g+1, where g is the genus of the curve. We will discuss in this talk the case where p<2g+2 and report on some new results on wild Z/pZ-quotient singularities of surfaces" |
April 11, 2018, 3:00 PM at Science Center 507 |
| INFORMAL GEOMETRY & DYAMICS SEMINAR |
Corey Bregman (BRANDEIS UNIVERSITY) |
Kaehler groups and surface bundles |
A question going back to Serre asks which groups arise as fundamental groups of smooth complex projective varieties, or more generally, compact Kaehler manifolds. These groups are called Kaehler groups. We first give a brief overview of this subject and some known results, then discuss Kaehler groups arising from surface bundles." |
April 11, 2018, 4:00 PM at Science Center 530 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Eric Larson (MIT) |
The Maximal Rank Conjecture |
Let C be a general curve of genus g, embedded via a general linear series of degree d in P^r. In this talk, we determine the Hilbert function of C" |
April 10, 2018, 3:00 PM at Science Center 507 |
| CMSA HOMOLOGICAL MIRROR SYMMETRY FOCUSED LECTURE SERIES |
Mauricio Romo (INSTITUTE FOR ADVANCED STUDY) |
Gauged Linear Sigma Models, Supersymmetric Localization and Applications, Part 1 |
In this series of lectures I will review various results on connections between gauged linear sigma models (GLSM) and mathematics. I will start with a brief introduction on the basic concepts about GLSMs, and their connections to quantum geometry of Calabi-Yaus (CY). In the first lecture I will focus on nonperturbative results on GLSMs on closed 2-manifolds, which provide a way to extract enumerative invariants and the elliptic genus of some classes of CYs. In the second lecture I will move to nonperturbative results in the case where the worldsheet is a disk, in this case nonperturbative results provide interesting connections with derived categories and stability conditions. We will review those and provide applications to derived functors and local systems associated with CYs. If time allows we will also review some applications to non-CY cases (in physics terms, anomalous GLSMs). " |
April 10, 2018, 3:00 - 5:00 pm at CMSA Building, 20 Garden Street, G02 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Brandon B. Meredith (EMBRY-RIDDLE AERONAUTICAL UNIVERSITY) |
Mirror Symmetry on Toric Surfaces via Tropical Geometry |
Mirror symmetry is a curious duality, first noticed by physicists and then excitedly embraced by mathematicians, between certain manifolds and their mirror spaces. This talk considers mirror symmetry on toric surfaces, which are varieties with certain convenient combinatorial properties and include many well-known surfaces. These surfaces are especially suited to being exploited by tropical geometry, which is a form of algebraic geometry over the tropical semi-ring. This talk will discuss the generalization of mirror symmetry to all toric surfaces (expanded from just the Fano case) following the Gross-Siebert Program wherein singularities are added to the tropical picture in order to pull more curves into view." |
April 09, 2018, 12:00 PM at CMSA Building, 20 Garden Street, G02 |
| THURSDAY SEMINAR |
Gijs Heuts (UTRECHT UNIVERSITY) |
Coalgebras and the Goodwillie tower of the Bousfield-Kuhn functor |
" |
April 05, 2018, 3:00 - 5:00 pm at Science Center 507 |
| INFORMAL GEOMETRY & DYNAMICS SEMINAR |
Francis Bonahon (UNIVERSITY OF SOUTHERN CALIFORNIA) |
What to do when you cannot confine your planes? TeichmĂŒller spaces of non-compact Riemann surfaces |
Traditionally, the Milnor-Schwartz states that the large scale geometry of the universal cover of a compact space is determined by that of its fundamental group. However, there exists interesting non-compact spaces, for which additional uniformity conditions need to be introduced. I will discuss the case of non-compact Riemann surfaces, and the construction of a Thurston-like boundary for their TeichmĂŒller spaces. This is joint work with Dragomir Saric" |
April 04, 2018, 4:00 pm at Science Center 530 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Ramesh Narayan (DEPARTMENT OF ASTRONOMY, HARVARD UNIVERSITY) |
Black Holes and Naked Singularities *Postponed from 3/21/18* |
Black Hole solutions in General Relativity contain Event Horizons and Singularities. Astrophysicists have discovered two populations of black hole candidates in the Universe: stellar-mass objects with masses in the range 5 to 30 solar masses, and supermassive objects with masses in the range million to several billion solar masses. There is considerable evidence that these objects have Event Horizons. It thus appears that astronomical black hole candidates are true Black Holes. Direct evidence for Singularities is much harder to obtain since, at least in the case of Black Holes, the Singularities are hidden inside the Event Horizon. However, General Relativity also permits Naked Singularities which are visible to external observers. Toy Naked Singularity models have been constructed, and some observational features of accretion flows in these spacetimes have been worked out" |
April 04, 2018, 4:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| NUMBER THEORY SEMINAR |
Jennifer Balakrishnan (BOSTON UNIVERSITY) |
Effective aspects of quadratic Chabauty |
I will describe how p-adic heights can be used to find rational or integral points on certain curves of genus at least 2, in the spirit of Kim s nonabelian Chabauty program. This is based on joint work with Amnon Besser, Netan Dogra, Steffen Mueller, Jan Tuitman, and Jan Vonk" |
April 04, 2018, 3:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Curtis McMullen (HARVARD UNIVERSITY) |
Billiards, quadrilaterals and moduli spaces |
" |
April 03, 2018, 3:00 PM at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Marcel Bischoff (OHIO UNIVERSITY) |
Quantum Symmetries and Conformal Nets |
A (rational) conformal net is a mathematical description of a chiral conformal field theory. Via its representation theory, it gives rise to a unitary modular tensor category, which gives a topological field theory and is a model for topological phases of matter. I will introduce a notion of quantum operations on a conformal net generalizing global symmetries which form a group. This gives a framework for quantum symmetries which also can be understood in the setting of unitary modular tensor categories. I will discuss how results involving global symmetries can be generalized" |
April 03, 2018, 4:00 PM at Jefferson 356 |
| LOGIC SEMINAR |
Warren Goldfarb () |
Two Notes on Weak Arithmetic |
Two results are proved: 1. Presburger Arithmetic is not finitely axiomatizable, and 2. There is a consistent recursive extension of Robinson Arithmetic that decides every diophantine sentence" |
April 03, 2018, 5:15 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Cheuk-Yu Mak (UNIVERSITY OF CAMBRIDGE) |
Discrete Legendre transform and tropical multiplicity from symplectic geometry |
There is a long history of enumerative invariants and related problems in mirror symmetry. One powerful approach to understand it is given by counting tropical curves with multiplicities. Tropical multiplicity formula in dimension two can be easily understood but the generalization to higher dimensions is less transparent. In this talk, we explain the relation between tropical multiplicities and the torsion of the first homology group of the associated Lagrangian submanifolds/cell complexes. It is a preparation talk for the talk Tropically constructed Lagrangians in mirror quintic threefolds, which explains the construction of associated Lagrangian submanifolds using degeneration of hypersurface in toric orbifold. It is a joint work with Helge Ruddat" |
April 02, 2018, 12:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Zhiwei Zheng (TSINGHUA UNIVERSITY) |
Moduli Spaces of Cubic Fourfolds with Automorphisms |
The period map is a powerful tool to study moduli spaces of many kinds of objects related to K3 surfaces and cubic fourfolds, thanks to the global Torelli theorems. In this spirit, Allcock-Carlson-Toledo (2003) realized the moduli of smooth cubic threefolds as an arrangement complement in a 10-dimensional arithmetic ball quotient and studied its compactifications (both GIT and Satake-Baily-Borel) and recently, Laza-Pearlstein-Zhang studied the moduli of pairs consisting of a cubic threefold and a hyperplane section. I will talk about a joint work with Chenglong Yu about the moduli space of cubic fourfolds with automorphism group specified, and its compactification. As examples, we recover some of the works by Allcock-Carlson-Toledo and Laza-Pearlstein-Zhang mentioned above" |
March 30, 2018, 9:30 - 11:00 am at Science Center 530 |
| SPECIAL DIFFERENTIAL GEOMETRY SEMINAR |
D.H. Phong (COLUMBIA UNIVERSITY) |
The Anomaly Flow and Fu-Yau Hessian Equations |
The Hull-Strominger system is a system of equations in 3 complex dimensions arising from string theory, but which is particularly interesting from the point of view of both non-K\âahler geometry and partial differential equations: there, metrics are not required to be K\âahler, but only conformally balanced, and they must satisfy a curvature condition which is quadratic in the curvature tensor. A key difficulty is to implement the conformally balanced condition, in the absence of a $d-\bar d$ Lemma as in K\âahler geometry. The Anomaly Flow is a flow of metrics designed to achieve this. However, in doing so, it has to forego properties which are normally desirable in fully non-linear PDE theory, such as concavity. A crucial test case is the case of Calabi-Eckmann fibrations, solved by J.X. Fu and S.T. Yau in 2006 by elliptic methods. We show that the Anomaly Flow performs even better than elliptic methods in this case. In fact, the resulting techniques also lead to the solution of a whole family of Hessian equations in arbitrary dimensions, of which the generalization proposed by Fu-Yau of their 2006 equation is just the simplest example. This is joint work with S. Picard and X.W. Zhang" |
March 30, 2018, 3:00 - 4:15 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MIRROR SYMMETRY SEMINAR |
Yu-Wei Fan (HARVARD UNIVERSITY) |
Systoles, Special Lagrangians, and Bridgeland stability conditions |
Motivated by Loewner s torus inequality which relates the least length of a non-contractible loop (systole) on a torus to its volume, one can ask whether there is a higher-dimensional analogue, with torus replaced by Calabi-Yau manifolds and loops replaced by special Lagrangian submanifolds. We attempt to answer this question in the case of mirror quartic K3 surfaces via mirror symmetry and Bridgeland stability conditions. We define the notion of categorical systole and systolic ratio of a Bridgeland stability condition, and show that the aforementioned question is related to a purely lattice-theoretic problem. We prove that the answer to the lattice-theoretic problem is finite and give an explicit upper bound" |
March 30, 2018, 11:00 - 12:00 at Science Center 530 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Koszul Duality II |
" |
March 29, 2018, 3:00 - 5:00 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Andrea Montanari (STANFORD UNIVERSITY) |
A Mean Field View of the Landscape of Two-Layers Neural Networks |
Multi-layer neural networks are among the most powerful models in machine learning and yet, the fundamental reasons for this success defy mathematical understanding. Learning a neural network requires to optimize a highly non-convex and high-dimensional objective (risk function), a problem which is usually attacked using stochastic gradient descent (SGD). Does SGD converge to a global optimum of the risk or only to a local optimum? In the first case, does this happen because local minima are absent, or because SGD somehow avoids them? In the second, why do local minima reached by SGD have good generalization properties? We consider a simple case, namely two-layers neural networks, and prove that --in a suitable scaling limit-- the SGD dynamics is captured by a certain non-linear partial differential equation. We then consider several specific examples, and show how the asymptotic description can be used to prove convergence of SGD to network with nearly-ideal generalization error. This description allows to `average-out some of the complexities of the landscape of neural networks, and can be used to capture some important variants of SGD as well. [Based on joint work with Song Mei and Phan-Minh Nguyen" |
March 28, 2018, 4:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| INFORMAL GEOMETRY & DYAMICS SEMINAR |
Curtis McMullen (HARVARD UNIVERSITY) |
Planes immersed in hyperbolic 3-manifolds |
" |
March 28, 2018, 4:00 PM at Science Center 530 |
| NUMBER THEORY SEMINAR |
Chuck Doran (UNIVERSITY OF ALBERTA AND ICERM) |
Arithmetic MIrror Symmetry for K3 Pencils and Hypergeometric Decomposition |
We will begin with an introduction to Calabi-Yau geometry and survey various forms of mirror symmetry, with an eye towards possible applications in arithmetic geometry. Specializing to a particular construction of mirror pairs, we analyze the factorization of the zeta function for certain symmetric K3 quartic pencils and the relationship with hypergeometric equations" |
March 28, 2018, 3:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Allen Knutson (CORNELL UNIVERSITY) |
Deformations of normal crossings |
The standard normal crossings divisor on A^n is given by the vanishing of the degree n polynomial prod_i(x_i). Let p be a polynomial with this as leading term, and consider the stratification it generates (by taking components, intersections thereof, and iterating). I ll prove some very nice properties of this stratification (via char p techniques), and show that Bruhat cells naturally come with such good stratifications. I ll explain a sense in which the Bruhat stratifications form an order ideal in the family of all such stratifications, and give a natural example that isn t itself Bruhat. Finally, I ll give examples of stratified projective varieties covered with charts isomorphic to Bruhat cells, such as Grassmannians and wonderful compactifications of groups" |
March 27, 2018, 3:00 PM at Science Center 507 |
| LOGIC SEMINAR |
Marcos Mazari Armida (CARNEGIE MELLON UNIVERSITY) |
Non-forking w-good frames |
The central notion of Shelah s book on AEC s is that of a good $\lambda$-frame, which is a forking-like notion for types of singletons in abstract elementary classes. In this talk, we will introduce the weaker notion of a w-good $\lambda$-frame. We show that the existence of a w-good frame implies the existence of larger models and show how to extend w-good frames under tameness and amalgamation. As an application(under some cardinal arithmetic hypothesis) we construct a model of size $\lambda^{+++}$ under the assumption of $\lambda$ and $\lambda^+$ categoricity, few models in $\lambda^{++}$ and $(\lambda, \lambda^+)$-tameness" |
March 27, 2018, 5:15 pm at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Feng Xu (UNIVERSITY OF CALIFORNIA, RIVERSIDE) |
On Questions Around the Reconstruction Program |
Given a unitary Modular Tensor Category M, the reconstruction program asks for the construction of a rational conformal field theory such that its representation category is isomorphic to M. This is a low dimensional version of the Dolpicher-Roberts/Deligne theory which is much richer due to nontrivial representations of braid group, and is strongly motivated by recent developments in subfactor theory. In this talk we will describe questions around this program and present recent progress. " |
March 27, 2018, 4:00 PM at Jefferson 356 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Yi Xie (SCGP) |
Surgery, Polygons and Instanton Floer homology |
Many classical numerical invariants (including Casson invariant, Alexander polynomial and Jones polynomial) for 3-manifolds or links satisfy surgery formulas relating three different 3-manifolds or links. All those invariants are categorified by certain Floer homologies (or Khovanov homology) which also satisfy so-called surgery exact triangles. In this talk I will discuss the notion of surgery exact polygons which appears in the SU(N)-instanton Floer homology theory. Roughly speaking, an n-gon is a relation among the Floer homology groups of 3-manifolds obtained by n different Dehn surgeries on a fixed knot. It generalizes the surgery exact triangle in SU(2)-instanton Floer homology. If time permits, I will also talk about a homological-mirror-symmetry-type conjecture which motivates this work. This is joint work with Lucas Culler and Aliakbar Daemi. " |
March 26, 2018, 12:00 PM at CMSA Building, 20 Garden Street, G02 |
| MATHEMATICAL PHYSICS SEMINAR |
Wei Zhang (MIT) |
Superpositivity of L-functions and âcompletion of squareâ |
We explain how the Riemann hypothesis and its generalization imply the positivity of the special values of all derivatives of normalized L-functions. This raises a question: can one interpret these positive values as squares? We present some examples of such interpretations, in the joint work with Xinyi Yuan and Shouwu Zhang over number fields on the Gross-Zagier formula, and with Zhiwei Yun over function fields on the Higher Gross-Zagier formula respectively" |
March 23, 2018, 3:00 PM at Jefferson 250 |
| CMSA SPECIAL LECTURE SERIES ON QUANTUM COHOMOLOGY, NAKAJIMA VARETIES AND QUANTUM GROUPS |
Artan Sheshmani (QGM & CMSA) |
GW Invariants via Quantum Cohomology |
The Quintic threefold cas" |
March 22, 2018, 1:00 - 3:00 pm at CMSA Building, 20 Garden Street, Room G10 |
| HARVARD LOGIC COLLOQUIUM |
Donald Martin (UCLA) |
Cantor's Grundlagen |
Cantorâs early (1883) Grundlagen einer allgemeinen Mannigfaltigkeitslehre is badly organized and has important errors and omissions. Nevertheless it is rich in content, and its concepts are in some ways superior to Cantorâs later ones. I will mainly concentrate on a few aspects of Grundlagen: (1) what might be called Cantorâs quasi- axiomatic, iterative account of ordinal numbers; (2) the role that something like a Replacement Axiom plays in this account; (3) the relation between the Grundlagen notion of absolute infinity and Cantorâs later notion of inconsistent multiplicities." |
March 22, 2018, 4:00 - 5:00 pm at Logic Center, 2 Arrow St, Rm 420 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Koszul Duality |
" |
March 22, 2018, 3:00 - 5:00 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Ramesh Narayan (DEPARTMENT OF ASTRONOMY, HARVARD UNIVERSITY) |
Black Holes and Naked Singularities |
Black Hole solutions in General Relativity contain Event Horizons and Singularities. Astrophysicists have discovered two populations of black hole candidates in the Universe: stellar-mass objects with masses in the range 5 to 30 solar masses, and supermassive objects with masses in the range million to several billion solar masses. There is considerable evidence that these objects have Event Horizons. It thus appears that astronomical black hole candidates are true Black Holes. Direct evidence for Singularities is much harder to obtain since, at least in the case of Black Holes, the Singularities are hidden inside the Event Horizon. However, General Relativity also permits Naked Singularities which are visible to external observers. Toy Naked Singularity models have been constructed, and some observational features of accretion flows in these spacetimes have been worked out" |
March 21, 2018, 4:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| NUMBER THEORY SEMINAR |
Ananth Shankar (MIT) |
Exceptional splitting of reductions of abelian surfaces |
Heuristics based on the Sato--Tate conjecture suggest that an abelian surface defined over a number field has infinitely many places of split reduction. We will discuss this problem over number fields and function fields, mainly focusing on the case when the surface has real multiplication. This is joint work with Tang and Maulik-Tang" |
March 21, 2018, 3:00 pm at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Kenneth Bromberg (UNIVERSITY OF UTAH) |
Bounds on renormalized volume and the volume of the convex core |
A conformally compact hyperbolic 3-manifold will have infinite volume (at least if the conformal boundary is non-empty). Krasnov and Schlenker defined a renormalized volume (motivated by work of Graham and Witten on conformally compact Einstein manifolds) that assigns a finite volume to such manifolds. This defines a function on the space of all conformally compact hyperbolic 3-manifolds. We will discuss the gradient flow of this function which seems to reveal, in ways we will make precise, the geometry of the manifolds. In particular, we will show how this gradient flow can be used to give bounds on the volume of the convex core of the manifolds. This is joint work with M. Bridgeman and J. Brock" |
March 21, 2018, 4:00 pm at Science Center 530 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Tathagata Basak (IOWA STATE) |
A complex ball quotient and the monster |
We shall talk about an arithmetic lattice M in PU(13,1) acting on the the unit ball B in thirteen dimensional complex vector space. Let X be the space obtained by removing the hypersurfaces in B that have nontrivial stabilizer in M and then quotienting the rest by M. The fundamental group G of the ball quotient X is a complex hyperbolic analog of the braid group. We shall state a conjecture that relates this fundamental group G and the monster simple group and describe our results (joint with D. Allcock) towards this conjecture. The discrete group M is related to the Leech lattice and has generators and relations analogous to Weyl groups. Time permitting, we shall give a second example in PU(9,1) related to the Barnes-Wall lattice for which there is a similar story" |
March 20, 2018, 3:00 PM at MIT 4-153 |
| CMSA SPECIAL LECTURE SERIES ON QUANTUM COHOMOLOGY, NAKAJIMA VARETIES AND QUANTUM GROUPS |
Artan Sheshmani (QGM & CMSA) |
GW Invariants via Quantum Cohomology |
The P^2 cas" |
March 20, 2018, 1:00 - 3:00 pm at CMSA Building, 20 Garden Street, Room G10 |
| MATHEMATICAL PHYSICS SEMINAR |
Jurg Frolich (ETH ZĂŒRICH) |
Physics in 2Dâ"from Kosterlitz-Thouless Transition to Topological Insulators |
A survey of âPhysics in 2Dâ is presented: The Mermin-Wagner-McBryan-Spencer Theorem is recalled. Crucial ideas (among others, energy-entropy arguments for defects) in a proof of existence of the K-T transition in the 2D classical XY model are highlighted. Subsequently, the Topological-Field-Theory Approach to the Fractional Quantum Hall Effect and to 2D time-reversal invariant Topological Insulators with chiral edge spin-currents (1993) is described. The roles of anomaly cancellation, of braid statistics and of bulk-edge duality in the analysis of such systems are explained. Some general conclusions about Physics in two dimensions are outlined" |
March 20, 2018, 4:00 PM at Jefferson 356 |
| DIFFERENTIAL GEOMETRY SEMINAR |
TamĂĄs Darvas (UNIVERSITY OF MARYLAND) |
Complex Monge-Ampere equations with prescribed singularity |
Given a Kahler manifold, finding smooth solutions to global complex Monge-Ampere equations goes back to Yau s solution of the Calabi conjecture in the seventies. In joint work with E. Di Nezza and C.H. Lu, we proposed to solve this same equation with the added constraint that the potential has prescribed singularity type. As it turns out, this problem is well posed only for a very specific class of model type singularities, and we solve the corresponding equation. As an application, we resolve the log-concavity conjecture for volumes of positive currents" |
March 20, 2018, 3:45 pm **change in time** at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Emanuel Scheidegger (ALBERT LUDWIGS UNIVERSITY OF FREIBURG) |
From Gauged Linear Sigma Models to Landau-Ginzburg orbifolds via central charge functions |
We review the categorical description of the Calabi-Yau/Landau-Ginzburg correspondence in terms of equivariant matrix factorizations in the gauged linear sigma model. We present the hemisphere partition function as a central charge function in the gauged linear sigma model. We study the relation of this function in the LG phase to the Chern character of equivariant matrix factorizations of the LG potential and generating functions of FJRW invariants" |
March 19, 2018, 12:00 PM at CMSA Building, 20 Garden Street, G02 |
| CMSA HOMOLOGICAL MIRROR SYMMETRY FOCUSED LECTURE SERIES |
Dmytro Shklyarov (TECHNISCHE UNIVERSITĂ€T CHEMNITZ) |
On categories of matrix factorizations and their homological invariants |
The talks will cover the following topics: 1. Matrix factorizations as D-branes. According to physicists, the matrix factorizations of an isolated hypersurface singularity describe D-branes in the Landau-Ginzburg (LG) B-model associated with the singularity. The talk is devoted to some mathematical implications of this observation. I will start with a review of open-closed topological field theories underlying the LG B-models and then talk about their refinements. 2. Semi-infinite Hodge theory of dg categories. Homological mirror symmetry asserts that the âclassicalâ mirror correspondence relating the number of rational curves in a CY threefold to period integrals of its mirror should follow from the equivalence of the derived Fukaya category of the first manifold and the derived category of coherent sheaves on the second one. The classical mirror correspondence can be upgraded to an isomorphism of certain Hodge-like data attached to both manifolds, and a natural first step towards proving the assertion wo" |
March 15, 2018, 3:00 - 4:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CMSA SPECIAL LECTURE SERIES ON QUANTUM COHOMOLOGY, NAKAJIMA VARETIES AND QUANTUM GROUPS |
Artan Sheshmani (QGM & CMSA) |
Quantum Cohomology |
WDVV equatio" |
March 15, 2018, 1:00 - 3:00 pm at CMSA Building, 20 Garden Street, Room G10 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Ariyan Javanpeykar (JOHANNES GUTENBERG UNIVERSITY MAINZ) |
Arithmetic, algebraic, and analytic hyperbolicity |
In the first part of this talk we will discuss different notions of hyperbolicity for algebraic varieties which are conjecturally related by conjectures of Green-Griffiths, Lang, and Vojta. Then, we introduce an analytic notion of hyperbolicity, which interpolates between being Brody hyperbolic and hyperbolically embedabble. I hope to give a survey of several known results in the first part. In the second part I will focus on arithmetic questions. For instance, Scholl proved that the moduli of del Pezzo surfaces is arithmetically hyperbolic. In joint work with Daniel Loughran, we investigate the analogous question for Fano threefolds. For instance, we show that the moduli of Fano threefolds is not arithmetically hyperbolic, by (explicitly) constructing an abelian surface which sits inside this moduli" |
March 13, 2018, 3:00 PM at MIT 4-153 |
| CMSA HOMOLOGICAL MIRROR SYMMETRY FOCUSED LECTURE SERIES |
Dmytro Shklyarov (TECHNISCHE UNIVERSITĂ€T CHEMNITZ) |
On categories of matrix factorizations and their homological invariants |
The talks will cover the following topics: 1. Matrix factorizations as D-branes. According to physicists, the matrix factorizations of an isolated hypersurface singularity describe D-branes in the Landau-Ginzburg (LG) B-model associated with the singularity. The talk is devoted to some mathematical implications of this observation. I will start with a review of open-closed topological field theories underlying the LG B-models and then talk about their refinements. 2. Semi-infinite Hodge theory of dg categories. Homological mirror symmetry asserts that the âclassicalâ mirror correspondence relating the number of rational curves in a CY threefold to period integrals of its mirror should follow from the equivalence of the derived Fukaya category of the first manifold and the derived category of coherent sheaves on the second one. The classical mirror correspondence can be upgraded to an isomorphism of certain Hodge-like data attached to both manifolds, and a natural first step towards proving the assertion wo" |
March 13, 2018, 3:00 - 4:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CMSA SPECIAL LECTURE SERIES ON QUANTUM COHOMOLOGY, NAKAJIMA VARETIES AND QUANTUM GROUPS |
Artan Sheshmani (QGM & CMSA) |
Quantum Cohomology |
GW potentia" |
March 13, 2018, 1:00 - 3:00 pm at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MIRROR SYMMETRY SEMINAR |
Guangbo Xu (PRINCETON UNIVERSITY) |
Open quantum Kirwan map |
(Joint work with Chris Woodward) Consider a Lagrangian submanifold $\bar L$ in a GIT quotient $\bar X = X//G$. Besides the usual Fukaya $A_\infty$ algebra $Fuk(\bar L)$ defined by counting holomorphic disks, another version, called the quasimap Fukaya algebra $Fuk^K(L)$, is defined by counting holomorphic disks in $X$ modulo group action. Motivated from the closed string quantum Kirwan map studied by Ziltener and Woodward, as well as the work of Fukaya--Oh--Ohta--Ono, Chan--Lau--Leung--Tseng, we construct an open string version of the quantum Kirwan map. This is an $A_\infty$ morphism from $Fuk^K(L)$ to a bulk deformation of $Fuk(\bar L)$. The deformation term is defined by counting affine vortices (point-like instantons) in the gauged sigma model, while the $A_\infty$ morphism is defined by counting point-like instantons with Lagrangian boundary condition. It has several useful consequences. For example, the weakly unobstructedness of $Fuk^K(L)$ (which is easy to check) implies the weak unobstructedness of $Fuk(\bar L)$ after bulk deformation (which is hard to check). It recovers the âopen mirror theoremâ of Chan--Lau--Leung--Tseng for semi-Fano toric manifolds which says the Lagrangian Floer potential coincides with the Hori--Vafa potential after a coordinate change, and extends to general toric manifolds" |
March 09, 2018, 9:30 - 11:00 am at Science Center 530 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MIRROR SYMMETRY SEMINAR |
Shinobu Hosono (GAKUSHUIN UNIVERSITY) |
Gluing monodromy nilpotent cones of a family of K3 surfaces |
I consider a K3 surface which is known as Cayley model of Reye congruences, and construct its mirror family. This mirror family turns out to have three degeneration points (LCSLs), for each of which we can define monodromy nilpotent cones. I will show that these nilpotent cones are naturally glued together to make a larger cone which can be identified with the ample cone of the Cayley model" |
March 09, 2018, 11:00 - 12:00 at Science Center 530 |
| THURSDAY SEMINAR |
Sander Kupers (HARVARD UNIVERSITY) |
The work of Arone-Dwyer |
" |
March 08, 2018, 3:00 - 5:00 pm at Science Center 507 |
| HARVARD LOGIC COLLOQUIUM |
Dima Sinapova (UNIVERSITY OF ILLINOIS AT CHICAGO) |
Stronger tree properties and the SCH |
Stronger tree properties capture the combinatorial essence of large cardinals. More precisely, for an inaccessible cardinal Îș, Îș has the strong, resp. super, tree property if and only if Îș is strongly compact, resp. supercompact. An old project in set theory is to get the tree property at every regular cardinal greater than Ï1. Even more ambitiously, can we get stronger tree properties at all regular cardinals above Ï1? A positive answer would require many violations the singular cardinal hypothesis (SCH). This leads to the question whether the strong tree property implies SCH above. A positive answer would be an analogue of Solovayâs theorem that SCH holds above a strongly compact cardinal. We will show that consistently we can have the super tree property (ITP) at some λ together with failure of SCH above λ, for a non limit singular cardinal. The case of a limit singular cardinal is still open. We will also show that there is a model where ITP holds at the double successor of a singular and there are club many non internally unbounded models. This is another result in the direction of showing that ITP does not imply SCH above. Finally, we will discuss the situation for smaller cardinals like â”Ï+2. This is joint work with Sherwood Hachtman, University of Illinois at Chicago" |
March 08, 2018, 4:00 - 5:00 pm at Logic Center, 2 Arrow St, Rm 420 |
| CMSA SPECIAL LECTURE SERIES ON QUANTUM COHOMOLOGY, NAKAJIMA VARETIES AND QUANTUM GROUPS |
Artan Sheshmani (QGM & CMSA) |
Quantum Cohomology |
Big Quantum Cohomology I" |
March 08, 2018, 1:00 - 3:00 pm at CMSA Building, 20 Garden Street, Room G10 |
| CMSA HOMOLOGICAL MIRROR SYMMETRY FOCUSED LECTURE SERIES |
Dmytro Shklyarov (TECHNISCHE UNIVERSITĂ€T CHEMNITZ) |
On categories of matrix factorizations and their homological invariants |
The talks will cover the following topics: 1. Matrix factorizations as D-branes. According to physicists, the matrix factorizations of an isolated hypersurface singularity describe D-branes in the Landau-Ginzburg (LG) B-model associated with the singularity. The talk is devoted to some mathematical implications of this observation. I will start with a review of open-closed topological field theories underlying the LG B-models and then talk about their refinements. 2. Semi-infinite Hodge theory of dg categories. Homological mirror symmetry asserts that the âclassicalâ mirror correspondence relating the number of rational curves in a CY threefold to period integrals of its mirror should follow from the equivalence of the derived Fukaya category of the first manifold and the derived category of coherent sheaves on the second one. The classical mirror correspondence can be upgraded to an isomorphism of certain Hodge-like data attached to both manifolds, and a natural first step towards proving the assertion wo" |
March 08, 2018, 3:00 - 4:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CMSA HOMOLOGICAL MIRROR SYMMETRY FOCUSED LECTURE SERIES |
Adam Jacob (UC DAVIS ) |
The deformed Hermitian-Yang-Mills equation (continued) |
In this series I will discuss the deformed Hermitian-Yang-Mills equation, which is a complex analogue of the special Lagrangian graph equation of Harvey-Lawson. I will describe its derivation in relation to the semi-flat setup of SYZ mirror symmetry, followed by some basic properties of solutions. Later I will discuss methods for constructing solutions, and relate the solvability to certain geometric obstructions. Both talks will be widely accessible, and cover joint work with T.C. Collins and S.-T. Yau" |
March 08, 2018, 4:00-5:00 pm at CMSA Building, 20 Garden St., G10 |
| INFORMAL GEOMETRY & DYAMICS SEMINAR |
Jesse Wolfson & Benson Farb (UC IRVINE & UNIVERSITY OF CHICAGO) |
The geometry of Hilbert's 13th problem |
" |
March 07, 2018, 4:00 PM at Science Center 530 |
| NUMBER THEORY SEMINAR |
Jesse Wolfson (UNIVERSITY OF CALIFORNIA, IRVINE) |
The theory of resolvent degree, after Hamilton, Klein, Hilbert, and Brauer |
Resolvent degree is an invariant of a branched cover which quantifies how hard is it to specify a point in the cover given a point under it in the base. Historically, this was applied to the branched cover $\P^n/S_{n-1} \to \P^n/S_n$, from the moduli of degree n polynomials with a specified root to the moduli of degree n polynomials. Classical enumerative problems and congruence subgroups provide two additional sources of branched covers to which this invariant applies. In ongoing joint work with Benson Farb, and with Benson Farb and Mark Kisin, we develop the theory of resolvent degree as an extension of Buhler and Reichstein s theory of essential dimension. We apply this theory to systematize an array of classical results and to relate the complexity of seemingly different problems such as finding roots of polynomials, lines on cubic surfaces, and level structures on Jacobians" |
March 07, 2018, 3:00 PM at Science Center 507 * please also note the talk at the Informal Geometry & Dynamics Seminar* |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Richard Kenyon (BROWN UNIVERSITY) |
Harmonic functions and the chromatic polynomial |
When we solve the Dirichlet problem on a graph, we look for a harmonic function with fixed boundary values. Associated to such a harmonic function is the Dirichlet energy on each edge. One can reverse the problem, and ask if, for some choice of conductances on the edges, one can find a harmonic function attaining any given tuple of edge energies. We show how the number of solutions to this problem is related to the chromatic polynomial, and also discuss some geometric applications. This talk is based on joint work with Aaron Abrams and Wayne Lam" |
March 07, 2018, 4:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| CMSA SPECIAL LECTURE SERIES ON QUANTUM COHOMOLOGY, NAKAJIMA VARETIES AND QUANTUM GROUPS |
Artan Sheshmani (QGM & CMSA) |
Quantum Cohomology |
Big Quantum Cohomology " |
March 06, 2018, 1:00 - 3:00 pm at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS HOMOLOGICAL MIRROR SYMMETRY |
Adam Jacob (UC DAVIS) |
The deformed Hermitian-Yang-Mills equation |
In this series I will discuss the deformed Hermitian-Yang-Mills equation, which is a complex analogue of the special Lagrangian graph equation of Harvey-Lawson. I will describe its derivation in relation to the semi-flat setup of SYZ mirror symmetry, followed by some basic properties of solutions. Later I will discuss methods for constructing solutions, and relate the solvability to certain geometric obstructions. Both talks will be widely accessible, and cover joint work with T.C. Collins and S.-T. Yau" |
March 06, 2018, 4:00 - 5:00 pm at CMSA Building, 20 Garden St., G10 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Michael Kemeny (STANFORD UNIVERSITY) |
Betti numbers of the canonical ring of a curve |
Understanding the structure of the canonical ring of a curve has long been of fundamental interest in algebraic geometry. This structure can be encoded in certain invariants called the graded Betti numbers. A conjecture of Mark Green (now essentially a theorem of Voisin) predicts exactly which of these invariants vanish, but little has been known about the values of those Betti numbers which do not vanish, and what geometric information they might contain. We will explain an approach to these problems using Hurwitz spaces and state a result proving that the extremal Betti number counts minimal pencils, modulo transversality hypotheses (verifying a philosophy of Schreyer)" |
March 06, 2018, 3:00 PM at MIT 4-153 |
| CMSA HOMOLOGICAL MIRROR SYMMETRY FOCUSED LECTURE SERIES |
Dmytro Shklyarov (TECHNISCHE UNIVERSITĂ€T CHEMNITZ) |
On categories of matrix factorizations and their homological invariants |
The talks will cover the following topics: 1. Matrix factorizations as D-branes. According to physicists, the matrix factorizations of an isolated hypersurface singularity describe D-branes in the Landau-Ginzburg (LG) B-model associated with the singularity. The talk is devoted to some mathematical implications of this observation. I will start with a review of open-closed topological field theories underlying the LG B-models and then talk about their refinements. 2. Semi-infinite Hodge theory of dg categories. Homological mirror symmetry asserts that the âclassicalâ mirror correspondence relating the number of rational curves in a CY threefold to period integrals of its mirror should follow from the equivalence of the derived Fukaya category of the first manifold and the derived category of coherent sheaves on the second one. The classical mirror correspondence can be upgraded to an isomorphism of certain Hodge-like data attached to both manifolds, and a natural first step towards proving the assertion would be to try to attach similar Hodge-like data to abstract derived categories. I will talk about some recent results in this direction and illustrate the approach in the context of the LG B-models. 3. Hochschild cohomology of LG orbifolds. The scope of applications of the LG mod- els in mirror symmetry is significantly expanded once we include one extra piece of data, namely, finite symmetry groups of singularities. The resulting models are called orbifold LG models or LG orbifolds. LG orbifolds with abelian symmetry groups appear in mir- ror symmetry as mirror partners of varieties of general type, open varieties, or other LG orbifolds. Associated with singularities with symmetries there are equivariant versions of the matrix factorization categories which, just as their non-equivariant cousins, describe D-branes in the corresponding orbifold LG B-models. The Hochschild cohomology of these categories should then be isomorphic to the closed string algebra of the models. I will talk about an explicit description of the Hochschild cohomology of abelian LG orbifolds" |
March 06, 2018, 3:00 - 4:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Shinobu Hosono (GAKUSHUIN UNIVERSITY) |
Movable vs monodromy nilpotent cones of Calabi-Yau manifolds |
I will show two interesting examples of mirror symmetry of Calabi-Yau complete intersections which have birational automorphisms of infinite order. I will first describe/observe mirror correspondences between the movable cones in birational geometry and the monodromy nilpotent cones which are defined at each boundary points (called LCSLs) in the moduli spaces and naturally glued together. In doing this, I will identify Picard-Lefschetzs monodromy transformations for flopping curves in the mirror families. If time permits, I will show one more example of Calabi-Yau complete intersections for which we observe similar correspondence between the birational geometry and monodromy nilpotent cones. However, in this example, we observe that the correspondence becomes complete when we include a non-toric boundary point in the mirror family. This is based on a recent paper with H. Takagi (arXiv:1707.08728)" |
March 05, 2018, 12:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CMSA SPECIAL MATHEMATICAL PHYSICS SEMINAR |
Emanuel Scheidegger (ALBERT LUDWIGS UNIVERSITY OF FREIBURG) |
Periods and quasiperiods of modular forms and the mirror quintic at the conifold |
We review the theory of periods of modular forms and extend it to quasiperiods. General motivic conjectures predict a relation between periods and quasiperiods of certain weight 4 Hecke eigenforms associated to hypergeometric one-parameter families of Calabi-Yau threefolds. We verify this prediction and discuss some of its implications" |
March 05, 2018, 11:00 - 12:00 at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MIRROR SYMMETRY SEMINAR |
Chuck Doran (UNIVERSITY OF ALBERTA AND ICERM) |
Mirror Symmetry for Lattice Polarized del Pezzo Surfaces |
We describe a notion of lattice polarization for rational elliptic surfaces and weak del Pezzo surfaces, and describe the complex moduli of the former and the KĂ€hler cone of the latter. We then propose a version of mirror symmetry relating these two objects, which should be thought of as a form of Fano-LG correspondence. Finally, we relate this notion to other forms of mirror symmetry, including Dolgachev-Nikulin-Pinkham mirror symmetry for lattice polarized K3 surfaces and the Gross-Siebert program. This is joint work with Alan Thompson based on arXiv:1709.00856" |
March 02, 2018, 11:00 - 12:00 at Science Center 530 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS HOMOLOGICAL MIRROR SYMMETRY FOCUSED LECTURE SERIES |
Colin Diemer (IHES) |
Moduli spaces of Landau-Ginzburg models and (mostly Fano) HMS |
Mirror symmetry as a general phenomenon is understood to take place near the large complex structure limit resp. large radius limit, and so implicitly involves degenerations of the spaces under consideration. Underlying most mirror theorems is thus a mirror map which gives a local identification of respective A-model and B-model moduli spaces. When dealing with mirror symmetry for Calabi-Yau s the role of the mirror map is well-appreciated. In these talks I ll discuss the role of moduli in mirror symmetry of Fano varieties (where the mirror is a Landau-Ginzburg (LG) model). Some topics I expect to cover are a general structure theory of moduli of LG models (follows Katzarkov, Kontsevich, Pantev), the interplay of the topology of LG models with autoequivalence relations in the Calabi-Yau setting, and the relationship between Mori theory in the B-model and degenerations of the LG A-model. For the latter topic we ll focus on the case of del Pezzo surfaces (due to unpublished work of Pantev) and the toric case (due to the speaker with Katzarkov and G. Kerr). Time permitting, we may make some speculations on the role of LG moduli in the work of Gross-Hacking-Keel (in progress work of the speaker with T. Foster)." |
March 01, 2018, 3:00 - 5:00 pm at CMSA Building, 20 Garden Street, Room G10 |
| CMSA SPECIAL LECTURE SERIES ON QUANTUM COHOMOLOGY, NAKAJIMA VARETIES AND QUANTUM GROUPS |
Artan Sheshmani (QGM & CMSA) |
Quantum Cohomology |
Small Quantum Cohomology (Definition and Properties) I" |
March 01, 2018, 1:00 - 3:00 pm at CMSA Building, 20 Garden Street, Room G10 |
| THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
Background for the work of Arone-Dwyer |
" |
March 01, 2018, 3:00 - 5:00 pm at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Yu-Shen Lin ( COLUMBIA UNIVERSITY) |
Tropical/Holomorphic Correspondence for HyperK\ |
*Note different day and location* The Strominger-Yau-Zaslow conjecture suggested that the Calabi-Yau manifolds admits a special Lagrangian fibration when they are close to the large complex structure limit points. Inspired by the conjecture, it is expected that the holomorphic curves degenerate into piecewise linear cylinders in the limit. The projection of the piecewise linear cyclinders to the base can be described by tropical geometry. In this talk, we will explain the how to count holomorphic discs with special Lagrangian torus boundary conditions via tropical geometry. Then we will discuss the applications in mirror symmetry and enumerative geometry." |
February 28, 2018, 4:15 PM at Science Center 232 |
| INFORMAL GEOMETRY & DYNAMICS SEMINAR |
Richard Schwartz (BROWN UNIVERSITY ) |
5 points on the sphere |
The question of which configurations of N points on the sphere minimize the total potential energy (say with respect to a power law) is a very difficult one except when N=1,2,3,4,6,12. I ll explain the progress I made on the problem when N=5. My main result is a computer-assisted proof that the triangular bi-pyramid is the optimal configuration with respect to a power law with exponents if and only s
| February 28, 2018, 4:00 PM at Science Center 530 | |
| NUMBER THEORY SEMINAR |
Wei Zhang (MIT) |
Special cycles on simple Shimura varieties |
This is a work in progress inspired by the the arithmetic Gan--Gross--Prasad conjecture where one is interested in the arithmetic diagonal cycle on the product of two Shimura varieties. We study special cycles on simple Shimura varieties attached to central simple algebras with an involution of second kind. We study some local questions arising from the relative trace formula approach" |
February 28, 2018, 3:00 PM at Sci Center 507 |
| CMSA SPECIAL LECTURE SERIES ON QUANTUM COHOMOLOGY, NAKAJIMA VARETIES AND QUANTUM GROUPS |
Artan Sheshmani (QGM & CMSA) |
Quantum Cohomology |
Small Quantum Cohomology (Definition and Properties) " |
February 27, 2018, 1:00 - 3:00 pm at CMSA Building, 20 Garden Street, Room G10 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Nick Salter (HARVARD UNIVERSITY) |
Vanishing cycles for linear systems on toric surfaces |
Given a linear system on a smooth complex toric surface (eg the projective plane or P^1 \times P^1), it is very natural to ask about the set of all possible vanishing cycles. That is, for a fixed identification of a smooth fiber with a topological surface, which simple closed curves can be shrunk to a point via a nodal degeneration of curves in the linear system? Recent work of mine gives a complete answer to this question. It turns out that the essential invariant that determines whether a simple closed curve is a vanishing cycle is an ``r-spin structure of the sort studied by Witten and others in the context of cohomological field theory. The techniques are essentially topological, and are based on a reformulation of the problem in terms of the mapping class group-valued monodromy representation of the linear system" |
February 27, 2018, 3:00 PM at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Hans Wenzl (UNIVERSITY OF CALIFORNIA, SAN DIEGO) |
Coideal Algebras and Subfactors |
It is well-known that any subgroup of a group G defines a module category over Rep G. Analogs of special embeddings of Lie groups, symmetric spaces, also exist for quantum groups as coideal subalgebras. This should also provide large classes of examples of module categories of fusion categories coming from quantum groups. This has been worked out for a number of important cases where one can explicitly calculate the corresponding algebra objects and indices of the corresponding subfactors" |
February 27, 2018, 4:00 PM at Jefferson 356 |
| CMSA HOMOLOGICAL MIRROR SYMMETRY FOCUSED LECTURE SERIES |
Colin Diemer (IHES) |
Moduli spaces of Landau-Ginzburg models and (mostly Fano) HMS |
Tuesday, Feb. 28 and Thursday, March 1: Mirror symmetry as a general phenomenon is understood to take place near the large complex structure limit resp. large radius limit, and so implicitly involves degenerations of the spaces under consideration. Underlying most mirror theorems is thus a mirror map which gives a local identification of respective A-model and B-model moduli spaces. When dealing with mirror symmetry for Calabi-Yau s the role of the mirror map is well-appreciated. In these talks I ll discuss the role of moduli in mirror symmetry of Fano varieties (where the mirror is a Landau-Ginzburg (LG) model). Some topics I expect to cover are a general structure theory of moduli of LG models (follows Katzarkov, Kontsevich, Pantev), the interplay of the topology of LG models with autoequivalence relations in the Calabi-Yau setting, and the relationship between Mori theory in the B-model and degenerations of the LG A-model. For the latter topic we ll focus on the case of del Pezzo surfaces (due to unpublished work of Pantev) and the toric case (due to the speaker with Katzarkov and G. Kerr). Time permitting, we may make some speculations on the role of LG moduli in the work of Gross-Hacking-Keel (in progress work of the speaker with T. Foster)." |
February 27, 2018, 3:00 - 4:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| LOGIC SEMINAR |
Alexander Van Abel (CITY UNIVERSITY OF NEW YORK) |
The Feferman-Vaught Theorem and the Product of All Prime Finite Fields |
The Feferman-Vaught Theorem in model theory gives a sort of upper bound on the complexity of definable subsets in a product structure. We show how this theorem implies that subsets whose boundary is dense (in the product topology where every factor structure has the discrete topology) are undefinable. We also show how the upper bound in the F.V. Theorem is the best possible, in the case of the language of rings where each factor structure is an integral domain. Finally, we apply these results to the ring $\prod_{p prime} F_p$, the product of all finite prime fields, and obtain a quantifier elimination result for the structure" |
February 27, 2018, 5:15 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Jordan Keller (BHI) |
Linear Stability of Schwarzschild Black Holes |
The Schwarzschild black holes comprise a static, spherically symmetric family of black hole solutions to the vacuum Einstein equations. The physical relevance of such solutions is intimately related to their stability under gravitational perturbations. We present results on the linear stability of the Schwarzschild black holes, joint work with Pei-Ken Hung and Mu-Tao Wang" |
February 26, 2018, 12:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Tom Hou (CALIFORNIA INSTITUTE OF TECHNOLOGY) |
Computer-assisted analysis of singularity formation of a regularized 3D Euler equation |
Whether the 3D incompressible Euler equation can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3D Navier-Stokes Equations. In a recent joint work with Dr. Guo Luo, we provided convincing numerical evidence that the 3D Euler equation develops finite time singularities. Inspired by this finding, we have recently developed an integrated analysis and computation strategy to analyze the finite time singularity of a regularized 3D Euler equation. We first transform the regularized 3D Euler equation into an equivalent dynamic rescaling formulation. We then study the stability of an approximate self-similar solution. By designing an appropriate functional space and decomposing the solution into a low frequency part and a high frequency part, we prove nonlinear stability of the dynamic rescaling equation around the approximate self-similar solution, which implies the existence of the finite time blow-up of the regularized 3D Euler equation. This is a joint work with Jiajie Chen, De Huang, and Dr. Pengfei Liu" |
February 26, 2018, 4:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| MATHEMATICAL PHYSICS SEMINAR |
Xinqi Gong (INSTITUTE FOR MATHEMATICAL SCIENCES, RENNIN UNIVERSITY OF CHINA) |
Mathematical Intelligence Applications in Bio-medical Problems |
The intersection among mathematics, information and biology has becoming more and more interesting and important. Many studies in this direction have led to developments of theories, methods and applications. But the too fast advancing of nowadays forefront information technology and biology knowledge, have triggered two obviously emerging phenomena, tremendous brand-new peaks accessible by new kinds of efforts, randomly meaningless results by in-correct intersections. Here I will show some of our recent results in developing and distinguishing efficiently intelligent approaches and applications for computational molecular biology and medical problems, such as protein structure-function-interaction prediction and pancreas cancer CT image analysis using algorithms like Fast Fourier transform, Monte Carlo, and deep learning, and some new designed physical and geometrical features" |
February 23, 2018, 3:00 pm at Jefferson 250 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Mustazee Rahman (MIT) |
On shocks in the TASEP |
The TASEP particle system runs into traffic jams when the particle density to the left is smaller than the density to the right. Macroscopically, the particle density solves Burgers equation and traffic jams correspond to its shocks. I will describe work with Jeremy Quastel on a specialization of the TASEP shock whereby we identify the microscopic fluctuations around the shock by using exact formulas for the correlation functions of TASEP and its KPZ scaling limit. The resulting laws are related to universal laws of random matrix theory" |
February 23, 2018, 3:30 pm at CMSA Building, 20 Garden Street, G02 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MIRROR SYMMETRY SEMINAR |
Jingyu Zhao (BRANDEIS & HARVARD) |
Connection on S^1-equivariant Floer theory |
We will discuss Seidel s construction of Getzler s connection on S^1-equivariant Floer cohomology on the closed string A-mode" |
February 23, 2018, 11:00 am at Science Center 530 |
| THURSDAY SEMINAR |
Jeremy Hahn (HARVARD UNIVERSITY) |
Chromatic convergence of the Goodwillie tower on spheres |
" |
February 22, 2018, 3:00 - 5:00 pm at Science Center 507 |
| CMSA SPECIAL LECTURE SERIES ON QUANTUM COHOMOLOGY, NAKAJIMA VARETIES AND QUANTUM GROUPS |
Artan Sheshmani (QGM & CMSA) |
Computing GW Invariants |
Genus zero invariants of Calabi-Yau threefold" |
February 22, 2018, 1:00 - 3:00 pm at CMSA Building, 20 Garden Street, Room G10 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Ian Biringer (BOSTON COLLEGE) |
Convex cores of thick hyperbolic 3-manifolds with bounded rank |
Iâll describe a geometric decomposition of the convex core of an epsilon-thick hyperbolic 3-manifold with bounded rank. As a consequence, every such convex core is (1,C)-quasi-isometric to a metric graph, for some uniform C" |
February 21, 2018, 4:00 PM at Science Center 530 |
| NUMBER THEORY SEMINAR |
Juan Rivera-Letelier (UNIVERSITY OF ROCHESTER) |
Hecke and Linnik |
A description of the equidistribution properties of Hecke correspondances acting on the moduli space of p-adic elliptic curves. As an application we show that for every finite set of primes S, there is at most a finite number of singular moduli that are S-units. A key ingredient is a p-adic version Linnik s theorem on the asymptotic distribution of integer points on spheres. This is a joint work with Sebastian Herrero and Ricardo Menares" |
February 21, 2018, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Don Rubin (HARVARD STATISTICS) |
Essential concepts of causal inference â" a remarkable history |
I believe that a deep understanding of cause and effect, and how to estimate causal effects from data, complete with the associated mathematical notation and expressions, only evolved in the twentieth century. The crucial idea of randomized experiments was apparently first proposed in 1925 in the context of agricultural field trails but quickly moved to be applied also in studies of animal breeding and then in industrial manufacturing. The conceptual understanding seemed to be tied to ideas that were developing in quantum mechanics. The key ideas of randomized experiments evidently were not applied to studies of human beings until the 1950s, when such experiments began to be used in controlled medical trials, and then in social science â in education and economics. Humans are more complex than plants and animals, however, and with such trials came the attendant complexities of non-compliance with assigned treatment and the occurrence of âHawthorne and placebo effects. The formal application of the insights from earlier simpler experimental settings to more complex ones dealing with people, started in the 1970s and continue to this day, and include the bridging of classical mathematical ideas of experimentation, including fractional replication and geometrical formulations from the early twentieth century, with modern ideas that rely on powerful computing to implement aspects of design and analysis" |
February 21, 2018, 4:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| LOGIC SEMINAR |
Andrew Brooke-Taylor (UNIVERSITY OF LEEDS) |
Products of CW complexes: the full story |
CW complexes are used extensively in algebraic topology as a suitable class of spaces to work with, but the product of two CW complexes need not be a CW complex, as shown by Dowker. Whitehead and Milnor gave sufficient conditions on the two spaces for the product to be a CW complex, but until now the known characterisations of those pairs of CW complexes with product a CW complex relied on set-theoretic assumptions about the whole universe, such as the Continuum Hypothesis. In this talk I will present a complete characterisation, valid without assuming any extra set-theoretic axioms, of those pairs of CW complexes whose product is a CW complex" |
February 20, 2018, 5:15 pm at Science Center 507 |
| CMSA SPECIAL LECTURE SERIES ON QUANTUM COHOMOLOGY, NAKAJIMA VARETIES AND QUANTUM GROUPS |
Artan Sheshmani (QGM & CMSA) |
Computing GW Invariants |
Genus zero invariants of the projective plan" |
February 20, 2018, 1:00 - 3:00 pm at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MIRROR SYMMETRY SEMINAR |
Man-Wai Cheung (HARVARD UNIVERSITY) |
Quiver representations and theta functions |
Scattering diagrams theta functions and broken lines were developed in order to describe toric degenerations of Calabi-Yau varieties and construct mirror pairs. Later, Gross-Hacking-Keel-Kontsevich unravel the relation of those objects with cluster algebras. In the talk, we will discuss how we can combine the representation theory with these objects. We will also see how the broken lines on scattering diagram give a stratification of quiver Grassmannians using this setting" |
February 16, 2018, 11:00 am at Science Center 530 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Reza Gheissari (NEW YORK UNIVERSITY) |
Dynamics of Critical 2D Potts Models |
The Potts model is a generalization of the Ising model to $q\geq 3$ states with inverse temperature $\beta$. The Gibbs measure on $\mathbb Z^2$ has a sharp transition between a disordered regime when $\beta<\beta_c(q)$ and an ordered regime when $\beta>\beta_c(q)$. At $\beta=\beta_c(q)$, when $q\leq 4$, the phase transition is continuous while when $q>4$, the phase transition is discontinuous and the disordered and ordered phases coexist. We will discuss recent progress, joint with E. Lubetzky, in analyzing the time to equilibrium (mixing time) of natural Markov chains (e.g., heat bath/Metropolis) for the 2D Potts model, where the mixing time on an $n \times n$ torus should transition from $O(\log n)$ at high temperatures to $\exp(c_\beta n)$ at low temperatures, via a critical slowdown at $\beta_c(q)$ that is polynomial in $n$ when $q \leq 4$ and exponential in $n$ when $q>4$" |
February 16, 2018, 3:30 pm at CMSA Building, 20 Garden Street, G02 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Jens Hoppe (KTH) |
New Constructions and Quantization of Minimal Surfaces |
Solution generating techniques for the construction of classical minimal hypersurfaces will be presented, and a general method to associate to the embedding functions x_i of a minimal surface operators X_i satisfying [[X_i, X_j],X_j] = " |
February 16, 2018, 9:30 am at Science Center 530 |
| CMSA SPECIAL LECTURE SERIES ON QUANTUM COHOMOLOGY, NAKAJIMA VARETIES AND QUANTUM GROUPS |
Artan Sheshmani (QGM & CMSA) |
Computing GW Invariants |
Three level GW classe" |
February 15, 2018, 1:00 - 3:00 pm at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Zhengwei Liu (HARVARD PHYSICS) |
A new program on quantum subgroups |
Quantum subgroups have been studied since the 1980s. The A, D, E classification of subgroups of quantum SU(2) is a quantum analogue of the McKay correspondence. It turns out to be related to various areas in mathematics and physics. Inspired by the quantum McKay correspondence, we introduce a new program that our group at Harvard is developing" |
February 14, 2018, 4:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Simion Filip (HARVARD UNIVERSITY) |
Hypergeometric equations and Lyapunov exponents (via Hodge theory) |
I will explain a connection between dynamical and geometric properties of the monodromy of certain hypergeometric equations. The necessary background will be provided" |
February 14, 2018, 4:00 PM at Science Center 530 |
| NUMBER THEORY SEMINAR |
Hansheng Diao (PRINCETON UNIVERSITY) |
Towards a $p$-adic Riemann-Hilbert correspondence |
On any smooth algebraic variety over a $p$-adic local field, we construct a tensor functor from the category of $p$-adic \ etale local systems to the category of filtered algebraic vector bundles with an integrable connection satisfying the Griffiths transversality, which we view as a $p$-adic analogue of Deligne s classical Riemann-Hilbert correspondence" |
February 14, 2018, 3:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Jesse Kass (UNIVERSITY OF SOUTH CAROLINA) |
How to count lines on a cubic surface arithmetically |
Salmon and Cayley proved the celebrated 19th century result that a smooth cubic surface over the complex numbers contains exactly 27 lines. By contrast, the count over the real numbers depends on the surface, and these possible counts were classified by Segre. Benedetti-ilhol, Finashin-Kharlamov and Okonek-Teleman made the striking observation that Segre s work shows a certain signed count is always 3. In my talk, I will explain how to extend this result to an arbitrary field. Although I will not use any homotopy, I will draw motivation from A1-homotopy theory. This is joint work with Kirsten Wickelgren" |
February 13, 2018, 3:00 PM at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Nicholas Early (UNIVERSITY OF MINNESOTA) |
Canonical Bases for Permutohedral Plates |
There is a natural construction according to which the set of all faces of an arrangement of hyperplanes can be made into a vector space, by taking linear combinations of their characteristic functions. Our space is equipped with a natural basis of characteristic functions of certain polyhedral cones called permutohedral cones, studied as plates by A. Ocneanu, which are labeled by ordered set partitions; these are in duality with faces of the arrangement of reflection hyperplanes xi=xj. We construct directly a certain canonical basis which is compatible with one or both of two quotients: neglecting characteristic functions of (1) nonpointed cones, and (2) cones of codimension at least 1. The essential feature here is that subsets of the canonical basis map to bases of the quotients. As a consequence, we obtain the straightening relations which were originally computed by Ocneanu through the introduction of an auxiliary space of formal linear combinations of layered trees" |
February 13, 2018, 4:00 PM at Jefferson 356 |
| CMSA SPECIAL LECTURE SERIES ON QUANTUM COHOMOLOGY, NAKAJIMA VARETIES AND QUANTUM GROUPS |
Artan Sheshmani (QGM & CMSA) |
Gromov-Witten invariants |
Virtual Fundamental Class II (computation in some cases" |
February 13, 2018, 1:00 - 3:00 pm at CMSA Building, 20 Garden Street, Room G10 |
| LOGIC SEMINAR |
Alice Medvedev () |
Unions of chains of signatures |
We meditate on a particularly naive notion of a limit of a sequence of theories: a union of conservative expansions. That is, we consider a sequence of nested signatures $L_1 \subset L_2 \subset \ldots$, each one a subsignature of the next, and a sequence of $L_i$-theories $T_i$, where each $T_i$ is precisely the set of $L_i$-consequences of $T_{i+1}$ (and hence is a subset of $T_{i+1}$). It turns out that many model-theoretic properties then pass from all $T_i$ to their union $T$; these include consistency, completeness, quantifier elimination, partial quantifier elimination such a model-completeness, elimination of imaginaries, stable embeddedness of some definable set, characterization of algebraic closure; stability, simplicity, rosiness, dependence. Our motivating example is the theory $T$ of fields with an action by $(Q; +)$, seen as a limit of (theories of) fields with $(Z; +)$-actions" |
February 12, 2018, 5:15 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Matthew Stroffregen (MIT) |
Equivariant Khovanov Spaces |
Associated to a link L in the three-sphere, Lipshitz-Sarkar constructed a topological space, well-defined up to stable homotopy, whose homology is the (even) Khovanov homology of L. We extend this to construct an ``odd Khovanov space of L, whose homology recovers odd Khovanov homology. We also equip the odd Khovanov space with a natural involution whose fixed point set is the (even) Khovanov space of Lipshitz-Sarkar, and show that the even Khovanov space admits its own natural involution. We outline some conjectures relating the even and odd Khovanov spaces. This is joint work with Sucharit Sarkar and Chris Scaduto" |
February 12, 2018, 12:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MIRROR SYMMETRY SEMINAR |
Dan Xie (CMSA, HARVARD) |
Three dimensional mirror symmetry |
I will discuss the basic features of three dimensional mirror symmetry. Several interesting class of examples will be discussed" |
February 09, 2018, 11:00 - 12:00 at Science Center 530 |
| THURSDAY SEMINAR |
Ben Knudsen (HARVARD UNIVERSITY) |
The derivatives of the identity functor |
" |
February 08, 2018, 3:00 - 5:00 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Fan Chung (UNIVERSITY OF CALIFORNIA, SAN DIEGO) |
Sequences: random, structured or something in between |
There are many fundamental problems concerning sequences that arise in many areas of mathematics and computation. Typical problems include finding or avoiding patterns; testing or validating various `random-likeâ behavior; analyzing or comparing different statistics, etc. In this talk, we will examine various notions of regularity or irregularity for sequences and mention numerous open problems" |
February 08, 2018, 5:00 pm at CMSA Building, 20 Garden Street, Room G10 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Phil Engel (HARVARD UNIVERSITY) |
Penrose Tilings of Riemann Surfaces |
In 1981, de Bruijn classified all Penrose tilings of the plane in terms of pentagrids---superpositions of five collections of evenly spaced parallel lines. I will begin by summarizing de Bruijn s beautiful work. Then, I will discuss joint work with Peter Smillie, very much in an early stage, on transporting pentagrids and similar structures onto Riemann surfaces. We expect that the moduli space of pairs (X,đ), where đ is a quintic differential, admits a quasicrystal of Penrose-tiled flat structures that is asymptotically equidistributed with respect to the Masur-Veech volume form. In analogy with recent work on enumeration of hexagon-, square-, and triangle-tiled surfaces, it seems plausible to conjecture that the generating functions for Penrose-tiled surfaces are quasimodular forms of level 5. Such a result would furnish an algorithm to compute the Masur-Veech volume of a stratum of the moduli space of quintic differentials." |
February 07, 2018, 4:00 PM at Science Center 530 |
| NUMBER THEORY SEMINAR |
Alex Kontorovich (RUTGERS AND IAS) |
Sphere Packings and Arithmetic |
We define a general class of sphere packings, and study the subclass of superintegral such. By connecting these to the theory of hyperbolic arithmetic reflection lattices, we prove that they only exist in finitely many dimensions, and in fact in finitely many commensurability classes, in principle allowing for a complete classification" |
February 07, 2018, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Linyuan Lu (UNIVERSITY OF SOUTH CAROLINA) |
Ricci-flat graphs with girth at leave five |
A graph is called Ricci-flat if its Ricci curvatures vanish on all edges. Here we use the definition of Ricci curvature on graphs given in [Lin-Lu-Yau, Tohoku Math., 2011], which is a variation of [Ollivier, J. Funct. Math., 2009]. We classified all Ricci-flat connected graphs with girth at least five: they are the infinite path, cycle $C_n$ ($n\geq 6$), the dodecahedral graph, the Petersen graph, the half-dodecahedral graph, and the Triplex graph. We also construct many Ricci-flat graphs with girth $3$ or $4$ by using the root systems of simple Lie algebras. (Joint work with Shing-Tung Yau and Yong Lin) .....Organized by Prof. Shing-Tung Ya" |
February 06, 2018, 4:30 PM at Science Center 530 |
| LOGIC SEMINAR |
Jesse Han (MCMASTER UNIVERSITY) |
Strong conceptual completeness for \omega-categorical theories |
Suppose we have some process to attach to every model of a first-order theory some (permutation) representation of its automorphism group, compatible with elementary embeddings. How can we tell if this is really an imaginary sort of our theory? In the 80s, Michael Makkai proved that the answer to our question is yes if and only if our given process is compatible with all ultraproducts and all formal comparison maps between them (generalizing e.g. the diagonal embedding into an ultrapower). This is known as /strong conceptual completeness/; formally, the statement is that the category Def(T) of definable sets can be reconstructed up to bi-interpretability as the category of ultrafunctors Mod(T) \to Set. \omega-categorical structures, having few definable sets, are exceptionally simple to understand, and in fact are determined up to bi-interpretability by the action of their automorphism groups. Any general framework which reconstructs theories from their categories of models should therefore be considerably simplified for \omega-categorical theories. Indeed, we show: 1. If T is Ï-categorical, then X : Mod(T) â Set is definable, i.e. isomorphic to (M \mapsto Ï(M)) for some formula Ï â T, if and only if X preserves ultraproducts and diagonal embeddings into ultrapowers. This means that all the preservation requirements for ultramorphisms, which a priori get unboundedly complicated, collapse to just diagonal embeddings when T is Ï-categorical. 2. This definability criterion fails if we remove the Ï-categoricity assumption. We construct examples of theories and non-definable functors Mod(T) \to Set exhibiting this" |
February 06, 2018, 5:15 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS HOMOLOGICAL MIRROR SYMMETRY FOCUSED LECTURE SERIES |
Ivan Losev (NORTHEASTERN UNIVERSITY) |
BGG category O: towards symplectic duality |
We will discuss a very classical topic in the representation theory of semisimple Lie algebras: the Bernstein-Gelfand-Gelfand (BGG) category O. Our aim will be to motivate and state a celebrated result of Beilinson, Ginzburg and Soergel on the Koszul duality for such categories, explaining how to compute characters of simple modules (the Kazhdan-Lusztig theory) along the way. The Koszul duality admits a conjectural generalization (Symplectic duality) that is a Mathematical manifestation of 3D Mirror symmetry. We will discuss that time permitting. Approximate (optimistic) plan of the lectures: 1) Preliminaries and BGG category O. 2) Kazhdan-Lusztig bases. Beilinson-Bernstein localization theorem. 3) Localization theorem continued. Soergel modules. 4) Koszul algebras and Koszul duality for categories O. Time permitting: other instances of Symplectic duality. Prerequisites: Semi-simple Lie algebras and their finite dimensional representation theory. Some Algebraic geometry. No prior knowledge of category O/ Geometric Representation theory is assumed" |
February 06, 2018, 3:00 PM at CMSA Building, 20 Garden Street, G02 |
| MATHEMATICAL PHYSICS SEMINAR |
Jacob Shapiro (ETH ZĂŒRICH) |
Bulk-Edge Duality and Complete Localization for Disordered Chiral Chains |
We study one dimensional insulators obeying a chiral symmetry in the single-particle picture where the Fermi energy is assumed to lie within a mobility gap. Topological invariants are defined for infinite (bulk) or half-infinite (edge) systems, and it is shown that for a given bulk system with nearest neighbor hopping, the invariant is equal to the induced-edge-system s invariant. We also give a new formulation of the topological invariant in terms of the Lyapunov exponents of the system, which sheds light on the conditions for topological phase transition extending to the mobility gap regime. We investigate the conditions for a mobility gap to exist in a probabilistic model, and give a proof of complete dynamical localization at all non-zero energies via Furstenberg s theorem and the fractional moments method. (Joint work with G. M. Graf" |
February 06, 2018, 4:00 PM at Jefferson 356 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Bhargav Bhatt (UNIVERSITY OF MICHIGAN) |
Prisms and deformations of de Rham cohomology |
In arithmetic geometry, there are multiple instances where the de Rham cohomology of a smooth variety admits a natural deformation (such as crystalline cohomology or the recently constructed A_{inf}-cohomology). I will explain a general site-theoretic approach, relying on a notion we call prisms, that produces such deformations. In addition to recovering the known deformations in a new and simple way, this framework also constructs some previously conjectural ones (q-deformations of de Rham cohomology, cohomological Breuil-Kisin or Wach modules). This is a report on work in progress with Peter Scholze" |
February 06, 2018, 3:00 PM at MIT - 4-153 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Hyungchul Kim (CMSA & HARVARD PHYSICS) |
Seiberg duality and superconformal index in 3d |
I will discuss 3d N=2 supersymmetric gauge theories with a unitary gauge group and two matter fields in the adjoint representation. The low energy spectrum of BPS states of the theory can be studied from the superconformal index. The information on the low energy spectrum including monopole operators is essential to construct a Seiberg-type dual theory. Superconformal indices for a dual pair of the theories should be the same, which is a physical basis for a mathematical identity." |
February 05, 2018, 12:00 PM at CMSA Building, 20 Garden Street, G02 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MIRROR SYMMETRY SEMINAR |
Minxian Zhu (YAU MATHEMATICAL SCIENCES CENTER, TSINGHUA UNIVERSITY) |
The hyperplane conjecture for periods of Calabi-Yau hypersurfaces in P^n |
Hosono, Lian, and Yau made a conjecture in the 90s describing the solutions to the Gelfand-Kapranov-Zelevinsky hypergeometric equations which arise as periods of CY hypersurfaces in a Gorenstein Fano toric variety. We will prove this conjecture for projective spaces. This is joint work with Bong Lian" |
February 02, 2018, 11:00 am at Science Center 530 |
| MATHEMATICAL PHYSICS SEMINAR |
Yunxiang Ren (TENNESSEE STATE UNIVERSITY) |
A New Skein Theory for One-Way Yang-Baxter Planar Algebras |
In this talk we will introduce One-Way Yang-Baxter subfactor planar algebras, which is a continuation of the classification program of subfactor planar algebras via skein theory started by Bisch and Jones. We will focus on discussing the subgroup subfactor S3 Ă S2 S5 which is naturally related to Petersen graph and the rank 3 permutation group. We showed that this planar algebra is generated by its 2-box space and provide a new skein theory for this planar algebra. Moreover, we will show that each member of the family of subfactors {Sn Ă S2 Sn+2 : n â„ 3} is also generated by its 2-box space and satisfies the similar type of skein theory in a uniform way" |
February 02, 2018, 4:00 PM at Jefferson 250 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Overview |
" |
February 01, 2018, 3:00 - 5:00 pm at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Curtis McMullen (HARVARD UNIVERSITY) |
The behavior of planes in confinement |
" |
January 31, 2018, 4:00 PM at Science Center 530 |
| NUMBER THEORY SEMINAR |
Chen Wan (INSTITUTE FOR ADVANCED STUDY) |
The local trace formula for the Ginzburg-Rallis model and the generalized Shalika model |
We will first discuss a local trace formula for the Ginzburg-Rallis model. This trace formula allows us to prove a multiplicity formula for the Ginzburg-Rallis model, which implies that the summation of the multiplicities on every tempered Vogan L-packet is always equal to 1. Then we will talk about an analogy of this trace formula for the generalized Shalika model, which implies that the multiplicity for the generalized Shalika model is a constant on every discrete Vogan L-packet" |
January 31, 2018, 3:00 - 4:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Cumrun Vafa (HARVARD PHYSICS) |
All genus Gromov-Witten invariants for Compact Calabi-Yau threefolds |
" |
January 30, 2018, 1 - 2:30 pm at CMSA Building, 20 Garden Street, Room G10 |
| LOGIC SEMINAR |
Rehana Patel () |
Stable regularity for finite relational structures |
Szemer\â{e}diâs regularity lemma for graphs says, roughly speaking, that any finite graph can be approximated by one that has a small structural âskeletonâ overlaid with randomness. Malliaris and Shelah have shown that under the model-theoretic tameness condition of stability, this approximation is especially well-behaved: bounds on the size of the so-called âregularity partitionâ are significantly improved; there are no âirregular pairsâ in the partition; and randomness is essentially eliminated. In this talk I will describe a generalisation of the Malliaris-Shelah result to stable finite structures in a finite relational language. This is joint work with Nate Ackerman and Cameron Freer" |
January 30, 2018, 5:15 - 6:15 pm at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Valentino Tosatti (NORTHWESTERN UNIVERSITY) |
Estimates for collapsing Calabi-Yau metrics |
Consider a compact Calabi-Yau manifold with a holomorphic fibration onto a lower-dimensional space, and consider a family of Ricci-flat Kahler metrics on the total space whose Kahler class is degenerating to the pullback of a class from the base. In earlier work I proved that the metric collapse, away from the singular fibers, to a limiting metric on the base, in the locally uniform topology (and smoothly if the fibers are tori). I will describe new estimates that prove a uniform Holder bound in general, and bounds for all derivatives when the smooth fibers are isomorphic to each other. Joint work with H.-J. Hein" |
January 30, 2018, 4:15 PM at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Kaifung Bu (HARVARD UNIVERSITY) |
De Finetti Theorems for Braiding Parafermions |
The de Finetti theorem is a powerful tool relating symmetry under the permutation group and independence of random variables. It also plays a significant role in quantum information theory. We prove a new type of de Finetti theorem for the braid group acting on the parafermion algebra. We show that a braid-invariant state is extremal if and only if it is a product state. Furthermore, we provide an explicit characterization of braid-invariant states, such that the parafermion algebras generates a factor under the Gelfand-Naimark-Segal construction." |
January 30, 2018, 4:00 PM at Jefferson 356 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Qiang Wen (YAU MATHEMATICAL SCIENCES CENTER, TSINGHUA UNIVERSITY) |
Holographic entanglement entropy in general spacetimes |
In the context of AdS/CFT correspondence, the entanglement in a quantum theory is related to a geometric quantity in the dual gravity by a simple relation, namely the Ryu-Takayanagi formula. I will briefly introduce this relation firstly and then talk about how to generalize this relation to holographic models beyond AdS/CFT" |
January 29, 2018, 12:00 - 1:00 pm at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MIRROR SYMMETRY SEMINAR |
Matthew Young (CHINESE UNIVERISTY OF HONG KONG) |
Algebra and geometry of orientifold Donaldson-Thomas theory |
This talk will be an overview of the orientifold Donaldson-Thomas theory of quivers. Roughly speaking, orientifold Donaldson-Thomas theory is a counting theory for principal orthogonal or symplectic bundles in three dimensional Calabi-Yau categories. I will explain an approach via geometrically defined representations of cohomological Hall algebras. In this way we are able to categorify the orientifold wall-crossing formula appearing in the string theory literature, formulate and prove an orientifold variant of the integrality conjecture of Kontsevich-Soibelman and give a geometric interpretation of orientifold Donaldson-Thomas invariants" |
January 26, 2018, 11:00-12:00pm at Science Center 530 |
| CMSA SPECIAL SEMESTER-LONG LECTURE SERIES |
Artan Sheshmani (QGM/CMSA) |
Quantum Cohomology, Nakajima Varieties and Quantum groups |
TUESDAYS AND THURSDAYS BEGINNING JANUARY 25, 2018. Topics include: Gromov-Witten invariants, Computing GW invariants, Quantum Cohomology, GW invariants via Quantum Cohomology, Nakajima varieties, Quantum cohomology of Nakajima varieties" |
January 25, 2018, 1:00 - 3:00pm at CMSA Building, 20 Garden St., G10 |
| HARVARD LOGIC COLLOQUIUM |
Aki Kanamori (BOSTON UNIVERSITY) |
Aspect-Perception and the History of Mathematics |
The meta-concept of aspect-perception is first discussed in connection with the history and practice of mathematics. Then, in its terms and to draw out the concept, a selection of vignettes are discussed: Pythagorean Theorem, Irrationality of n, the Derivative of Sine, and the Pigeonhole Principle." |
January 25, 2018, 4:00-5:00 PM at Logic Center, Room 420, 2 Arrow St |
| CMSA HOMOLOGICAL MIRROR SYMMETRY FOCUSED LECTURE SERIES |
Ivan Losev (NORTHEASTERN UNIVERSITY ) |
BGG category O: towards symplectic duality |
FOUR DATE SERIES: 01/23, 01/25, 01/30, 02/01. We will discuss a very classical topic in the representation theory of semisimple Lie algebras: the Bernstein-Gelfand-Gelfand (BGG) category O. Our aim will be to motivate and state a celebrated result of Beilinson, Ginzburg and Soergel on the Koszul duality for such categories, explaining how to compute characters of simple modules (the Kazhdan-Lusztig theory) along the way. The Koszul duality admits a conjectural generalization (Symplectic duality) that is a Mathematical manifestation of 3D Mirror symmetry. We will discuss that time permitting. Approximate (optimistic) plan of the lectures: 1) Preliminaries and BGG category O. 2) Kazhdan-Lusztig bases. Beilinson-Bernstein localization theorem. 3) Localization theorem continued. Soergel modules. 4) Koszul algebras and Koszul duality for categories O. Time permitting: other instances of Symplectic duality. Prerequisites: Semi-simple Lie algebras and their finite dimensional representation theory. Some Algebraic geometry. No prior knowledge of category O/ Geometric Representation theory is assumed" |
January 25, 2018, 3:00 - 5:00pm at CMSA Building, 20 Garden St., G10 |
| MATHEMATICAL PHYSICS SEMINAR |
Bin Gui (VANDERBILT UNIVERSITY) |
A Unitary Tensor Product Theory for Unitary Vertex Operator Algebra Modules |
A modular tensor category (MTC) structure for 2d rational conformal field theory was found in physics by Moore-Seiberg, and was proved mathematically by Huang-Lepowsky using the language of vertex operator algebras (VOAs). However, it is unclear whether this MTC has a unitary structure. In this talk, I will define an inner product on the tensor product of two unitary representations of a unitary rational VOA, under which the MTC becomes unitary" |
January 23, 2018, 4:00 PM at Jefferson 356 |
| CMSA SPESIAL SEMINAR |
Shannon Ray (FLORIDA ATLANTIC UNIVERSITY) |
Wang and Yauâs Quasi-Local Energy for an Extreme Kerr Spacetime |
There exist constant radial surfaces, S, that may not be globally embeddable in R3 for Kerr spacetimes with a>3M/2. One must isometrically embed S into R3 to compute the Brown and York (B-Y) quasi-local energy (QLE). On the other hand, the Wang and Yau (W-Y) QLE embeds S into Minkowski space. In this talk, the W-Y QLE for surfaces that may or may not be globally embeddable in R3 is examined. Their energy functional, E[Ï], has a critical point at Ï=0 for all constant radial surfaces in t=constant hypersurfaces using Boyer-Lindquist coordinates. For Ï=0, the W-Y QLE reduces to the B-Y QLE. To examine the W-Y QLE in these cases, the energy functional is written explicitly in terms of Ï under the assumption that Ï is only a function of Ξ. Then, Ï(Ξ) is written as a Fourier expansion to explore the values of E[Ï(Ξ)] in the space of coefficients. An open region of complex values for E[Ï(Ξ)] was discovered from this analysis. The physical properties of the smallest real value of E[Ï(Ξ)], which lies on the boundary separating real and complex energies, is also discussed. The results of this analysis suggest that one must consider non-axi-symmetric embeddings of S into Minkowski space to minimize E[Ï]. This talk is based on joint work with Warner Miller, Mu-Tao Wang and Shing-Tung Yau" |
January 19, 2018, 4:00pm at CMSA Building, 20 Garden St., G10 |
| MATHEMATICAL PHYSICS SEMINAR |
Marco De Renzi (UNIVERSITY OF PARIS 7) |
Renormalized Hennings Invariants and TQFTs |
Non-semisimple constructions in quantum topology produce strong invariants and TQFTs with unprecedented properties. The first family of non-semisimple quantum invariants of 3-manifolds was defined by Hennings in 1996. The construction enabled Lyubashenko to build mapping class groups representations out of every finite-dimensional factorizable ribbon Hopf algebra. Further attempts at extending these constructions to TQFTs only produced partial results, as the vanishing of Hennings invariants in many crucial situations made it impossible to treat non-connected surfaces. We will show how to overcome these problems. In order to do so, we will first renormalize Hennings invariants through the use of modified traces. When working with factorizable Hopf algebras, we further show that the universal construction of Blanchet, Habegger, Masbaum and Vogel produces a fully monoidal TQFT which extends Lyubashenkoâs mapping class group representations. This is a joint work with Nathan Geer and Bertand Patureau" |
January 16, 2018, 4:00 PM at Jefferson 356 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Marco Gualtieri (UNIVERSITY OF TORONTO) |
Holomorphic symplectic Morita equivalence and the generalized Kaehler potential |
Since the introduction of generalized Kaehler geometry in 1984 by Gates, Hull, and Rocek in the context of two-dimensional supersymmetric sigma models, we have lacked an understanding of the degrees of freedom inherent in the geometry. In particular, the description of a usual Kaehler structure in terms of a complex manifold together with a local Kaehler potential function is not available for generalized Kaehler structures, despite many positive indications in the literature over the last two decades. I will explain recent work showing that a generalized Kaehler structure may be viewed in terms of a holomorphic Morita equivalence between Poisson manifolds; this allows us to solve the problem of existence of a generalized Kaehler potential" |
December 12, 2017, 3:00 pm at Science Center Hall A |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Sara Venkatesh (COLUMBIA UNIVERSITY) |
Closed-string mirror symmetry for subdomains |
We construct a symplectic cohomology theory for Liouville cobordisms that detects non-trivial elements of the Fukaya category. This theory is conjecturally mirror to the Jacobian ring of a Landau-Ginzburg superpotential on an affinoid subdomain. We illustrate this manifestation of mirror symmetry by examining cobordisms contained in negative line bundles" |
December 06, 2017, 12:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Eveline Legendre (INSTITUT DE MATHĂ©MATIQUES DE TOULOUSE, UNIVERSITĂ© PAUL SABATIER ) |
An application of the equivariant localization formula in Sasaki geometry |
We apply an extension of the Duistermaat--Heckman Theorem to study the volume, the total scalar curvature and the Einstein-Hilbert functionals defined on the Reeb cone of a Sasaki manifold and prove that they are all proper. This implies that there exists a Reeb vector field with (transversal) Futaki invariant in any the Reeb cone" |
December 06, 2017, 4:15 PM at Science Center 507 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Phillipe Rigollet (MIT) |
Exact recovery in the Ising blockmodel |
Over the past fifteen years, the problem of learning Ising models from independent samples has been of significant interest in the statistics, machine learning, and statistical physics communities. Much of the effort has been directed towards finding algorithms with low computational cost for various restricted classes of models, primarily in the case where the interaction graph is sparse. In parallel, stochastic blockmodels have played a more and more preponderant role in community detection and clustering as an average case model for the minimum bisection model. In this talk, we introduce a new model, called Ising blockmodel for the community structure in an Ising model. It imposes a block structure on the interactions of a dense Ising model and can be viewed as a structured perturbation of the celebrated Curie-Weiss model. We show that interesting phase transitions arise in this model and leverage this probabilistic analysis to develop an algorithm based on semidefinite programming that recovers exactly the community structure when the sample size is large enough. We also prove that exact recovery of the block structure is actually impossible with fewer samples. This is joint work with Quentin Berthet (University of Cambridge) and Piyush Srivastava (Tata Institute)" |
December 06, 2017, 2:00 - 3:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Ankur Moitra (MIT) |
A New Approach to Approximate Counting and Sampling |
Over the past sixty years, many remarkable connections have been made between statistical physics, probability, analysis and theoretical computer science through the study of approximate counting. While tight phase transitions are known for many problems with pairwise constraints, much less is known about problems with higher-order constraints. Here we introduce a new approach for approximately counting and sampling in bounded degree systems. Our main result is an algorithm to approximately count the number of solutions to a CNF formula where the degree is exponential in the number of variables per clause. Our algorithm extends straightforwardly to approximate sampling, which shows that under Lovasz Local Lemma-like conditions, it is possible to generate a satisfying assignment approximately uniformly at random. In our setting, the solution space is not even connected and we introduce alternatives to the usual Markov chain paradigm" |
December 06, 2017, 3:00 - 4:00 pm at CMSA Building, 20 Garden Street, Room G10 |
| NUMBER THEORY SEMINAR |
Robert Lemke Oliver (TUFTS UNIVERSITY) |
Tate-Shafarevich groups in quadatric twist families |
In recent joint work with Bhargava, Klagsbrun, and Shnidman, we determined the average size of the Selmer group of a degree 3 isogeny of abelian varieties in the family of quadratic twists. We used this work to derive consequences for the ranks of these quadratic twists. In this talk, we explain followup work in which we obtain consequences for Tate-Shafarevich groups. In particular, we give the first systematic examples of elliptic curves over Q for which a positive proportion of twists have an element of order 3 in Sha; for some curves, this positive proportion can in fact be taken to be a vast majority. Our techniques work equally well over number fields, where we find curves for which a positive proportion of twists have an element of order p in Sha, for p an odd prime, and an absolutely simple abelian threefold for which a similar conclusion may be obtained" |
December 06, 2017, 3:15 pm *sharp at Science Center 507 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Comparison of Stable and Unstable v_n-Periodic Homotopy |
" |
November 30, 2017, 4:00 - 6:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Renee Bell (MIT) |
Local-to-Global Lifting for Curves in Characteristic p |
Given a Galois cover of curves X to Y with Galois group G which is totally ramified at a point x and unramified elsewhere, restriction to the punctured formal neighborhood of x induces a Galois extension of Laurent series rings k((u))/k((t)). If we fix a base curve Y , we can ask when a Galois extension of Laurent series rings comes from a global cover of Y in this way. Harbater proved that over a separably closed field, this local-to-global principle holds for any base curve if G is a p-group, and gave a condition for the uniqueness of such an extension. Using a generalization of Artin-Schreier theory to non-abelian p-groups, we characterize the curves Y for which this lifting property holds and when it is unique, but over a more general ground field" |
November 29, 2017, 3:15 pm *sharp at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Jane Wang (MIT) |
Finitely many algebraically primitive TeichmĂŒller curves in genus g at least 3 |
In this talk, we will build up the background and context leading up to the recent result that there are only finitely many algebraically primitive TeichmĂŒller curves in any genus at least three. Then, we ll give a sketch of a proof of this result, following work of Ursula HamenstĂ€dt" |
November 29, 2017, 4:00 PM at Science Center 530 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
David Gamarink (MIT) |
(Arguably) Hard on Average Constraint Satisfaction Problems |
Many combinatorial optimization problems defined on random instances such as random graphs, exhibit an apparent gap between the optimal value, which can be estimated by non-constructive means, and the best values achievable by fast (polynomial time) algorithms. Through a combined effort of mathematicians, computer scientists and statistical physicists, it became apparent that a potential and in some cases a provable obstruction for designing algorithms bridging this gap is an intricate geometry of nearly optimal solutions, in particular the presence of chaos and a certain Overlap Gap Property (OGP), which we will introduce in this talk. We will demonstrate how for many such problems, the onset of the OGP phase transition indeed nearly coincides with algorithmically hard regimes. Our examples will include the problem of finding a largest independent set of a graph, finding a largest cut in a random hypergrah, random NAE-K-SAT problem, the problem of finding a largest submatrix of a random matrix, and a high-dimensional sparse linear regression problem in statistics. Joint work with Wei-Kuo Chen, Quan Li, Dmitry Panchenko, Mustazee Rahman, Madhu Sudan and Ilias Zadik" |
November 29, 2017, 3:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Amitai Zernik (INSTITUTE FOR ADVANCED STUDY) |
Computing the Aâ algebra of RP^2m âȘ CP^2m using open fixed-point localization |
I ll explain how to compute the equivariant quantum Aâ algebra A associated with the Lagrangian embedding of RP^2m in CP^2m, using a new fixed-point localization technique that takes into account contributions from all the corner strata. It turns out that A is rigid, so its structure constants are independent of all choices. When m = 1 and in the non-equivariant limit, they specialize to give Welschinger s counts of real rational planar curves passing through some generic, conjugation invariant configurations of points in CP^2m. So we get a diagrammatic expression for computing Welschinger invariants, which I ll demonstrate with some examples. Time permitting, I ll discuss a formal extension to higher genus which satisfies string and dilation" |
November 29, 2017, 12:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Valentijn Karemaker (UNIVERSITY OF PENNSYLVANIA) |
Dynamics of Belyi maps |
A (genus 0) Belyi map is a finite map from the projective line to itself, branched exactly at 0, 1, and infinity. Such maps can be described combinatorially by their generating systems. Assuming further that 0, 1, and infinity are both fixed points and the unique ramification points above 0, 1, and infinity respectively yields dynamical Belyi maps, since the resulting maps can be iterated and will therefore exhibit dynamical behaviour. In this talk, we will discuss several results on the dynamics, reductions, and monodromy of dynamical Belyi maps, and the interplay between these. (This is joint work with J. Anderson, I. Bouw, O. Ejder, N. Girgin, and M. Manes." |
November 28, 2017, 3:00 PM at MIT 4-237 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Gabor Szekelyhidi (UNIVERSITY OF NOTRE DAME) |
New Calabi-Yau metrics on C^n |
I will discuss the construction of Calabi-Yau metrics on C^n with maximal volume growth, with singular tangent cones at infinity. These generalize recent examples constructed independently by Yang Li and Conlon-Rocho" |
November 28, 2017, 4:15 PM at Science Center 507 |
| SPECIAL SEMINAR ON GEOMETRY |
Ryosuke Takahashi (TOHOKU UNIVERSITY) |
A new parabolic flow approach to the Kahler-Einstein problem |
We introduce the ``Ding-Mabuchi flow , a new parabolic flow which is designed to deform a given Kahler metric to a Kahler-Einstein one, and fit Donaldson s new GIT picture. We provide three results about the Ding-Mabuchi flow: (1) Long-time existence and smooth convergence on canonically polarized manifolds (2) Long-time existence and strong convergence on anti-canonically polarized manifolds with Kahler-Einstein metrics, and discrete automorphism group (3) Relation between the Ding-Mabuchi flow and optimal destabilizer on Ding-unstable toric Fano manifolds. In the canonically polarized case, the large time behavior of the Ding-Mabuchi flow is similar to that of the Kahler-Ricci flow. On the other hand, the Ding-Mabuchi flow on Ding-unstable Fano manifolds has a different aspect. We observe that it encodes the optimal destabilizing information about Kahler/algebro-geometric structure in the case when the manifold is toric. This talk is based on the joint work with T.Collins (Harvard Univ) and T. Hisamoto (Nagoya Univ)" |
November 22, 2017, 4:00 - 5:15 pm at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Dhruv Ranganathan (MIT) |
Curves, maps, and singularities in genus one |
I will introduce a framework in which to study genus one curve singularities using logarithmic and tropical geometry, and its relationship to the moduli space of curves and maps. This builds on work of Speyer, Smyth, Viscardi, and Vakil-Zinger and leads to the construction of non-singular modular compactifications of the space elliptic curves in projective space, in particular recovering a construction of Vakil and Zinger. I will discuss an appropriate generalization of this result to the pairs case for toric targets. In this setting, there is a fruitful interplay between the geometry of the space of maps and a subtle theorem of Speyer in tropical geometry from 2005. Time permitting, I will explain how the same framework leads to modular factorizations of the rational maps among Smythâs spaces of pointed elliptic curves. This is joint work with Keli Santos-Parker and Jonathan Wise" |
November 21, 2017, 3:00 PM at Science Center Hall A |
| DIFFERENTIAL GEOMETRY SEMINAR |
Siu-Cheong Lau (BOSTON UNIVERSITY) |
Moduli theory of Lagrangian immersions and mirror symmetry |
In this talk, we consider the moduli space of Lagrangian immersions coming from a pair-of-pants decomposition and use it to construct mirror symmetry. It is a joint work with Cheol-Hyun Cho and Hansol Hong" |
November 21, 2017, 4:15 PM at Science Center 507 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Yue M. Lu (HARVARD JOHN A. PAULSON SCHOOL OF ENGINEERING AND APPLIED SCIENCES) |
Asymptotic Methods for High-Dimensional Inference: Precise Analysis, Fundamental Limits, and Optimal Designs |
Extracting meaningful information from the large datasets being compiled by our society presents challenges and opportunities to signal and information processing research. On the one hand, many classical methods, and the assumptions they are based on, are simply not designed to handle the explosive growth of the dimensionality of the modern datasets. On the other hand, the increasing dimensionality offers many benefits: in particular, the very high-dimensional settings allow one to apply powerful asymptotic methods from probability theory and statistical physics to obtain precise characterizations that would otherwise be too complicated in moderate dimensions. I will mention recent work on exploiting such blessings of dimensionality via sharp asymptotic methods. In particular, I will show (1) the exact characterization of a widely-used spectral method for nonconvex signal recoveries; (2) the fundamental limits of solving the phase retrieval problem via linear programming; and (3) how to use scaling and mean-field limits to analyze nonconvex optimization algorithms for high-dimensional inference and learning. In these problems, asymptotic methods not only clarify some of the fascinating phenomena that emerge with high-dimensional data, they also lead to optimal designs that significantly outperform commonly used heuristic choices" |
November 20, 2017, 12:00 PM at Science Center 232 |
| LEARNING SEMINAR ON THE FARGUES-FONTAINE CURVE |
Laurent Fargues (INSTITUTE OF MATHEMATICS OF JUSSIEU) |
Structure of the Picard stack and the Abel-Jacobi morphism for the curve. |
" |
November 20, 2017, 4:00 - 6:00 PM at Science Center 507 |
| BRANDEIS, HARVARD, MIT, NORTHEASTERN JOINT COLLOQUIUM AT HARVARD |
Spencer Bloch (UNIVERSITY OF CHICAGO) |
Periods, motivic gamma functions, and Hodge structures |
Golyshev and Zagier showed how, using the Frobenius method to generate inhomogeneous solutions to Picard Fuchs equations near points of maximal unipotent monodromy for certain familys of K3 surfaces, one could generate what seemed to be infinite sequences of periods. In joint work with M. Vlasenko, we study motivic gamma functions and extensions of Hodge structure associated to the Golyshev-Zagier construction" |
November 16, 2017, Tea at 4 pm, Talk at 4:30 pm at Science Center Hall A |
| LEARNING SEMINAR ON THE FARGUES-FONTAINE CURVE |
Matthew Morrow (INSTITUTE OF MATHEMATICS OF JUSSIEU) |
Perfectoid after-party: pro-etale topology |
" |
November 15, 2017, 5:00 pm *note special day/time* at Science Center 507 |
| HARVARD LOGIC COLLOQUIUM |
Steve Jackson (UNIVERSITY OF NORTH TEXAS) |
Combinatorics of Definable Sets |
Recent years have seen an interest in the combinatorics of definable sets. Definable has several interpretations including Borel, or as existing in a model of determinacy. The definable theory differs markedly from the ZFC context. This theory can be viewed as simultaneously generalizing dynamics, where Borel actions of countable groups on Polish spaced are studied, and the descriptive set theory of determinacy models. We will survey and present some recent results of the speaker and others." |
November 15, 2017, 4:00 - 5:00 pm at Logic Center, 2 Arrow St, Rm 420 |
| NUMBER THEORY SEMINAR |
Lucia Mocz (PRINCETON UNIVERSITY) |
A New Northcott Property for Faltings Height |
The Faltings height is a useful invariant for addressing questions in arithmetic geometry. In his celebrated proof of the Mordell and Shafarevich conjectures, Faltings shows the Faltings height satisfies a certain Northcott property, which allows him to deduce his finiteness statements. In this work we prove a new Northcott property for the Faltings height. Namely we show, assuming the Colmez Conjecture and the Artin Conjecture, that there are finitely many CM abelian varieties of a fixed dimension which have bounded Faltings height. The technique developed uses new tools from integral p-adic Hodge theory to study the variation of Faltings height within an isogeny class of CM abelian varieties. In special cases, we are able to use these techniques to moreover develop new Colmez-type formulas for the Faltings height" |
November 15, 2017, 3:15 pm *sharp at Science Center 507 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Daniel Sussman (BOSTON UNIVERSITY) |
Multiple Network Inference: From Joint Embeddings to Graph Matching |
Statistical theory, computational methods, and empirical evidence abound for the study of individual networks. However, extending these ideas to the multiple-network framework remains a relatively under-explored area. Individuals today interact with each other through numerous modalities including online social networks, telecommunications, face-to-face interactions, financial transactions, and the sharing and distribution of goods and services. Individually these networks may hide important activities that are only revealed when the networks are studied jointly. In this talk, weâll explore statistical and computational methods to study multiple networks, including a tool to borrow strength across networks via joint embeddings and a tool to confront the challenges of entity resolution across networks via graph matching" |
November 15, 2017, 4:00 - 5:00 pm *note change in time* at CMSA Building, 20 Garden Street, G02 |
| MATHEMATICAL PHYSICS SEMINAR |
Dennis Gaitsgory (HARVARD UNIVERSITY) |
Higher Representation Theory |
" |
November 14, 2017, 4:00 PM at Jefferson 356 |
| LOGIC SEMINAR |
Linda Brown Westrick (UNIVERSITY OF CONNECTICUT) |
Towards a notion of computable reducibility for discontinuous functions |
If X and Y are computably presented uncountable metric spaces, the collection of all functions from X to Y has cardinality too large to allow such functions to be represented as elements of Baire space. Nevertheless, we have some intuitive idea of what it should mean for one discontinuous function to compute another. I will discuss the problem of defining an appropriate notion of computable reducibility on this space. Joint work with Adam Day, Rod Downey and Takayuki Kihara" |
November 14, 2017, 5:15 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Yusuf Baris Kartal (MIT) |
Dynamical invariants of categories associated to mapping tori |
One can construct the symplectic mapping torus for a given a symplectic manifold with a symplectomorphism and use the flux invariant to distinguish the mapping tori of maps of different order. The essential argument is that the flow in a certain direction have different periods depending on the order of the symplectomorphism. In this talk, we will introduce an abstract categorical version of the mapping torus- associated to an $A_\infty$ category and an auto-equivalence. Then, we will construct a family of bimodules analogous to the flow and discuss how to characterize it intrinsically and how to use it to distinguish different categorical mapping tori" |
November 13, 2017, 12:30 - 1:30 pm at CMSA Building, 20 Garden Street, G02 |
| LEARNING SEMINAR ON THE FARGUES-FONTAINE CURVE |
Matthew Morrow (INSTITUTE OF MATHEMATICS OF JUSSIEU) |
Foundations of perfectoid spaces-IV |
" |
November 13, 2017, 4:00 - 6:00 PM at Science Center 507 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Zhe Wang (NYU) |
A Driven Tagged Particle in One-dimensional Simple Exclusion Process |
We study the long-time behavior of a driven tagged particle in a one- dimensional non-nearest- neighbor simple exclusion process. We will discuss two scenarios when the tagged particle has a speed. Particularly, for the ASEP, the tagged particle can have a positive speed even when it has a drift with negative mean; for the SSEP with removals, we can compute the speed explicitly. We will characterize some nontrivial invariant measures of the environment process by using coupling arguments and color schemes" |
November 10, 2017, 12:00 PM at Science Center 232 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Siqi He (CALIFORNIA INSTITUTE OF TECHNOLOGY) |
The extended Bogomolny Equations, Generalized Nahm Pole, and SL(2,R) Higgs bundle |
We will discuss Witten s gauge theory approach to Jones polynomial and Khovanov homology by counting solutions to some gauge theory equations with singular boundary conditions. When we reduce these equations to 3-dimensional, we call them the extended Bogomolny equations. We develop a Donaldson-Uhlenbeck-Yau type correspondence for the moduli space of the extended Bogomolny equations on Riemann surface ÎŁ times R^+ with Nahm pole singularity at ÎŁ Ă {0} and the Teichmuller component of the stable SL(2, R) Higgs bundle, this verifies a conjecture of Gaiotto and Witten. The proof is based on an observation that the extended Bogomolny equations can be reduced to a Kazdan-Warner type equation. We will also discuss a partial correspondence for solutions with knot singularities in this program, corresponding to the non-Teichmuller components in the moduli space of stable SL(2, R) Higgs bundles. This is joint work with Rafe Mazzeo" |
November 10, 2017, 3:30 - 4:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Coanalytic Functors |
" |
November 09, 2017, 4:00 - 6:00 PM at Science Center 507 |
| BRANDEIS, HARVARD, MIT, NORTHEASTERN JOINT COLLOQUIUM AT HARVARD |
Jeremy Quastel (UNIVERSITY OF TORONTO) |
The KPZ fixed point |
The KPZ universality class contains one dimensional growth models, directed random polymers, stochastic Hamilton-Jacobi equations (e.g. the eponymous Kardar-Parisi-Zhang equation, which led to a 2014 Fields medal). It is characterized by unusual scale of fluctuations, some of which, surprisingly, come from random matrix theory, and which are model independent but do depend on the initial data. The physical explanation is that in the space of Markov processes, these models are all being rescaled to a universal fixed point. But this scaling invariant fixed point was completely unknown, even by the physicists, until this year, when we managed to compute it in joint work with Konstantin Matetski and Daniel Remenik. It is a new type of âstochastic integrable systemâ. In the talk I will describe it, as well as how it was obtained by solving a special model in the class called TASEP" |
November 09, 2017, Tea at 4 pm, Talk at 4:30 pm at Math Common Room & Science Center Hall A |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Eduard Duryev (HARVARD UNIVERSITY) |
Square-tilings of modular curves X(d) |
In my talk I will define certain flat metrics on modular curves X(d), in which they decompose into unit squares identified along parallel sides. In particular, we will see pagoda structures of X(d) that arise in the case of prime d. I will discuss this structures in more details and relate them to the classification of TeichmĂŒller curves in M_2" |
November 08, 2017, 4:00 PM at Science Center 530 |
| NUMBER THEORY SEMINAR |
Kazim Buyuboduk (UC DUBLIN AND HARVARD UNIVERSITY) |
Non-ordinary symmetric squares and Euler systems of rank 2 |
I will report on joint work with A. Lei, D. Loeffler and G. Venkat, where we develop a signed-splitting procedure for non-integral Beilinson-Flach classes associated to the symmetric squares of p-non-ordinary forms. The novelty in this procedure is that it works even though the cyclotomic deformations of Beilinson-Flach classes do not possess an interpolation property that covers the full critical range. This is consistent with Perrin-Riou s conjectures on rank 2 Euler systems; as a matter of fact, our methods are inspired by the implications of her conjecture. In certain cases, A. Lei and I are able to prove that the integral classes we obtain indeed lift to a non-trivial rank 2 Euler system, confirming Perrin-Riou s predictions. This has applications to the Iwasawa theory of symmetric squares" |
November 08, 2017, 3:15 pm *sharp at Science Center 507 |
| HARVARD LOGIC COLLOQUIUM |
Victoria Gitman (CUNY GRADUATE CENTER) |
Virtual Large Cardinal Principles |
Abstract: http://logic.harvard.edu/colloquium.ph" |
November 08, 2017, 4:00 - 5:00 pm at Logic Center, 2 Arrow St, Rm 420 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Elchanan Mossel (MIT) |
Optimal Gaussian Partitions |
How should we partition the Gaussian space into k parts in a way that minimizes Gaussian surface area, maximize correlation or simulate a specific distribution. The problem of Gaussian partitions was studied since the 70s first as a generalization of the isoperimetric problem in the context of the heat equation. It found a renewed interest in context of the double bubble theorem proven in geometric measure theory and due to connection to problems in theoretical computer science and social choice theory. I will survey the little we know about this problem and the major open problems in the area." |
November 08, 2017, 3:00 - 4:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| MATHEMATICAL PHYSICS SEMINAR |
Liming Ge (UNH AND CHINESE ACADEMY OF SCIENCES) |
From Riemann and Hilbert to Kadison-Singer |
" |
November 07, 2017, 4:00 PM at Jefferson 356 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Matthew Morrow (CNRS) |
(Topological) Hochschild homology and and crystalline cohomology |
Cyclic homology and its variants (periodic cyclic homology, negative cyclic homology) were introduced by Alain Connes and Boris Tsygan in the 1980s by exploiting the action of the circle on Hochschild homology. For smooth varieties over a field of characteristic zero, classical theorems in the subject show that they encode the de Rham cohomology and the Hodge filtration; the trace map from K-theory to cyclic homology is then a manifestation of the de Rham character. I will give an overview of this classical story and then pass to finite characteristic, in which a similar framework now exists â at the expense of working instead with topological Hochschild and cyclic homology. Joint work with Bhargav Bhatt and Peter Scholze" |
November 07, 2017, 3:00 PM at Science Center Hall A |
| DIFFERENTIAL GEOMETRY SEMINAR |
Julius Ross (UNIVERSITY OF ILLINOIS AT CHICAGO) |
The Monge-Ampere Equation and the Hele-Shaw flow |
I shall describe duality between solutions of the Dirichlet problem to the complex Monge-Amp\`ere Equation and a flow coming from fluid dynamics called the Hele-Shaw flow. Using this, we can give examples of boundary data for which solutions to this Dirichlet problem exhibit previously unknown phenomena, and use analytic results from complex geometry to deduce new statements about this classical flow. This work is joint with David Witt Nystr\om" |
November 07, 2017, 4:15 PM at Science Center 507 |
| LEARNING SEMINAR ON THE FARGUES-FONTAINE CURVE |
Matthew Morrow (INSTITUTE OF MATHEMATICS OF JUSSIEU) |
Foundations of perfectoid spaces-III |
" |
November 06, 2017, 4:00 - 6:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Pietro Benetti Genolini (UNIVERSITY OF OXFORD) |
Topological AdS/CFT |
I will describe a holographic dual to the Donaldson-Witten topological twist of gauge theories on a Riemannian four-manifold. Specifically, I will consider asymptotically locally hyperbolic solutions to Romansâ gauged supergravity in five dimensions with the four-manifold as conformal boundary, and show that the renormalised supergravity action is independent of the choice of boundary metric. This is a first step in the direction of combining topological quantum field theory with the AdS/CFT correspondence" |
November 06, 2017, 12:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Kevin Sackel (MIT) |
Perverse sheaves from complex Lagrangian intersections |
Following work of Bussi, we will construct a canonical perverse sheaf on the intersection of two complex Lagrangians in a complex symplectic manifold. The construction is local, using the gluing property of perverse sheaves to produce a global object. It is conjectured by Joyce that the hypercohomology of this perverse sheaf is Lagrangian Floer cohomology" |
November 03, 2017, 3:30 - 4:30 PM at Science Center 507 |
| CMSA ALGEBRAIC GEOMETRY SEMINAR |
Alexander Moll (IHES) |
Hibert Schemes from Geometric Quantization of Dispersive Periodic Benjamin-Ono Waves |
By Grojnowski and Nakajima, Fock spaces are cohomology rings of Hilbert scheme of points in the plane. On the other hand, by Pressley-Segal, Fock spaces are spaces of J-holomorphic functions on the loop space of the real line that appear in geometric quantization with respect to the KĂ€hler structure determined by the Sobolev regularity s= -1/2 and the Hilbert transform J. First, we show that the classical periodic Benjamin-Ono equation is a Liouville integrable Hamiltonian system with respect to this KĂ€hler structure. Second, we construct an integrable geometric quantization of this system in Fock space following Nazarov-Sklyanin and describe the spectrum explicitly after a non-trivial rewriting of our coefficients of dispersion \ebar = e_1 + e_2 and quantization \hbar = - e_1 e_2 that is invariant under e_2 <-> e_1. As a corollary of Lehn s theorem, our construction gives explicit creation and annihilation operator formulas for multiplication by new explicit universal polynomials in the Chern classes of the tautological bundle in the equivariant cohomology of our Hilbert schemes, in particular identifying \ebar with the deformation parameter of the Maulik-Okounkov Yangian and \hbar with the handle-gluing element. Our key ingredient is a simple formula for the Lax operators as elliptic generalized Toeplitz operators on the circle together with the spectral theory of Boutet de Monvel and Guillemin. As time permits, we discuss the relation of dispersionless \ebar -> 0 and semi-classical \hbar \rightarrow 0 limits to Nekrasov s BPS/CFT Correspondence" |
November 02, 2017, 3:00 PM at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS ALGEBRAIC GEOMETRY SEMINAR |
Shamil Shakirov (HARVARD UNIVERSITY) |
Undulation invariants of plane curves |
One of the general problems in algebraic geometry is to determine algorithmically whether or not a given geometric object, defined by explicit polynomial equations (e.g. a curve or a surface), satisfies a given property (e.g. has singularities or other distinctive features of interest). A classical example of such a problem, described by Cayley and Salmon in 1852, is to determine whether or not a given plane curve of degree r > 3 has undulation points -- the points where the tangent line meets the curve with multiplicity four. Cayley proved that there exists an invariant of degree (r - 3)(3 r - 2) that vanishes if and only if the curve has undulation points. We construct this invariant explicitly for quartics (r=4) as the determinant of a 21 times 21 matrix with polynomial entries, and we conjecture a generalization for r = 5" |
November 01, 2017, 5:00 PM *note time change* at CMSA Building, 20 Garden Street, Room G10 |
| JOINT MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Kay Kirkpatrick (UIUC MATH AND PHYSICS, MIT MATH ) |
Quantum groups, Free Araki-Woods Factors, and a Calculus for Moments |
We will discuss a central limit theorem for quantum groups: that the joint distributions with respect to the Haar state of the generators of free orthogonal quantum groups converge to free families of generalized circular elements in the large (quantum) dimension limit. We also discuss a connection to free Araki-Woods factors, and cases where we have surprisingly good rates of convergence. This is joint work with Michael Brannan. Time permitting, we ll mention another quantum central limit theorem for Bose-Einstein condensation and work in progress" |
November 01, 2017, 2:00 - 3:00 pm at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Alexander Smith (HARVARD UNIVERSITY) |
$2^\infty$-Selmer groups, $2^\infty$-class groups, and Goldfeld's conjecture |
Take $E/\mathbb{Q}$ to be an elliptic curve with full rational $2$-torsion (satisfying some extra technical assumptions). In this talk, we will show that $100\%$ of the quadratic twists of $E$ have rank less than two, thus proving that the BSD conjecture implies Goldfeld s conjecture in these families. To do this, we will extend Kane s distributional results on the $2$-Selmer groups in these families to $2^k$-Selmer groups for any $k > 1$. In addition, using the close analogy between $2^k$-Selmer groups and $2^{k+1}$-class groups, we will prove that the $2^{k+1}$-class groups of the quadratic imaginary fields are distributed as predicted by the Cohen-Lenstra heuristics for all $k > 1$" |
November 01, 2017, 3:15 pm *sharp at Science Center 507 |
| INFORMAL GEOMETRY & DYNAMICS SEMINAR |
Bena Tshishiku (HARVARD UNIVERSITY) |
Cohomology of arithmetic groups and characteristic classes of manifold bundles |
Much recent work has gone toward computing the ring H*( BDiff(M) ) of characteristic classes of smooth fiber bundles with fiber M. For some M (e.g. surfaces) we have a good understanding of the cohomology in the stable range, but very little is known beyond that. In this talk we will discuss some new characteristic classes that come from the unstable cohomology of arithmetic groups." |
November 01, 2017, 4:00 PM at Science Center 530 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Wei-Ming Wang (CNRS) |
Quasi-periodic solutions to nonlinear PDE's |
We present a new approach to the existence of time quasi-periodic solutions to nonlinear PDE s. It is based on the method of Anderson localization, harmonic analysis and algebraic analysis. This can be viewed as an infinite dimensional analogue of a Lagrangian approach to KAM theory, as suggested by J. Moser" |
November 01, 2017, 3:00 - 4:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Chenglong Yu (HARVARD UNIVERSITY ) |
Picard-Fuchs systems of zero loci of vector bundle sections |
We propose an explicit construction for Picard-Fuchs systems of zero loci of vector bundle sections. When the vector bundle admits large symmetry, the system we constructed is holonomic. This is a joint work with Huang, Lian and Yau" |
November 01, 2017, 12:30 - 1:30 pm at CMSA Building, 20 Garden St, G10 |
| LOGIC SEMINAR |
Sebastien Vasey (HARVARD UNIVERSITY) |
Non-elementary classification theory |
The classification theory of elementary classes was started by Michael Morley in the early sixties, when he proved that a countable first-order theory with a single model in some uncountable cardinal has a single model in all uncountable cardinals. The proof of this result, now called Morley s categoricity theorem, led to the development of forking, a joint generalization of linear independence in vector spaces and algebraic independence of fields, which is now a central pillar of modern model theory. In recent years, it has become apparent that the theory of forking can also be developed in several non-elementary contexts. Prime among those is the axiomatic framework of abstract elementary classes (AECs), encompassing the class of models of any L_{infinity, omega}-theory and closely connected to the more general framework accessible categories. A test question to judge progress in this direction is the forty year old eventual categoricity conjecture of Shelah, which says that a version of Morley s categoricity theorem should hold of any AEC. I will survey recent developments, including the connections with category theory and large cardinals as well as my resolution of the eventual categoricity conjecture for classes of models axiomatized by a universal L_{infty, omega}-theory" |
October 31, 2017, 5:15 pm at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Nick Rozenblyum (UNIVERSITY OF CHICAGO) |
Shifted symplectic structures and quantization |
Many moduli problems of interest, such as moduli spaces of coherent sheaves or principal G-bundles, come equipped with a natural symplectic structure. Moreover, quantization of these symplectic structures is closely related to counting problems in geometry and topology, such as Donaldson-Thomas invariants and their generalizations, as well as Feynman integration in physics. The theory of shifted symplectic structures introduced provides a vast generalization of algebraic symplectic geometry, provides a natural framework for constructing and studying such symplectic structures and their quantizations. I will give a brief overview of this theory and describe several geometric applications" |
October 31, 2017, 3:00 PM at MIT 4-237 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Bill Goldman (BROWN UNIVERSITY AND UNIVERSITY OF MARYLAND) |
Dynamics on moduli spaces of flat connections |
We describe dynamical systems arising from the classification of locally homogeneous geometric structures are flat connections on topological manifolds. These arise from natural mapping class group actions on character varieties. The mapping class group action is a discrete version of a continuous object, namely the extension of the Teichmueller flow to a universal character variety over the tangent bundle of Teichmuller space. We give several examples of this construction and discuss joint work with Giovanni Forni on a mixing property of this suspended flow. Finally we discuss specific examples of these dynamics for surfaces with rank two fundamental group (Euler characteristic -1)" |
October 31, 2017, 4:15 PM at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Zhenghan Wang (MICROSOFT) |
Reconstructing chiral CFTs/VOAs from 2D TQFTs/MTCs |
Inspired by the bulk-edge relation of 2D topological phases of matter and Tannaka-Krein duality, we consider the reconstruction of chiral CFTs, mathematically vertex operator algebras (VOAs), from their representation categories---modular tensor categories (MTCs)" |
October 31, 2017, 4:00 PM at Jefferson 356 |
| LEARNING SEMINAR ON THE FARGUES-FONTAINE CURVE |
Matthew Morrow (INSTITUTE OF MATHEMATICS OF JUSSIEU) |
Foundations of perfectoid spaces-II |
" |
October 30, 2017, 4:00 - 6:00 PM at Science Center 507 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Piotr Suwara (MIT) |
The Category of Perverse Sheaves is a Stack, cont'd |
For a complex manifold $X$, we define a full subcategory of the category of constructible sheaves on $X$, which is called the category of perverse sheaves. We also state a gluing property satisfied by perverse sheaves" |
October 27, 2017, 3:30 - 4:30 PM at Science Center 507 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Noga Alon (TEL AVIV UNIVERSITY ) |
Random Cayley Graphs |
The study of random Cayley graphs of finite groups is related to the investigation of Expanders and to problems in Combinatorial Number Theory and in Information Theory. I will discuss this topic, describing the motivation and focusing on the question of estimating the chromatic number of a random Cayley graph of a given group with a prescribed number of generators. Several intriguing questions that remain open will be mentioned as well" |
October 25, 2017, 3:00 - 4:00 PM at CMSA Building, 20 Garden St, G10 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Sander Kupers (HARVARD UNIVERSITY) |
The metastable homology of mapping class groups |
We will explain how techniques from homotopy theory allow one to prove a secondary version of Harer s celebrated stability result for the homology of mapping class groups. Along the way, we will compute a previously unknown homology group in the unstable range: H_3(\Gamma_{4,1};Q). This is joint work with Soren Galatius and Oscar Randal-Williams." |
October 25, 2017, 4:00 PM at Science Center 530 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Subhabrata Sen (MICROSOFT AND MIT) |
Partitioning sparse random graphs: connections with mean-field |
The study of graph-partition problems such as Maxcut, max-bisection and min-bisection have a long and rich history in combinatorics and theoretical computer science. A recent line of work studies these problems on sparse random graphs, via a connection with mean field spin glasses. In this talk, we will look at this general direction, and derive sharp comparison inequalities between cut- sizes on sparse Erd\ Ì{o}s-R\ {e}nyi and random regular graphs. Based on joint work with Aukosh Jagannath" |
October 25, 2017, 2:00 - 3:00 pm at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Pierre Colmez (UPMC AND IAS) |
On the cohomology of p-adic analytic curves |
I will explain how the various cohomologies of a p-adic analytic curve are related. The case of coverings of the p-adic upper half-plane has applications to the p-adic local Langlands correspondence" |
October 25, 2017, 3:15 pm *sharp at Science Center 507 |
| LOGIC SEMINAR |
Will Boney (HARVARD UNIVERSITY) |
Interpolation beyond $\mathbb{L}_{\omega_1, \omega}$ |
For a logic $\mathcal{L}$, interpolation holds in $\mathcal{L}$ iff for every implication $\phi \to \psi$, there is a sentence $\chi$ in their common language (in $\mathcal{L}$) such that $\phi \to \chi$ and $\chi \to \psi$. It is well-known that $\mathbb{L}_{\omega, \omega}$ and $\mathbb{L}_{\omega_1, \omega}$ satisfy interpolation, but no other $\mathbb{L}_{\kappa, \lambda}$ does. We discuss a logic $\mathbb{L}^1_\kappa$ developed by Shelah that (for $\kappa = \beth_\kappa$) is intermediate between $\mathbb{L}_{\kappa, \omega}$ and $\mathbb{L}_{\kappa, \kappa}$ and satisfies interpolation" |
October 24, 2017, 5:15 pm at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Yevgeniy Liokumovich (MIT) |
Heegaard splittings isotopic to an index 1 minimal surface |
Let $M$ be a $3$-manifold that has no one-sided embedded surfaces and $\Sigma$ a strongly irreducible Heegaard surface in $M$. We show that for a generic Riemannian metric on $M$ surface $\Sigma$ is isotopic to a minimal surface of index $1$, confirming a conjecture of Pitts and Rubinstein. This is a joint work with Daniel Ketover and Antoine Song" |
October 24, 2017, 4:15 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
David Hansen (COLUMBIA UNIVERSITY) |
Vanishing theorems in rigid analytic geometry |
I will review some classical cohomological vanishing theorems due to Andreotti-Frankel and Artin, and then explain an analogous result in rigid analytic geometry. I will also explain how I was convinced that excellent rings deserve their name, and why Ofer Gabber is the master of us all" |
October 24, 2017, 1:30 - 2:30 pm *note change in time at MIT 2-4449 *note change in location |
| LEARNING SEMINAR ON THE FARGUES-FONTAINE CURVE |
Matthew Morrow (INSTITUTE OF MATHEMATICS OF JUSSIEU) |
Review of foundations of perfectoid spaces |
" |
October 23, 2017, 4:00 - 6:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Florian Beck (UNIVERSITY OF HAMBURG) |
Hitchin systems in terms of Calabi-Yau threefolds |
Integrable systems are often constructed from geometric and/or Lie-theoretic data. Two important example classes are Hitchin systems and Calabi-Yau integrable systems. A Hitchin system is constructed from a compact Riemann surface together with a complex Lie group with mild extra conditions. In contrast, Calabi-Yau integrable systems are constructed from a priori purely geometric data, namely certain families of Calabi-Yau threefolds. Despite their different origins there is a non-trivial relation between Hitchin and Calabi-Yau integrable systems. More precisely, we will see in this talk that any Hitchin system for a simply-connected or adjoint simple complex Lie group is isomorphicto a Calabi-Yau integrable system (away from singular fibers)" |
October 23, 2017, 12:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| JOINT DEPARTMENT OF MATHEMATICS AND CMSA RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Madhu Sudan (CS, HARVARD) |
General Strong Polarization |
A recent discovery (circa 2008) in information theory called Polar Coding has led to a remarkable construction of error-correcting codes and decoding algorithms, resolving one of the fundamental algorithmic challenges in the field. The underlying phenomenon studies the ``polarization of a ``bounded martingale. A bounded martingale, X_0,...,X_t,... is one where X_t in [0,1]. This martingale is said to polarize if Pr[lim_{t\to infty} X_t \in {0,1}] = 1. The questions of interest to the results in coding are the rate of convergence and proximity: Specifically, given epsilon and tau > 0 what is the smallest t after which it is the case that Pr[X_t in (tau,1-tau)] < epsilon? For the main theorem, it was crucial that t <= min{O(log(1/epsilon)), o(log(1/tau))}. We say that a martingale polarizes strongly if it satisfies this requirement. We give a simple local criterion on the evolution of the martingale that suffices for strong polarization. A consequence to coding theory is that a broad class of constructions of polar codes can be used to resolve the afore-mentioned algorithmic challenge. In this talk I will introduce the concepts of polarization and strong polarization. Depending on the audience interest I can explain why this concept is useful to construct codes and decoding algorithms, or explain the local criteria that help establish strong polarization (and the proof of why it does so). Based on joint work with Jaroslaw Blasiok, Venkatesan Guruswami, Preetum Nakkiran, and Atri Rudra" |
October 23, 2017, 12:00 - 1:00 PM at Science Center 232 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Piotr Suwara (MIT) |
The Category of Perverse Sheaves is a Stack |
For a complex manifold $X$, we define a full subcategory of the category of constructible sheaves on $X$, which is called the category of perverse sheaves. We also state a gluing property satisfied by perverse sheaves" |
October 20, 2017, 3:30 - 4:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
The Bousfield-Kuhn functor |
" |
October 19, 2017, 4:00 - 6:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Nati Blaier (CMSA, HARVARD ) |
Geometry of the symplectic Torelli group |
This talk has two parts. In the first part of the talk, I will introduce the group of symplectomorphism and try to convince you that it is a very important object in symplectic topology by surveying some known structural results and drawing a comparison with the situation in the smooth and Kahler geometries as well as the world of low-dimensional topology. In the second part, I ll discuss the symplectic Torelli group for higher dimensional symplectic manifolds, and an ongoing project to use Gromov-Witten theory to detect interesting elements" |
October 18, 2017, 12:00 PM at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
V. Kumar Murty (UNIVERSITY OF TORONTO) |
The Lindelof class of L-functions |
This class of L-functions was defined about ten years ago and contains the Selberg class. The class is defined in terms of growth conditions and elements need not have an Euler product or functional equation. Moreover, the Lindelof class has a natural ring structure. In joint work with Anup Dixit, we establish some properties of this ring. Actually, we work with a variant of this ring which seems to have better properties.Â" |
October 18, 2017, 3:15 pm at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Rohini Ramadas (HARVARD UNIVERSITY) |
Algebraic dynamics from topological and holomorphic dynamics |
Let f:S^2 â> S^2 be an orientation-preserving branched covering from the 2-sphere to itself whose postcritical set P := { f^n(x) | x is a critical point of f and n > 0 } is finite. Thurston studied the dynamics of f using an induced holomorphic self-map T(f) of the Teichmuller space of complex structures on (S^2, P). Koch found that this holomorphic dynamical system on Teichmuller space descends to algebraic dynamical systems: 1. T(f) always descends to a multivalued self map H(f) of the moduli space M_{0,P} of markings of the Riemann sphere by the finite set P 2. When P contains a point x at which f is fully ramified, under certain combinatorial conditions on f, the inverse of T(f) descends to a rational self-map M(f) of projective space CP^n. When, in addition, x is a fixed point of f, i.e. f is a `topological polynomialâ, the induced self-map M(f) is regular. The dynamics of H(f) and M(f) may be studied via numerical invariants called dynamical degrees: the k-th dynamical degree of an algebraic dynamical system measures the asymptotic growth rate, under iteration, of the degrees of k-dimensional subvarieties. I will introduce the dynamical systems T(f), H(f) and M(f), and dynamical degrees. I will then discuss why it is useful to study H(f) (resp. M(f)) simultaneously on several compactifications of M_{0,P}. We find that the dynamical degrees of H(f) (resp. M(f)) are algebraic integers whose properties are constrained by the dynamics of f on the finite set P. In particular, when M(f) exists, then the more f resembles a topological polynomial, the more M(f) : CP^n - - -> CP^n behaves like a regular map." |
October 18, 2017, 4:00 PM at Science Center 530 |
| LOGIC SEMINAR |
Cameron Freer (BORELIAN AND REMINE) |
Feedback Computability |
The notion of a feedback query is a natural generalization of choosing for an oracle the set of indices of halting computations. Notice that, in that setting, the computations being run are different from the computations in the oracle: the former can query an oracle, whereas the latter cannot. A feedback computation is one that can query an oracle, which itself contains the halting information about all feedback computations. Although this is self-referential, sense can be made of at least some such computations. We ll discuss feedback around Turing computability. In one direction, we examine feedback Turing machines, and show that they provide exactly hyperarithmetic computability. In the other direction, Turing computability is itself feedback primitive recursion (at least, one version thereof). We ll also briefly consider notions for parallel computation, and for Borel maps on Cantor space. Joint work with Nate Ackerman and Bob Lubarsky" |
October 17, 2017, 5:15 pm at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Dave Jensen (UNIVERSITY OF KENTUCKY) |
Linear Systems on General Curves of Fixed Gonality |
The geometry of an algebraic curve is governed by its linear systems. While many curves exhibit bizarre and pathological linear systems, the general curve does not. This is a consequence of the Brill-Noether theorem, which says that the space of linear systems of given degree and rank on a general curve has dimension equal to its expected dimension. In this talk, we will discuss a generalization of this theorem to general curves of fixed gonality. To prove this result, we use tropical and combinatorial methods. This is joint work with Dhruv Ranganathan, based on prior work of Nathan Pflueger" |
October 17, 2017, 3:00 PM at Science Center Hall A |
| DIFFERENTIAL GEOMETRY SEMINAR |
Gang Liu (NORTHWESTERN) |
Recent progress of Yau's uniformization conjecture |
Yauâs uniformization conjecture states that a complete noncompact Kahler manifold with positive bisectional curvature is biholomorphic to the complex Euclidean space. We confirm this conjecture when the manifold has maximal volume growth" |
October 17, 2017, 4:00 PM at Science Center 507 |
| LEARNING SEMINAR ON THE FARGUES-FONTAINE CURVE |
Zijian Yao (HARVARD UNIVERSITY) |
Properties of the curve (incl. line bundles) |
" |
October 16, 2017, 4:00 - 6:00 PM at Science Center 507 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Jiangfeng Lin (MIT) |
Nearby cycles and vanishing cycles |
We will give the definition of nearby cycles and vanishing cycles, explain the intuition behind them and then discuss some of their fundamental properties." |
October 13, 2017, 3:30 - 4:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY ) |
v_n-Periodic Homotopy Groups |
" |
October 12, 2017, 4:00 - 6:00 PM at Science Center 507 |
| SPECIAL MATHEMATICAL PHYSICS SEMINAR |
Yasayuki Kawahigashi (UNIVERSITY OF TOKYO) |
From Vertex Operator Algebras to Operator Algebras and Back |
We present a construction of a local conformal net of operator algebras to describe a chiral conformal field theory from a vertex operator algebra. We also discuss its representation theoretic aspect. " |
October 12, 2017, 2:00 pm *please note special date, time and location at Jefferson 453 |
| NUMBER THEORY SEMINAR |
Joseph Silverman (BROWN UNIVERSITY) |
Moduli Spaces of Rational Maps and a Dynamical Shafarevich Theorem |
We study the moduli space M_d[P] of rational degree d maps on P^1 with portrait level structure P, modulo the conjugation action of PGL_2. The structure of this space is closely related to a generalized Shafarevich conjecture for rational maps, which we prove for sufficiently large P, and we raise a number of questions in the case that P is small" |
October 11, 2017, 3:15 pm *sharp at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
Reflection Positivity and Invertible Topological Phases |
In a recent joint paper with Dan Freed the classification of symmetry protected phases of fermionic systems is approached using the methods of cobordism and stable homotopy theory. This talk will survey this relationship and describe some of the classification results" |
October 10, 2017, 4:00 PM at Jefferson 356 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Man-Wai Cheung (HARVARD UNIVERSITY) |
Quiver representations and theta functions |
Scattering diagrams theta functions and broken lines were developed in order to describe toric degenerations of Calabi-Yau varieties and construct mirror pairs. Later, Gross-Hacking-Keel-Kontsevich unravel the relation of those objects with cluster algebras. In the talk, we will discuss how we can combine the representation theory with these objects. We will also see how the broken lines on scattering diagram give a stratification of quiver Grassmannians using this setting" |
October 10, 2017, 3:00 PM at Science Center 411 |
| LOGIC SEMINAR |
Nate Ackerman (HARVARD UNIVERSITY ) |
Trees, Sheaves and Definition by Recursion |
We will show there is a topological space for which presheaves are the same thing as trees. We will further show that there is a sheaf on this topological space which has an important relationship with Baire space. We will then use these connections to show how a definition by transfinite recursion can be thought of as an operation on sheaves, and how the well-definedness of such a definition can be thought of as a property of the sheaf we are working on. This will then allow us to define a second order tree as a sheaf on a tree and to expand our notion of definition by transfinite recursion to all well-founded second order trees (even those which are ill-founded as normal trees). We will then mention how these techniques can be used to prove a variant of the Suslin-Kleene Separation theorem" |
October 10, 2017, 5:15 PM at Science Center 507 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Jianfeng Lin (MIT) |
Constructible sheaves and nearby cycles |
We will give the definition of constructible sheaves and discuss their properties. Time permitting, we will also discuss some basic idea of nearby/vanishing cycle" |
October 06, 2017, 3:30 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
David Corwin (MIT) |
Etale Homotopy Obstructions for Rational Points Applied to Open Subvarieties |
In 2008, Bjorn Poonen announced the construction of a variety without rational points but no Ă©tale-Brauer obstruction to the existence of rational points. We attempt to create a new obstruction that explains Poonen s example by applying the Ă©tale-Brauer obstruction to a Zariski open cover of a variety. On the one hand, we prove a general result that this new obstruction explains every variety without rational points, over quadratic imaginary and totally real number fields. On the other hand, this method is not effective, as the set of adelic points of a non-proper variety is non-compact. Nonetheless, we show how this new obstruction can be applied in Poonen s example. In doing so, we analyze the example from an algebro-topological perspective via the Ă©tale homotopy obstruction of Harpaz-Schlank and prove some results of independent interest in this direction" |
October 04, 2017, 3:15 pm at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Nattalie Tamam (TEL AVIV UNIVERSITY) |
Divergent trajectories in arithmetic homogeneous spaces of rational rank two |
In the theory of Diophantine approximations, singular points are ones for which Dirichletâs theorem can be infinitely improved. It is easy to see that all rational points are singular. In the special case of dimension one, the only singular points are the rational ones. In higher dimensions, points lying on a rational hyperplane are also obviously singular. However, in this case there are additional singular points. In the dynamical setting the singular points are related to divergent trajectories. In the talk I will define obvious divergent trajectories and explain the relation to rational points. In addition, I will present the more general setting involving Q-algebraic groups. Lastly I will discuss results concerning classification of divergent trajectories in Q-algebraic groups." |
October 04, 2017, 4:00 PM at Science Center 530 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Dingxin Zhang (BRANDEIS UNIVERSITY) |
<1 part of slopes under degeneration |
For a smooth family of projective varieties over a field of characteristic p > 0, it is known that the Newton polygon of fibers goes up under specialization. In this talk, we will show that when the family acquires singular members, the less than one part of the slopes of the Newton polygon goes up under specialization. This could be viewed as a characteristic p analogue of a simple phenomenon in Hodge theory" |
October 04, 2017, 12:00 - 1:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Yuchen Liu (YALE UNIVERSITY) |
K-stability of cubic threefolds |
We prove the K-moduli space of cubic threefolds is identical to their GIT moduli. More precisely, the K-(semi,poly)-stability of cubic threefolds coincide to the corresponding GIT stabilities, which could be explicitly calculated. In particular, this implies that all smooth cubic threefolds admit KĂ€hler-Einstein metric as well as provides a precise list of singular KE ones. To achieve this, the main new ingredient is an estimate in dimension three of the normalized volumes of kawamata log terminal singularities introduced by Chi Li. This is a joint work with Chenyang Xu" |
October 03, 2017, 3:00 PM at MIT 4-237 |
| LOGIC SEMINAR |
Jason Rute () |
A uniform reducibility in computably presented Polish spaces |
(Joint work with Tim McNicholl.) In this talk we will define a new uniform computable reducibility between computable Polish spaces. No specialized knowledge of computability theory is required. Given computably presented Polish spaces X and Y, we say x in X is reducible to y in Y if there is a Pi^0_1 subset P of Y and a computable map f : P -> X such that f(y)=x. For each space X one may consider the corresponding degree structure deg(X). For example, deg(2^omega) is (isomorphic to) the truth-table degrees, whereas both deg(omega^omega) and deg(reals) are proper extensions of deg(2^omega). This new reducibility has many motivations. First, it is based on the notion of truth-table reducibility (which we will define). Truth-table reducibility on 2^omega is too restrictive of a setting for working within Baire space or the real numbers. For example, there are functions f in omega^omega not truth-table reducible to any X in 2^omega and sequences X in 2^omega such that X/3 is not truth-table reducible to X. Our reducibility gives the correct generalization of truth-table reducibility to these spaces. Second, this project mirrors Miller s non-trivial work extending Turing reducibility to computably presented Polish spaces. Last, our reducibility grew naturally out of work of the first author on computable arcs and the second author on Schnorr randomness. For example, we show that, for the vector space R^d, every Schnorr random is found in some computable arc" |
October 03, 2017, 5:15 pm at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Alina Vdovina (UNIVERSITY OF NEWCASTLE AND NEW YORK UNIVERSITY) |
Buildings, surfaces and quaternions |
Buildings are exciting objects which have geometric, algebraic and number theoretical aspects. We will give elementary constructions of several classes of buildings as universal covers of finite complexes. Then (as a geometric application) we will show a connection of our results with Gromov s surface subgroup question and (as an arithmetic application) we will give explicit examples of quaternionic lattices" |
October 03, 2017, 4:00 PM at Jefferson 356 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Valentino Tosatti (NORTHWESTERN UNIVERSITY) |
Special Kahler geometry and collapsing |
Special Kahler geometry was first discovered in the context of N=2 supersymmetric 4D gauge theories, and it also plays a prominent role in mirror symmetry. A key observation of Donagi-Witten is that the base of every algebraic integrable system admits a special Kahler metric, while the total space admits a hyperkahler metric. Z. Lu proved that special Kahler manifolds are never complete unless they are flat. I will explain how special Kahler geometry arises in the collapsing of hyperkahler metrics on the total space of an algebraic integrable system (i.e. a projective irreducible holomorphic symplectic manifold with a holomorphic Lagrangian torus fibration), when the volume of the torus fibers shrinks to zero. Furthermore, the global collapsed Gromov-Hausdorff limit is equal to the metric completion of the special Kahler metric, and has singularities in real codimension 2, as predicted by the SYZ conjecture. This solves a conjecture of Kontsevich-Soibelman and Gross-Wilson in this settin" |
October 03, 2017, 4:15 PM at Science Center 507 |
| LEARNING SEMINAR ON THE FARGUES-FONTAINE CURVE |
Jacob Lurie (HARVARD UNIVERSITY) |
Constructing Functions on Y: Power Series in the Variable p |
" |
October 02, 2017, 4:00 - 6:00 PM at Science Center 507 |
| BOSTON GRADUATE TOPOLOGY SEMINAR |
Cliff Taubes (HARVARD UNIVERSITY) |
What are Z/2 harmonic forms? |
Abstract: Z/2 harmonic forms are closed and coclosed differential forms with values in a real line bundle that is defined only on the complement of a subset of the zero locus of the form itself. Their topological significance is not understood at present--but they do have some significance because they characterize (in part) the non-compactness of the moduli spaces of solutions to certain generalizations of the self-dual Yang-Mills equations. (Very little is known about these objects." |
September 30, 2017, 9:30 - 10:15 am at Science Center 507 |
| BOSTON GRADUATE TOPOLOGY SEMINAR |
Yu Pan (MIT) |
Augmentations and Exact Lagrangian cobordisms |
To a Legendrian knot, one can associate an Aâ category, the augmentation category. An exact Lagrangian cobordism between two Legendrian knots gives a functor of the augmentation categories of the two knots. We study the functor and establish a long exact sequence relating the corresponding cohomology of morphisms of the two ends. As applications, we prove that the functor between augmentation categories is injective on the level of equivalence classes of objects and find new obstructions to the existence of exact Lagrangian cobordisms in terms of linearized contact homology and ruling polynomials" |
September 30, 2017, 11:30 am - 12:15 pm at Science Center 507 |
| BOSTON GRADUATE TOPOLOGY SEMINAR |
Melissa Zhang (BOSTON COLLEGE) |
Annular Khovanov homology of 2-periodic links |
In the late 1970 s, Murasugi studied knots exhibiting p-fold symmetry and produced formulas relating the Alexander and Jones polynomials of these periodic knots with those of their quotient knots. Today, we are armed with richer, categorified link invariants such as knot Floer homology (HFK) and Khovanov homology (Kh). Their homological nature allows us to apply algebraic methods to obtain spectral sequences, which in turn produce rank inequalities and Murasugi-type formulas. By the Smith conjecture, the data of a periodic link specifies an unknotted braid axis in the 3-sphere. Since deleting the braid axis places the link inside a solid torus, or a thickened annulus, it is natural to study its annular Khovanov homology (AKh). In this talk, we exhibit a spectral sequence relating the AKh of a 2-periodic link with that of its quotient, and derive various decategorified consequences. Curiously, our method also hints at a similar spectral sequence from Kh of the periodic link to the AKh of the quotient link; we discuss partial results and open questions on this fron t" |
September 30, 2017, 10:30 - 11:15 am at Science Center 507 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Boyu Zhang (HARVARD UNIVERSITY) |
Orientation and duality |
We will give a proof of the Poincare-Verdier duality theorem and discuss its applications. Then we will define cohomologically constructible sheaves and their dual sheaves" |
September 29, 2017, 3:30 - 4:30 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
David Rohrlich (BOSTON UNIVERSITY) |
Counting Artin representatives |
Recently there has been a resurgence of interest in asymptotic counting problems in number theory, or ``arithmetic statistics, growing out of the extraordinary advances made by Bhargava and his students and collaborators in counting discriminants of quartic and quintic number fields, Selmer ranks of elliptic curves over the rationals, and many other quantities of number-theoretic interest. In this talk we consider a few problems in the arithmetic statistics of Artin representations. A classic result in this domain is Siegel s formula for averages of class numbers of binary quadratic forms, which implies that for $x\to \infty$, \[ \vartheta ^{\mathrm{di}}(x)\sim \dfrac{\pi}{36\zeta(3)^2} x^{3/2}, \] where $\vartheta ^{\mathrm{di}}(x)$ is the number of isomorphism classes of dihedral Artin representations of $\Q$ of conductor $\leqslant x$. We shall describe some variants of this formula and then pose the following question: Are most Artin representations abelian? Results of Ambrose, Pomerance, and Zelinsky suggest that this may not be an easy question to answer" |
September 27, 2017, 3:15 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Yu-Wei Fan (HARVARD UNIVERSITY) |
Weil-Petersson geometry on the space of Bridgeland stability conditions |
Inspired by mirror symmetry, we define Weil-Petersson geometry on the space of Bridgeland stability conditions on a Calabi-Yau category. The goal is to further understand the stringy Kahler moduli space of Calabi-Yau manifolds. This is a joint work with A. Kanazawa and S.-T. Yau" |
September 27, 2017, 12:00 - 1:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Yusheng Luo (HARVARD UNIVERSITY) |
Trees in degenerating families of rational maps and isometric G-actions |
Trees appear naturally in studying a degenerating family of rational maps or a sequence of degenerating representations of a finitely generated group into the isometry group of a negatively curved space. In the later case, the tree can be constructed in a more algebraic way using valuations on a function field of the character variety by Morgan and Shalen,...; there is also a more geometric construction using Gromov-Hausdorff convergence of G-spaces, or measured laminations on a hyperbolic surfaces by Thurston, Bestivina, Paulin,⊠For degenerating families of rational maps, one algebraic way is to study the induced rational map on the Berkovich projective line. We will introduce a more geometric construction using Douady-Eerle extension (barycentric extension) and compare all these different constructions" |
September 27, 2017, 4:00 PM at Science Center 530 |
| RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Herbert Spohn (TECHNICAL UNIVERSITY MUNICH & COLUMBIA) |
Hydrodynamics of integrable classical and quantum systems |
In the cold atoms community there is great interest in developing Euler-type hydrodynamics for one-dimensional integrable quantum systems, in particular with application to domain wall initial states. I provide some mathematical physics background and also compare with integrable classical systems" |
September 27, 2017, 3:00 - 4:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| LOGIC SEMINAR |
Gabriel Goldberg (HARVARD UNIVERSITY) |
The least strongly compact cardinal and the Ultrapower Axiom |
It is consistent that the least strongly compact cardinal is the least supercompact cardinal, but it is also consistent that the least strongly compact cardinal is the least measurable cardinal. Which is it? The Ultrapower Axiom is an abstract comparison principle motivated by inner model theory that roughly states that any pair of ultrapowers can be ultrapowered to a common ultrapower. We give a characterization of supercompact cardinals in terms of the Mitchell order and use this to prove that the least strongly compact cardinal is supercompact assuming the Ultrapower Axiom and the GCH" |
September 26, 2017, 5:15 pm at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Alina Marian (NORTHEASTERN UNIVERSITY) |
On the intersection theory of Hilbert schemes of points on a surface |
I will describe the structure of natural intersection-theoretic invariants coming from Chern classes of tautological vector bundles over Hilbert schemes of points on a smooth projective surface. The subject has a long history; I will explain aspects of it, as well as recent contributions in joint work with D. Oprea and R. Pandharipande" |
September 26, 2017, 3:00 PM at Science Center Hall A |
| MATHEMATICAL PHYSICS SEMINAR |
Jinsong Wu (HARVARD UNIVERSITY) |
The Brascamp-Lieb Inequalities for Planar Algebras |
The Brascamp-Lieb inequalities for a Euclidean space generalized many important inequalities such as Hölderâs inequality, Youngâs inequality, the Loomis-Whitney inequality. They have Gaussian functions as their extremizers under certain conditions. The bi-shift of bi-projections for planar algebras introduced by C. Jiang, Z. Liu, and J. Wu have many properties analogous to the Gaussian functions for Euclidean spaces. In this talk, we introduce the Brascamp-Lieb inequalities for planar algebras" |
September 26, 2017, 4:00 PM at Jefferson 356 |
| LEARNING SEMINAR ON THE FARGUE-FONTAINE CURVE |
Dennis Gaitsgory (HARVARD UNIVERSITY) |
The relative Fargues-Fontaine curve and ``untilts", continued |
" |
September 25, 2017, 4:00 - 5:30 PM at Science Center 507 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Boyu Zhang (HARVARD UNIVERSITY) |
Derived category of sheaves and the six functors |
In this talk we will define the derived category of sheaves, and introduce the six functors between such categories. We will then discuss the properties of sheaves on manifolds and state the Poincare-Verdier duality theorem" |
September 22, 2017, 3:30 - 4:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
Unstable chromatic localizations |
" |
September 21, 2017, 4:00 - 6:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Koji Shimizu (HARVARD UNIVERSITY) |
Local constancy of generalized Hodge-Tate weights of a p-adic local system |
Based on a work of Tate, Sen studied Galois cohomologies of a p-adic field and attached to each p-adic Galois representation a multiset of numbers called generalized Hodge-Tate weights. In this talk, we discuss how the multiset behaves in a geometric family. More precisely, we consider a p-adic local system on a rigid analytic variety over a p-adic field and show that the multiset of generalized Hodge-Tate weights of the local system is locally constant" |
September 20, 2017, 3:15 - 4:15 pm at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Nick Salter (HARVARD UNIVERSITY) |
Plane curves, (higher) spin structures, and mapping class groups |
The family of smooth degree-d plane curves (over C) has a monodromy representation valued in the mapping class group of the underlying topological surface that is a geometric lift of the âcohomologicalâ monodromy familiar to algebraic geometers. The ultimate goal of this talk is to describe some of the ideas involved in my recent work that shows that this monodromy group is *not* surjective, but is still âas large as possible. I will touch on the following topics: the adjunction formula, higher spin structures on Riemann surfaces, Picard-Lefschetz theory, braid monodromy, Artin groups, curve complexes, and the Torelli group. No familiarity with algebraic geometry will be assumed." |
September 20, 2017, 4:00 PM at Science Center 530 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Giulia Sacca (MIT) |
Degenerations of hyperkahler manifolds |
The problem of understanding semistable degenerations of K3 surfaces has been greatly studied and is completely understood (Kulikov-Pinkham-Persson). The aim of this talk is to presentjoint work with J. Kollår, R. Laza, and C. Voisin generalizing some of these results to higher dimensional hyperkÀhler (HK) manifolds. I will also present some applications, including a generalization of theorem of Huybrechts to possibly singular symplectic varieties and shortcuts to showing that certain HK manifolds are of a given deformation type" |
September 19, 2017, 3:00 PM at MIT 4-237 |
| LOGIC SEMINAR |
Will Boney (HARVARD UNIVERSITY) |
Model-theoretic characterizations of large cardinals |
Compact cardinals get their names from a characterization in terms of the compactness of L_{\kappa, \kappa}. Measurable and supercompact cardinals also have characterizations in these terms, and Magidor has used second-order logic to characterize supercompacts and extendible cardinals in this way. We will continue this line of model-theoretic characterizations and discuss the characterizations of large cardinals in terms of compactness for omitting types focusing on three logics: L_{\kappa, \kappa}, second-order, and sort logic" |
September 19, 2017, 5:15 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Peter Smillie (HARVARD UNIVERSITY) |
Weingarten foliations of three dimensional Lorentzian spaceforms |
We study the existence of foliations of three dimensional Lorentzian spaceforms by families of spacelike Weingarten surfaces and the induced flows on Teichmuller spac" |
September 19, 2017, 4:00 - 5:15 pm at Science Center 507 |
| LEARNING SEMINAR ON THE FARGUE-FONTAINE CURVE |
Dennis Gaitsgory (HARVARD UNIVERSITY) |
The Fargues-Fontaine curve and "untilts" |
" |
September 18, 2017, 4:00 - 5:30 PM *note earlier ending at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Yoosik Kim (BOSTON UNIVERSITY) |
Monotone Lagrangian tori in cotangent bundles |
As an attempt to classify Lagrangian submanifolds and due to their importance in Floer theory, monotone Lagrangian tori have been got attention. In this talk, we provide a way producing monotone Lagrangian tori in the cotangent bundles of some manifolds including spheres or unitary groups. The construction is based on the classification of Lagrangian fibers of a certain completely integrable system on a partial flag manifolds of various types. We then discuss when their Floer cohomologies (under a certain deformation by non-unitary flat line bundles) do not vanish. This talk is based on joint work with Yunhyung Cho and Yong-Geun Oh" |
September 18, 2017, 12:00 - 1:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Boyu Zhang (HARVARD UNIVERSITY) |
Flat SL_2(C) connections and complex Lagrangian intersections |
This is the first talk of the reading seminar on Abouzaid, Manolescu: A sheaf-theoretic model for SL(2,C) Floer homology. We will give an overview of the categorification of complex Lagrangian intersections and show that it leads to a SL_2(C) Floer theory for closed three manifolds" |
September 15, 2017, 3:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
The Bousfield-Kuhn functor |
" |
September 14, 2017, 4:00 - 6:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS ALGEBRAIC GEOMETRY SEMINAR |
Yu-Wei Fan (HARVARD UNIVERSITY) |
Entropy of an autoequivalence on Calabi-Yau manifolds |
We will recall the notion of entropy of an autoequivalence on triangulated categories, and provide counterexamples of a conjecture by Kikuta-Takahashi" |
September 14, 2017, 3:30 - 4:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Philip Engel (HARVARD UNIVERSITY) |
Tilings and Hurwitz Theory |
An elliptic orbifold is a quotient of the plane by an orientation-preserving wallpaper group. Building on work of Eskin and Okounkov, we outline a proof that natural counts of ramified covers of an elliptic orbifold form the Fourier coefficients of a quasi-modular form of specified level and weight. This theorem allows us to answer questions such as: How many combinatorially inequivalent ways are there to tile an oriented surface by 1000 quadrilaterals, so that the valences of the vertices are 3, 3, 4, 4, ..., 4, 4, 5, 5? Declaring each tile to be metrically square, tiled surfaces form a uniformly distributed lattice within a stratum of flat surfaces---a moduli space of pairs (X, Ï), where X is a Riemann surface and Ï is a quartic differential with specified orders of zeroes and poles. The asymptotic behavior as the number of tiles goes to infinity determines the volume of the moduli space. One may conclude that the volumes of strata of quartic (and similarly cubic) differentials are polynomial in pi or infinite, naturally generalizing a conjecture of Kontsevich and Zorich" |
September 13, 2017, 4:00 - 6:00 PM at Science Center 530 |
| NUMBER THEORY SEMINAR |
Ari Shnidman (BOSTON COLLEGE) |
Ranks of abelian varieties in quadratic twist families |
We analyze the behavior of Selmer groups in the quadratic twist family of any abelian variety A admitting an isogeny of degree 3 (over a number field F). If A is an elliptic curve, we deduce that the average Mordell-Weil rank in the twist family is bounded, and, if F is totally real, that a positive proportion of twists have rank 0. I ll describe similar results for higher dimensional A, in the presence of extra level and endomorphism structure. This is based off joint work with Bhargava, Klagsbrun, and Lemke Oliver" |
September 13, 2017, 3:15 - 4:15 pm at Science Center 507 |
| LOGIC SEMINAR |
Sebastien Vasey (HARVARD UNIVERSITY) |
Internal sizes in $\mu$-abstract elementary classes |
The internal size of an object $M$ inside a given category is, roughly, the least infinite cardinal $\lambda$ such that any morphism from M into the colimit of a $\lambda^+$-directed system factors through one of the components of the system. In the category of set, the internal size of an object is its cardinality. In the category of vector spaces, the internal size is the dimension, and in the category of metric spaces, the internal size is the least cardinality of a dense subset. We will discuss questions around internal sizes in the framework of $\mu$-abstract elementary classes ($\ÎŒ$-AECs), which are, up to equivalence of categories, the same as accessible categories with all morphisms monomorphisms. We will in particular examine an example of Shelah---a certain class of sufficiently-closed constructible models of set theory---which shows that the categoricity spectrum can behave very differently depending on whether we look at categoricity in cardinalities or in internal sizes. This is joint work with Michael Lieberman and JiĆĂ RosickĂœ" |
September 12, 2017, 5:15 pm at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Rohini Ramadas (HARVARD UNIVERSITY) |
Dynamics on the moduli space of point-configurations on the Riemann Sphere |
Hurwitz correspondences are a special family of algebraic discrete dynamical systems on the moduli space M_{0,n} parametrizing configurations of n points on P^1. Hurwitz correspondences arise in the study of the topological dynamics of self-maps of P^1. Dynamical degrees are numerical invariants associated to algebraic discrete dynamical systems. I will discuss the dynamical degrees of Hurwitz correspondences" |
September 12, 2017, 3:00 PM at Science Center 411 |
| MATHEMATICAL PHYSICS SEMINAR |
William Norledge (HARVARD UNIVERSITY) |
A Construction of Lattices in Buildings |
In this talk, we give an introduction to buildings, which are highly symmetrical combinatorial and geometric mathematical structures with a wide range of applications. We also describe a new way of constructing the quotients of buildings, from which we obtain lattice subgroups of the automorphism groups of buildings" |
September 12, 2017, 4:00 PM at Jefferson 356 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Jordan Keller (HARVARD BLACK HOLE INITIATIVE) |
Linear Stability of Higher Dimensional Schwarzschild Black Holes |
The Schwarzschild-Tangherlini black holes are higher-dimensional generalizations of the Schwarzschild spacetimes, comprising a static, spherically symmetric family of black hole solutions to higher-dimensional vacuum gravity. The physical relevance of such solutions is intimately related to their stability under gravitational perturbations. This talk will address results on the linear stability of the Schwarzschild-Tangherlini black holes, part of ongoing joint work with Pei-Ken Hung and Mu-Tao Wang" |
September 12, 2017, 4:00 - 5:15 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Yu-Shen Lin (HARVARD - CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS) |
From the Decomposition of Picard-Lefschetz Transformation to Tropical Geometry |
Picard-Lefschetz transformation tells the monodromy of a fibration with good singular fibres. In the case of fibres are Lagrangian in a symplectic $4$-manifold, there is a natural decomposition of Picard-Lefschetz transformation into two elementary transformations from Floer theory. The idea will help to develop the tropical geometry for some hyperKahler surfaces" |
September 11, 2017, 12:00 - 1:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| LEARNING SEMINAR ON THE FARGUES-FONTAINE CURVE |
Jacob Lurie (HARVARD UNIVERSITY) |
An Overview |
" |
September 11, 2017, 4:00 - 6:00 PM at Science Center 232 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
To Rational Homotopy Theory and Beyond |
" |
September 07, 2017, 4:00 - 6:00 PM *note new time* at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Arthur Jaffe and Zhengwei Liu (HARVARD UNIVERSITY) |
Introduction to the Mathematical Picture Language Project |
" |
September 05, 2017, 4:00 PM at Jefferson 356 |
| LOGIC SEMINAR |
Nate Ackerman (HARVARD UNIVERSITY) |
Vaught's Conjecture for a Grothendieck topos |
In this talk we will give background on $\mathcal{L}_{\infty, \omega}(L)$, categorical logic as well as Grothendieck toposes. We will then show how to make precise a version of Vaught s conjecture for a Grothendieck topos as well as discuss various analogs of Morley s theorem which hold in all Grothendeick toposes (under mild set theoretic assumptions). If we have time we will also discuss analogs of other theorems of $\mathcal{L}_{\infty, \omega}$ for Grothendieck toposes" |
September 05, 2017, 5:00 - 6:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL ALGEBRAIC GEOMETRY SEMINAR |
Will Donovan (KAVLI IPMU) |
Twists and braids for general threefold flops |
If a complex surface contains a (-2)-curve, this curve corresponds to a spherical object in the derived category of coherent sheaves on the surface. For certain arrangements of such curves, Seidel and Thomas used these objects to establish a braid group action on the derived category. I explain joint work with Michael Wemyss giving a generalisation to curves on threefolds: this uses braid-type groups associated to hyperplane arrangements, and relative spherical objects over noncommutative base rings" |
August 31, 2017, 3:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS SPECIAL SEMINAR |
Juven Wang (IAS) |
Link Invariants of Topological Quantum Matter and New Topological Boundary Conditions |
I will describe how the geometric topology property of spacetime manifolds and their surgery can constrain quantum statistics data, focusing on 2+1 and 3+1 spacetime dimensions. This gives rise to analogous Verlinde formulas in higher dimensions, presumably useful to bootstrap topological phases of matter. On the other hand, from a different perspective, I will also approach the problem based on lattice models and TQFTs realizable / emergeable in condensed matter (âso far theoretically and numericallyâ). Then we can derive various new link invariants, braiding statistics data (modular S and T matrices) and ground state degeneracy as physical observables to fully characterize those 2+1 and 3+1 dimensional systems. As an example, we can use this tool to one-to-one identify and characterize Z8 classification of Z2xZ2^f-symmetric fermionic Topological Superconductors (realized by stacking layers of a valentine pair of p+ip and pâ ip superconductors, where boundary supports non-chiral Majorana-Weyl modes). Work based on: https://arxiv.org/abs/1602.05951 and https://arxiv.org/abs/1612.09298. If time permits, I will comment on the recent work on new exotic types of gapped Topological Boundary Conditions of TQFTs (e.g. SPT and SET states) in any dimension: https://arxiv.org/abs/1705.0672" |
May 24, 2017, 11:30 AM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Zheng-Cheng Gu (CHINESE UNIVERSITY OF HONG KONG) |
A topological world: from topological material to the origin of elementary particles |
" |
May 23, 2017, 12:00 pm at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Kwok Wai Chan (CHINESE UNIVERSITY OF HONG KONG) |
Scattering diagrams from asymptotic analysis on Maurer-Cartan equations |
In 2005, a program was set forth by Fukaya aiming at investigating SYZ mirror symmetry by asymptotic analysis on Maurer-Cartan equations. In this talk, I will explain some results which implement part of Fukaya s program. More precisely, I will show how semi-classical limits of Maurer-Cartan solutions give rise naturally to consistent scattering diagrams, which are known to encode Gromov-Witten data on the mirror side and have played an important role in the works of Kontsevich-Soibelman and Gross-Siebert on the reconstruction problem in mirror symmetry. This talk is based on joint work with Conan Leung and Ziming Ma, which was substantially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CUHK14302015)" |
May 17, 2017, 3:30 - 4:30 pm at CMSA Building, 20 Garden St, G10 |
| SPECIAL LECTURE SERIES |
Jean-Pierre Serre (COLLĂšGE DE FRANCE) |
Cohomological invariants mod 2 of Weyl groups, Pt. 2 |
The first lecture will mostly be a résumé of the first part of AMS ULECT 28; the second lecture will give an explicit description of the cohomological invariants of the Weyl groups. *Afternoon tea will follow at 3:15 pm in the Math Department Common Room, 4th Floor" |
May 09, 2017, 2:00 pm at Science Center 507 |
| SPECIAL LECTURE SERIES |
Jean-Pierre Serre (COLLĂšGE DE FRANCE) |
Cohomological invariants mod 2 of Weyl groups, Pt. 1 |
The first lecture will mostly be a résumé of the first part of AMS ULECT 28; the second lecture will give an explicit description of the cohomological invariants of the Weyl groups. *Afternoon tea will follow at 4:15 pm in the Math Department Common Room, 4th Floor" |
May 08, 2017, 3:00 pm at Science Center 507 |
| GAUGE THEORY, TOPOLOGY AND SYMPLECTIC GEOMETRY SEMINAR |
Daniel Cristofaro-Gardiner (HARVARD UNIVERSITY) |
Two or infinity |
A central goal in symplectic and contact geometry is to better understand the dynamics of âReebâ vector fields. About a decade ago, Taubes showed that any Reeb vector field on a closed three-manifold has at least one closed orbit. I will discuss recent joint work showing that, under some hypotheses, any Reeb vector field on a closed three-manifold has either two, or infinitely many, closed orbits. Key tools are an identity relating the lengths of certain sets of Reeb orbits to the volume of the three-manifold, and the theory of global surfaces of section as developed by Hofer, Wysocki, and Zehnder" |
May 05, 2017, 3:30 - 4:30 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Xue-Mei Li (UNIV. OF WARWICK) |
Perturbation to conservation law and stochastic averaging |
A deterministic or random system with a conservation law is often used to approximate dynamics that are also subjected to smaller deterministic or random influences. Consider for example dynamical descriptions for Brownian motions and singular perturbed operators arising from rescaled Riemmannian metrics. In both cases the conservation laws, which are maps with values in a manifold, are used to separate the slow and fast variables. We discuss stochastic averaging and diffusion creation arising from these contexts. Our overarching question is to describe stochastic dynamics associated with the convergence of Riemannian manifolds and metric spaces" |
May 03, 2017, 4:30 PM at Science Center 507 |
| JOINT DEPT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Ilya Soloveychik (HARVARD SCHOOL OF ENGINEERING & APPLIED SCIENCES) |
Deterministic Random Matrices |
In many applications researchers and engineering need to simulate random symmetric sign (+/-1) matrices (Wigner s matrices). The most natural way to generate an instance of such a matrix is to toss a fair coin, fill the upper triangular part of the matrix with the outcomes and reflect it part into the lower triangular part. For large matrix sizes such approach would require a very powerful source of randomness due to the independence condition. In addition, when the data is generated by a truly random source, atypical non-random looking outcomes have non-zero probability of showing up. Yet another issue is that any experiment involving tossing a coin would be impossible to reproduce exactly, which may be crucial in computer scientific applications. In this talk we focus on the problem of generating n by n symmetric sign matrices based on the similarity of their spectra to Wigner s semicircular law. We develop a simple completely deterministic construction of symmetric sign matrices whose spectra converge to the semicircular law when n grows to infinity. The Kolmogorov complexity of the proposed algorithm is as low as 2 log (n) bits implying that the real amount of randomness conveyed by the semicircular property is quite small" |
May 03, 2017, 3:00 pm at CMSA Building, 20 Garden St, G02 |
| INFORMAL GEOMETRY & DYNAMICS SEMINAR |
Ahmad Rafiqi (CORNELL UNIVERSITY) |
Surface homeomorphisms from matrices and typical properties of biPerron numbers |
" |
May 03, 2017, 4:00 - 6:00 pm at Science Center 507 |
| SPECIAL BASIC NOTIONS SEMINAR |
Jean-Pierre Serre (COLLĂšGE DE FRANCE) |
Some simple facts on lattices and orthogonal group representations |
Afternoon tea will follow at 4:15 pm in the Math Department Common Room, 4th floor" |
May 03, 2017, 3:00 pm at Science Center Hall D |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Simona Cocco (CNRS & ECOLE NORMALE SUPĂ©RIEURE, PARIS, FRANCE) |
Reverse modeling of protein sequence data: from graphical models to structural and functional predictions. |
A fundamental yet largely open problem in biology and medicine is to understand the relationship between the amino-acid sequence of a protein and its structure and function. Protein databases such as Pfam, which collect, align, and classify protein sequences into families containing similar (homologous) sequences are growing at a fast pace thanks to recent advances in sequencing technologies. What kind of information about the structure and function of proteins can be obtained from the statistical distribution of sequences in a protein family? To answer this question I will describe recent attempts to infer graphical models able to reproduce the low-order statistics of protein sequence data, in particular amino acid conservation and covariation. I will also review how those models have led to substantial progress in protein structural and functional predictions" |
May 02, 2017, 4:00pm at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS SPECIAL SEMINAR |
David Carchedi (GEORGE MASON UNIVERSITY ) |
Dg-manifolds as a model for derived manifolds |
Given two smooth maps of manifolds Æ : Î â L and g : N â L, if they are not transverse, the fibered product M Ă L N may not exist, or may not have the correct cohomological properties. Thus lack of transverality obstructs many natural constructions in topology and differential geometry. Derived manifolds generalize the concept of smooth manifolds to allow arbitrary (iterative) intersections to exist as smooth objects, regardless of transversality. In this talk we will describe recent progress of ours with D. Roytenberg on giving an accessible geometric model for derived manifolds using differential graded manifolds" |
April 27, 2017, 2:00 - 3:00 pm at CMSA Building, 20 Garden St, G10 |
| THURSDAY SEMINAR |
Marc Hoyois (MIT) |
Bloch-Kato implies Beilinson-Lichtenbaum |
" |
April 27, 2017, 4:00 - 6:00 pm *note change in time this week* at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Mehran Kardar (MIT) |
Levitation by Casimir forces in and out of equilibrium |
Equilibrium fluctuation-induced forces are abundant in nature, ranging from quantum electrodynamic (QED) Casimir and van der Waals forces, to their thermal analogs in fluctuating soft matter. Repulsive Casimir forces have been proposed for a variety of shapes and materials. A generalization of Earnshaw s theorem constrains the possibility of levitation by Casimir forces in equilibrium. The scattering formalism, which forms the basis of this proof, can be used to study fluctuation-induced forces for different materials, diverse geometries, both in and out of equilibrium. Conformal field theory methods suggest that critical (thermal) Casimir forces are not subject to a corresponding constraint" |
April 27, 2017, 3:00 pm at CMSA Building, 20 Garden St, G10 |
| INFORMAL GEOMETRY & DYNAMICS SEMINAR |
Eduard Duryev (HARVARD UNIVERSITY) |
Dilation surfaces: geometry, dynamics and moduli space. Part 2 |
" |
April 26, 2017, 4:00 - 6:00 pm at Science Center 530 |
| RANDOM MATRIX & PROBABILITY SEMINAR |
Ashkan Nikeghbali (UNIVERSITY OF ZURICH) |
Random Matrix models in number theory: an infinite dimension point of view. |
" |
April 26, 2017, 2:00 - 3:00 pm at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Henri Darmon (MCGILL UNIVERSITY) |
Singular moduli for real quadratic fields: a rigid analytic approach. |
A definition of analogues of singular moduli for real quadratic fields is proposed, involving the special values of rigid meromorphic period functions at real quadratic irrationalities. This is a work in progress with Jan Vonk" |
April 26, 2017, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Georgios Daskalopoulos (BROWN UNIVERSITY) |
Rigidity of Group Actions in General NPC Spaces |
The goal of this talk is to describe different approaches of using harmonic maps into general metric spaces of non-positive curvature in the sense of Alexandrov (NPC spaces) and describe how one can obtain enough regularity to extend the classical Bochner formulas in this setting" |
April 25, 2017, 4:15 pm at Science Center 507 |
| HARVARD MIT ALGEBRAIC GEOMETRY SEMINAR |
Yaim Cooper (HARVARD UNIVERSITY) |
A Fock Space Approach to Severi Degrees |
I will describe an approach to curve counting on some rational surfaces such as P2 and Hirzebruch surfaces using operators on a Fock space. As a consequence, we obtain formulas comparing Gromov-Witten invariants and enumerative curve counting on these surfaces, extending a result of Abramovich and Bertram comparing enumerative curve counts on F0 and F2 to F1 and F3. We also find a pair of differential equations satisfied by relative Gromov-Witten invariants of Fk, one of which recovers a formula of Getzler and Vakil. This work is partly joint with R. Pandharipande" |
April 25, 2017, 3:00 pm at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Fei Wei (UNIVERSITY OF NEW HAMPSHIRE) |
On divisor function in arithmetic progressions (joint work with Yitang Zhang and Boqing Xue) |
For large moduli exceeding the square root of the length, a new estimate on the distribution of the general divisor functions in arithmetic progressions is obtained" |
April 25, 2017, 2:45 PM at Jefferson 453 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Patrick Jefferson (HARVARD UNIVERSITY) |
Towards A Classification of 5d N = 1 SCFTs |
I will discuss a new proposal for classifying five-dimensional SCFTs with N = 1 supersymmetry and a simple gauge algebra. This classification program entails studying supersymmetry-protected quantities on the Coulomb branch of moduli space using only representation-theoretic data, and subsumes all known predictions in the literature while predicting the existence of novel theories. Geometric constructions of 5d N = 1 theories via string compactifications interpret the supersymmetric protected data as geometric data associated to a local Calabi-Yau threefold, suggesting the possibility of translating this program into a partial cataloguing of Calabi-Yau geometries" |
April 24, 2017, 12:00 pm at CMSA Building, 20 Garden St, G10 |
| GAUGE THEORY, TOPOLOGY AND SYMPLECTIC GEOMETRY SEMINAR |
Jonathan Weitsman (NORTHWESTERN UNIVERSITY) |
On the geometric quantization of (some) Poisson manifolds |
We review geometric quantization in the symplectic case, and show how the program of formal geometric quantization can be extended to certain classes of Poisson manifolds equipped with appropriate Hamiltonian group actions. These include b-symplectic manifolds, where the quantization turns out to be finite dimensional, as well as more singular examples ($b^k$-symplectic manifolds) where the quantization is finite dimensional for odd $k$ and infinite dimensional, with a very simple asymptotic behavior, where $k$ is even. If time permits we will also discuss some preliminary results for pseudoconvex domains. (joint with Victor Guillemin and Eva Miranda" |
April 21, 2017, 3:30 - 4:30 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL LECTURE SERIES ON DONALDSON-THOMAS AND GROMOV-WITTEN THEORIES |
Artan Sheshmani (THE QGM AARHUS AND CMSA HARVARD ) |
Proof of S-duality conjecture on quintic threefold II |
I will talk about an algebraic-geometric proof of the S-duality conjecture in superstring theory, made formerly by physicists Gaiotto, Strominger, Yin, regarding the modularity of DT invariants of sheaves supported on hyperplane sections of the quintic Calabi-Yau threefold. We use degeneration and localization techniques to reduce the threefold theory to a certain intersection theory over the relative Hilbert scheme of points on surfaces and then prove modularity. More precisely, we have proven that the generating series, associated to the top intersection numbers of the Hilbert scheme of points, relative to an effective divisor, on a smooth quasi-projective surface is a modular form. This is a generalization of the result of Okounkov-Carlsson, where they used representation theory and the machinery of vertex operators to prove this statement for absolute Hilbert schemes. These intersection numbers eventually, together with the generating series of Noether-Lefschetz numbers as I will explain, will provide the ingredients to achieve an algebraic-geometric proof of S-duality modularity conjecture" |
April 21, 2017, 9:00 - 10:30 AM at CMSA Building, 20 Garden St, G10 |
| THURSDAY SEMINAR |
Dan Berwick-Evans (UNIVERSITY OF ILLINOIS URBANA-CHAMPAIGN) |
Field theories and elliptic cohomology from the vantage of characters |
" |
April 21, 2017, 3:00 pm at MIT 2-131 *note special location* |
| INFORMAL GEOMETRY & DYNAMICS SEMINAR |
Jane Wang (MIT) |
Dilation surfaces: geometry, dynamics and moduli space. Part 1 |
" |
April 19, 2017, 4:00 PM at Science Center 530 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS COLLOQUIUM |
Cumrun Vafa (HARVARD PHYSICS) |
String Swampland |
In this talk I review the idea behind identification of the string swampland. In particular I discuss the weak gravity conjecture as one such criterion and explain a no-go theorem for non-supersymmetric AdS/CFT holography." |
April 19, 2017, 4:30 PM at CMSA Building, 20 Garden St, G10 |
| JOINT DPT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Weijun Xu (UNIVERSITY OF WARWICK) |
Meaing of infinities in KPZ and Phi^4_3 |
Many interesting stochastic PDEs arising from statistical physics are ill-posed in the sense that they involve products between distributions, so the solutions to these equations are obtained after renormalisations, which typically change the original equation by a quantity that is infinity. I will use KPZ and Phi^4_3 as two examples to explain the meanings of these infinities. As a consequence, we will see how these two equations, interpreted after suitable renormalisations, arise naturally as (weakly) universal limits for two distinct classes of systems. Part of the talk based on joint works with Martin Hairer, Cyril Labbe and Hao Shen" |
April 19, 2017, 3:00 - 4:00 PM *note correction of time* at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL LECTURE SERIES ON DONALDSON-THOMAS AND GROMOV-WITTEN THEORIES |
Artan Sheshmani (THE QGM AARHUS AND CMSA HARVARD ) |
Proof of S-duality conjecture on quintic threefold I |
I will talk about an algebraic-geometric proof of the S-duality conjecture in superstring theory, made formerly by physicists Gaiotto, Strominger, Yin, regarding the modularity of DT invariants of sheaves supported on hyperplane sections of the quintic Calabi-Yau threefold. We use degeneration and localization techniques to reduce the threefold theory to a certain intersection theory over the relative Hilbert scheme of points on surfaces and then prove modularity. More precisely, we have proven that the generating series, associated to the top intersection numbers of the Hilbert scheme of points, relative to an effective divisor, on a smooth quasi-projective surface is a modular form. This is a generalization of the result of Okounkov-Carlsson, where they used representation theory and the machinery of vertex operators to prove this statement for absolute Hilbert schemes. These intersection numbers eventually, together with the generating series of Noether-Lefschetz numbers as I will explain, will provide the ingredients to achieve an algebraic-geometric proof of S-duality modularity conjecture" |
April 19, 2017, 9:00 - 10:30 AM at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Noam Elkies (HARVARD UNIVERSITY) |
Remarks on isogenies between elliptic curves over low-degree number fields |
We consider cyclic N-isogenies over a varying number field K of given degree. For 11 values of N in the range [30,71], there are finitely many such isogenies with [K:Q] = 3 up to twist, even though there are infinitely many with [K:Q] = 2. Moreover the finite list can be computed. We put this in the context of Mazur s torsion and isogeny theorems and the still-elusive isogeny theorem corresponding to Merel s torsion theorem. We explore in detail the case N=48 which has several further nice features. Time permitting, we discuss similar phenomena for other such questions" |
April 19, 2017, 3:00 pm at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Fangyang Zheng (OHIO STATE UNIVERSITY ) |
On compact Kahler manifolds with positive or negative holomorphic sectional curvature |
In this talk, I will discuss some recent progress in the study of holomorphic sectional curvature H on compact Kahler manifolds. In the positively curved case, a goal is to understand what kind of manifolds can admit such a metric, and in the negatively curved case, there is the recent breakthrough by Wu and Yau which establishes the ampleness of the canonical line bundle for such manifolds. We will discuss an existence result for compact Kahler manifolds with positive H and a splitting result for projective Kahler manifolds with semi-negative H, in terms of the nef dimension" |
April 18, 2017, 4:15 pm at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Charles Zhaoxi Xiong (HARVARD UNIVERSITY ) |
What generalized cohomology theories may have to do with symmetry protected topological phases |
Ubiquitous in the modern language of condensed matter physics, symmetry protected topological (SPT) phases are deformation classes of gapped symmetric systems of a certain kind. A concerted effort in the last decade has led to approximate classifications of such phases, while the complete classification remains at large. In this talk, I will review the notion of SPT phases, and contend that the complete classification of SPT phases should constitute a generalized cohomology theory in the sense of algebraic topology. The latter can be defined in terms of a sequence of topological spaces that supposedly describe short-range entangled states in various physical dimensions. I will explain how these remarks may be leveraged to make physically meaningful predictions, such as the well- definedness of strong and weak topological indices for interacting systems [1]. [1] https://arxiv.org/abs/1701.0000" |
April 18, 2017, 2:45 PM at Jefferson 453 |
| HARVARD MIT ALGEBRAIC GEOMETRY SEMINAR |
Angelo Vistoli (SCUOLA NORMALE) |
Motive classes of classifying spaces |
If G is an affine group over a field k, Behrend-Dhillon and Ekedahl have defined the class {BG} of the classifying space BG in an appropriate localization of the Grothendieck ring of varieties. I will discuss the little that is known about these classes, and the suggestive, if completely hypothetical, connection with the problem of rationality of fields of invariants" |
April 18, 2017, 3:00 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Ingmar Saberi (UNIVERSITĂ€T HEIDELBERG) |
Holographic lattice field theories |
Recent developments in tensor network models (which are, roughly speaking, quantum circuits designed to produce analogues of the ground state in a conformal field theory) have led to speculation that such networks provide a natural discretization of the AdS/CFT correspondence. This raises many questions: just to begin, is there any sort of dynamical model or lattice field theory underlying this connection? And how much of the usual AdS/CFT dictionary really makes sense in a discrete setting? I ll describe some recent work that proposes a setting in which such questions can perhaps be addressed: a discrete spacetime whose bulk isometries nevertheless match its boundary conformal symmetries. Many of the first steps in the AdS/CFT dictionary carry over without much alteration to lattice field theories in this background, and one can even consider natural analogues of BTZ black hole geometries." |
April 17, 2017, 12:00 pm at CMSA Building, 20 Garden St, G10 |
| GAUGE THEORY, TOPOLOGY AND SYMPLECTIC GEOMETRY SEMINAR |
Alvaro Pelayo (UC SAN DIEGO) |
Introduction to symplectic and spectral geometry of finite dimensional integrable systems |
This is an introductory talk for a general audience to the symplectic geometry of classical integrable Hamiltonian systems and the spectral geometry of the quantum counterparts" |
April 14, 2017, 3:30 - 4:30 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL LECTURE SERIES ON DONALDSON-THOMAS AND GROMOV-WITTEN THEORIES |
Artan Sheshmani (AARHUS UNIVERSITY/CMSA) |
DT versus MNOP invariants and S_duality conjecture on general complete intersections |
Motivated by S-duality modularity conjectures in string theory, we define new invariants counting a restricted class of two-dimensional torsion sheaves, enumerating pairs ZâH in a CalabiâYau threefold X. Here H is a member of a sufficiently positive linear system and Z is a one-dimensional subscheme of it. The associated sheaf is the ideal sheaf of ZâH, pushed forward to X and considered as a certain JoyceâSong pair in the derived category of X. We express these invariants in terms of the MNOP invariants of X" |
April 14, 2017, 9:00 - 10:30 am at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Lothar Göttsche (ICTP) |
Virtual refinements of the Vafa-Witten formula |
(joint work with Martijn Kool) Partially based of physics arguments Vafa and Witten made predictions about the Euler numbers of moduli spaces of sheaves on surfaces. They give explicit generating functions in terms of modular forms. These moduli spaces are in general very singular, but they have a perfect obstruction theory, and thus a virtual fundamental class and a virtual Tangent bundle, and thus virtual Chern numbers and in particular a virtual Euler number. We interpret the prediction as being about the virtual Euler numbers. Then a formula of Mochizuki allows to compute the virtual Euler numbers in terms of integrals on Hilbert schemes of points, which we do via reduction to toric surfaces and localization. This allows to check the conjecture in a wide variety of cases up to high expected dimensions of the moduli spaces. We then extend the conjecture first to the $\chi_y$-genus and then to the elliptic genus, where we obtain generating functions similar to that of Dijkgraaf-Moore-Verlinde-Verlinde for Hilbert schemes of points. Finally we extend the conjectures to the virtual cobordism class of the moduli spaces" |
April 13, 2017, 9:30 am at CMSA Building, 20 Garden St, G10 |
| HARVARD, BRANDEIS, MIT, NORTHEASTERN JOINT COLLOQUIUM AT HARVARD |
Tom Church (STANFORD UNIVERSITY) |
Asymptotic representation theory over Z |
Representation theory over Z is famously intractable, but representation stability provides a way to get around these difficulties, at least asymptotically, by enlarging our groups until they behave more like commutative rings. Moreover, it turns out that important questions in topology / number theory / representation theory / ... correspond to asking whether familiar algebraic properties hold for these rings. I ll explain how these connections work; describe what we know and don t know; and give a wide sampling of concrete applications in different fields. No knowledge of representation theory will be required -- indeed, that s sort of the whole point" |
April 13, 2017, Tea at 4:00 PM, the Austine & Chilton McDonnell Common Room, Science Center 4th Floor, Talk at 4:30 pm at Science Center Hall A |
| MATHEMATICAL PHYSICS SEMINAR |
Nima Arkani-Hamed (IAS, PRINCETON) |
The Amplituhedron and Scattering Amplitudes as Binary Code |
**please note special day - Thursday*" |
April 13, 2017, 2:45 pm at Jefferson 453 |
| JOINT DPT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Oanh Nguyen (YALE UNIVERSITY) |
Roots of random polynomials |
Random polynomials, despite their simple appearance, remain a mysterious object with a large number of open questions that have attracted intensive research for many decades. In this talk, we will discuss some properties of random polynomials including universality and asymptotic normality. I will also talk about some interesting open questions. The talk is based on joint works with Yen Do, Hoi Nguyen, and Van Vu" |
April 12, 2017, 2:00 - 3:00 pm at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Shlomo Razamat (ISRAEL INSTITUTE OF TECHNOLOGY) |
Complicated four dimensional physics and simple mathematics |
We will discuss SCFTs in four dimensions obtained from compactifications of six dimensional models. We will discuss the relation of the partition functions, specifically the supersymmetric index, of the SCFTs to certain special functions, and argue that the partition functions are expected to be naturally expressed in terms of eigenfunctions of generalizations of Ruijsenaars-Schneider models. We will discuss how the physics of the compactifications implies various precise mathematical identities involving the special functions, most of which are yet to be proven" |
April 12, 2017, 4:30 pm at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL LECTURE SERIES ON DONALDSON-THOMAS AND GROMOV-WITTEN THEORIES |
Artan Sheshmani (AARHUS UNIVERSITY/CMSA) |
Stable pair PT invariants on nodal fibrations: perverse sheaves, Wallcrossings, and an analog of fiberwise T-duality |
Following lecture 4, we continue the study of stable pair invariants of K3-fibered threefolds., We investigate the relation of these invariants with the perverse (non-commutative) stable pair invariants of the K3-fibration. In the case that the fibration is a projective Calabi-Yau threefold, by means of wall-crossing techniques, we write the stable pair invariants in terms of the generalized Donaldson-Thomas invariants of 2-dimensional Gieseker semistable sheaves supported on the fibers" |
April 12, 2017, 9:00 - 10:30 am at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Jan Vonk (MCGILL UNIVERSITY) |
Crystalline cohomology of towers of curves |
Motivated by a number of numerical observations on infinite slope modular forms, we try to investigate the non-ordinary part of Eichler-Shimura cohomology. This leads us to consider crystalline cohomology for a nice class of towers of curves, whose ordinary part admits analogues of the main theorems of Hida theory" |
April 12, 2017, 3:00 pm at Science Center 507 |
| JOINT DEPT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Subhajit Goswami (UNIVERSITY OF CHICAGO) |
Liouville first-passage percolation and Watabiki's prediction |
In this talk I will give a brief introduction to Liouville first-passage percolation (LFPP) which is a model of random metric on a finite planar grid graph. It was studied primarily as a way to make sense of the random metric associated with Liouville quantum gravity (LQG), one of the major open problems in contemporary probability theory. I will discuss some recent results on this metric and the main focus will be on estimates of the typical distance between two points. I will also discuss about the apparent disagreement of these estimates with a prediction made in the physics literature about LQG metric. The talk is based on a joint work with Jian Ding" |
April 12, 2017, 3:00 pm at CMSA Building, 20 Garden St, G10 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Luca Spolaor (MIT) |
Optimal regularity for three dimensional mass minimizing cones in arbitrary codimension |
In this talk I will present the following regularity results: the singular set of a mass minimizing three dimensional cone in the Euclidean space is at most the union of finitely many half lines (joint with C. De Lellis and E. Spadaro)" |
April 11, 2017, 4:15 pm at Science Center 507 |
| HARVARD MIT ALGEBRAIC GEOMETRY SEMINAR |
Mihnea Popa (NORTHWESTERN UNIVERSITY) |
Hodge ideals |
I will present joint work with M. Mustata, in which we study a sequence of ideals arising naturally from M. Saito s Hodge filtration on the localization along a hypersurface. The multiplier ideal of the hypersurface appears as the first step in this sequence, which as a whole provides a more refined measure of singularities. We give applications to the comparison between the Hodge filtration and the pole order filtration, adjunction and restriction theorems, and the singularities of theta divisors on abelian varieties" |
April 11, 2017, 3:00 pm at MIT 4-153 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Burkhard Schwab (CMSA) |
Large Gauge symmetries in Supergravity |
In the recent literature, a class of new symmetries -- collectively known as large gauge symmetries -- has emerged that governs the scattering of massless particles of very low energy on asymptotically flat space times. I will show that this statement extends to supergravity where an infinite family of fermionic symmetries can be derived. The algebra of these fermionic symmetries close in the BMS group and their Ward identity is the factorization of soft gravitinos in the S-matrix" |
April 10, 2017, 12:00 pm at CMSA Building, 20 Garden St, G10 |
| HARVARD MIT ALGEBRAIC GEOMETRY SEMINAR |
Mihnea Popa (NORTHWESTERN UNIVERSITY) |
Families of varieties and Hodge theory |
Allowing the isomorphism class of algebraic varieties to vary in a family usually imposes strong conditions on the space parametrizing that family. This has been thoroughly studied for families of varieties whose canonical bundle is positive, leading to what is called the hyperbolicity of the moduli stack of such varieties. I will explain how recent advances in Hodge theory and in the study of holomorphic forms, facilitated especially by M. Saito s theory of Hodge modules, allow us to answer well-known questions regarding the base spaces of more general (and conjecturally arbitrary) families of varieties. Most of this is joint work with C. Schnell" |
April 10, 2017, 12:00 pm **Special Talk** at MIT 2-361 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL LECTURE SERIES ON DONALDSON-THOMAS AND GROMOV-WITTEN THEORIES |
Artan Sheshmani (AARHUS UNIVERSITY/CMSA) |
Stable pair PT invariants on nodal fibrations: perverse sheaves, Wallcrossings, and an analog of fiberwise T-duality |
Following lecture 4, we continue the study of stable pair invariants of K3-fibered threefolds., We investigate the relation of these invariants with the perverse (non-commutative) stable pair invariants of the K3-fibration. In the case that the fibration is a projective Calabi-Yau threefold, by means of wall-crossing techniques, we write the stable pair invariants in terms of the generalized Donaldson-Thomas invariants of 2-dimensional Gieseker semistable sheaves supported on the fibers" |
April 07, 2017, 9:00 - 10:30 am at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
John Loftin (RUTGERS UNIVERSITY) |
Families of projective domains and neck-separating degenerations of convex $RP^2$ surfaces |
Given a bounded convex domain $\Omega$ in $RP^n$, Cheng-Yau provide a unique solution to the Monge-Ampere equation $\det v_{ij} = (-1/v)^{n+2}$, for convex $v$ and Dirichlet boundary value $v=0$. This solution $v$ then determines a unique hypersurface, a hyperbolic affine sphere, asymptotic to the boundary of the cone over $\Omega$ in $R^{n+1}$. The hyperbolic affine sphere carries tensors, the Blaschke metric and cubic form, which are invariant under special linear automorphisms of the cone. These tensors descend to $\Omega$ to be projectively invariant. Benoist-Hulin show that if $\Omega_i\to\Omega$ in the Hausdorff topology, then these tensors converge in the local $C^\infty$ topology. A 2-dimensional hyperbolic affine sphere carries a conformal structure induced by the Blaschke metric, and the cubic tensor is equivalent to a holomorphic cubic differential. A quotient of such a domain $\Omega$ by a subgroup of $PGL(3,R)$ acting discretely and properly discontinuously then is called a real projective surface, and the conformal structure and cubic differential descend to the quotient. We will discuss a recent result relating degenerations of convex real projective surfaces along necks in terms of the geometry of the bundle of regular cubic differentials over the Deligne-Mumford compactification of the moduli space of Riemann surfaces. In addition to the Benoist-Hulin convergence results mentioned above, the proof also uses analytic techniques of Dumas-Wolf and Wolpert" |
April 06, 2017, 3:00 - 4:30 pm at Science Center 232 |
| NUMBER THEORY SEMINAR |
Frank Calegari (UNIVERSITY OF CHICAGO) |
Modularity lifting theorems beyond Shimura varieties |
Recent work of Caraiani-Scholze has opened the possibility of proving modularity lifting theorems for GL(n) with n>2. We discuss joint work in progress in this direction with Allen, Caraiani, Gee, Helm, LeHung, Newton, Scholze, Taylor, and Thorne, and give some applications of these results" |
April 05, 2017, 3:00 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL LECTURE SERIES ON DONALDSON-THOMAS AND GROMOV-WITTEN THEORIES |
Artan Sheshmani (AARHUS UNIVERSITY/CMSA) |
Stable pair PT invariants on smooth fibrations |
We study Pandharipande-Thomasâs stable pair theory on smooth K3 fibrations over curves with possibly nodal fibers. We describe stable pair invariants of the fiberwise irreducible curve classes in terms of Kawai-Yoshiokaâs formula for the Euler characteristics of moduli spaces of stable pairs on K3 surfaces and Noether-Lefschetz numbers of the fibration" |
April 05, 2017, 9:00 - 10:30 am at CMSA Building, 20 Garden St, G10 |
| JOINT DEPT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Steven Heilman (UCLA) |
Noncommutative Majorization Principles and Grothendieck's Inequality |
The seminal invariance principle of Mossel-O Donnell-Oleszkiewicz implies the following. Suppose we have a multilinear polynomial Q, all of whose partial derivatives are small. Then the distribution of Q on i.i.d. uniform {-1,1} inputs is close to the distribution of Q on i.i.d. standard Gaussian inputs. The case that Q is a linear function recovers the Berry-Esseen Central Limit Theorem. In this way, the invariance principle is a nonlinear version of the Central Limit Theorem. We prove the following version of one of the two inequalities of the invariance principle, which we call a majorization principle. Suppose we have a multilinear polynomial Q with matrix coefficients, all of whose partial derivatives are small. Then, for any even K>1, the Kth moment of Q on i.i.d. uniform {-1,1} inputs is larger than the Kth moment of Q on (carefully chosen) random matrix inputs, minus a small number. The exact statement must be phrased carefully in order to avoid being false. Time permitting, we discuss applications of this result to anti-concentration, and to computational hardness for the noncommutative Grothendieck inequality. (joint with Thomas Vidick) https://arxiv.org/abs/1603.0562" |
April 05, 2017, 3:00 pm at CMSA Building, 20 Garden St, G10 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Chiu-Chu Melissa Liu (COLUMBIA UNIVERSITY) |
GW theory, FJRW theory, and MSP fields |
Gromov-Witten (GW) invariants of the quintic Calabi-Yau 3-fold are virtual counts of parametrized holomorphic curves to the quintic 3-fold. Fan-Jarvis-Ruan-Witten (FJRW) invariants of the Fermat quintic polynomial are virtual counts of solutions to the Witten equation associated to the Fermat quintic polynomial. In this talk, I will describe the theory of Mixed-Spin-P (MSP) fields interpolating GW theory of the quintic 3-fold and FJRW theory of the Fermat quintic polynomial, based on joint work with Huai-Liang Chang, Jun Li, and Wei-Ping Li" |
April 04, 2017, 4:15 pm *change in time this week* at Science Center 507 *change in location this week* |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Scott Mullane (HARVARD UNIVERSITY) |
Extremal effective divisors in Mg,n |
An abelian differential defines a flat metric with singularities at its zeros and poles, such that the underlying Riemann surface can be realised as a polygon whose edges are identified pairwise via translation. A number of questions about geometry and dynamics on Riemann surfaces reduce to studying the strata of abelian differentials with prescribed number and multiplicities of zeros and poles. In this talk, we will focus on the divisorial strata closures that form special codimension-one subvarieties in the the Deligne-Mumford compactified moduli space of Riemann surfaces. For genus g>1 curves with n>g marked points, we show that infinitely many of these divisors form extremal rays of the cone of effective divisors. Hence these effective cones are not rational polyhedral" |
April 04, 2017, 3:00 pm at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Zhengwei Liu (HARVARD UNIVERSITY) |
Quon language in mathemtics |
In joint work with Arthur Jaffe and Alex Wozniakowski, we introduced quon language motivated by quantum information. Now letâs use quon language to touch many concepts in mathematics" |
April 04, 2017, 2:45 pm at Jefferson 453 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Nathan Haouzi (UC BERKELEY) |
Little Strings and Classification of surface defects |
The so-called 6d (2,0) conformal field theory in six dimensions, labeled by an ADE Lie algebra, has become of great interest in recent years. Most notably, it gave new insights into lower dimensional supersymmetric field theories, for instance in four dimensions, after compactification. In this talk, I will talk about a deformation of this CFT, the six-dimensional (2,0) little string theory: its origin lies in type IIB string theory, compactified on an ADE singularity. We further compactify the 6d little string on a Riemann surface with punctures. The resulting defects are D-branes that wrap the 2-cycles of the singularity. This construction has many applications, and I will focus on one: I will provide the little string origin of the classification of surface defects of the 6d (2,0) CFT, for ADE Lie algebras. Furthermore, I will give the physical realization of the so-called Bala-Carter labels that classify nilpotent orbits of these Lie algebras" |
April 03, 2017, 12:00 pm at CMSA Building, 20 Garden St, G02 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY ) |
Etale motivic cohomolgy II |
" |
March 30, 2017, 3:00 - 5:00 PM at Science Center 507 |
| BRANDEIS, HARVARD, MIT, NORTHEASTERN JOINT MATHEMATICS COLLOQUIUM AT HARVARD |
Alexander Goncharov (YALE UNIVERSITY) |
Quantum Hodge Field Theory |
We introduce quantum Hodge correlators. They have the following format. Take a family X â B of compact Kahler manifolds. Let S be an oriented topological surface with special points on the boundary, considered modulo isotopy. We assign to each interval between special points an irreducible local system Li on X , and to each special point an Ext between the neighboring local systems. A quantum Hodge correlator is assigned to this data and lives on the base B. It is a sum of finite dimensional convergent Feynman type integrals. The simplest Hodge correlators are given by the Rankin-Selberg integrals for L-functions. Quantum Hodge correlators can be perceived as Hodge-theoretic analogs of the invariants of knots and threefolds provided by the perturbative Chern-Simons theory. Here is an example. Hodge theory suggests to view a Riemann surface ÎŁ as a threefold, and a point x on ÎŁ as a knot in the threefold. Then the Green function G(x, y) on ÎŁ - the basic Hodge correlator, is an analog of the linking number - the simplest Chern-Simons type invariant. What do the quantum Hodge correlators do? Let B be a point, and Li are constant sheaves. 1. Hodge correlators (S is a disc) describe an action of the Hodge Galois group by Aâ- automorphisms of the cohomology algebra Hâ (X , C) preserving the Poincare pairing. 2. Quantum Hodge correlators (S is any surface) describe an action of the Hodge Galois group by quantum Aâ-automorphisms of the algebra Hâ (X , C) with the Poincare pairing" |
March 30, 2017, 4:30 pm, Tea at 4 pm in the Math Common Room at Science Center Hall A |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Rak-Kyeong Seong (UPPSALA UNIVERSITY) |
The Mirror and the Elliptic Genus of Brane Brick Models |
I will present recent progress in improving with the help of mirror symmetry our understanding of Type IIA brane configurations that encode 2d (0,2) gauge theories on the worldvolume of D1-branes probing toric Calabi-Yau 4-folds. We call these brane configurations brane brick models. The mirror of brane brick models consists of D5-branes wrapping 4-spheres whose intersections determine the corresponding 2d gauge theories. I will show how in the mirror picture 2d (0,2) phenomena such as Gadde-Gukov-Putrov triality have a natural description in terms of geometric transitions. In this context, I will also illustrate the computation of the elliptic genus for brane brick models and match it with the elliptic genus of the corresponding non-linear sigma model whose target space is the probed Calabi-Yau 4-fold" |
March 30, 2017, 3:00 pm at CMSA Building, 20 Garden St, G02 |
| INFORMAL GEOMETRY & DYNAMICS SEMINAR |
Matt Bainbridge (INDIANA UNIVERSITY) |
Smooth compactifications of strata of abelian differentials |
" |
March 29, 2017, 4:00 pm at Science Center 530 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Leslie Greengard (COURANT INSTITUTE) |
Inverse problems in acoustic scattering and cryo-electron microscopy |
A variety of problems in image reconstruction give rise to large-scale, nonlinear and non-convex optimization problems. We will show how recursive linearization combined with suitable fast solvers are bringing such problems within practical reach, with an emphasis on acoustic scattering and protein structure determination via cryo-electron microscopy" |
March 29, 2017, 4:00 pm at CMSA Building, 20 Garden St, G10 |
| JOINT DEPT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Nina Holden (MIT) |
Percolation-decorated triangulations and their relation with SLE and LQG |
The Schramm-Loewner evolution (SLE) is a family of random fractal curves, which is the proven or conjectured scaling limit of a variety of two-dimensional lattice models in statistical mechanics, e.g. percolation. Liouville quantum gravity (LQG) is a model for a random surface which is the proven or conjectured scaling limit of discrete surfaces known as random planar maps (RPM). We prove that a percolation-decorated RPM converges in law to SLE-decorated LQG in a certain topology. This is joint work with Bernardi and Sun. We then discuss a work in progress where we try to strengthen the topology of convergence of a RPM to LQG by considering conformal embeddings of the RPM into the complex plane. This is joint work with Sun and with Gwynne, Miller, Sheffield, and Sun" |
March 29, 2017, 3:00 pm at CMSA Building, 20 Garden St, G02 |
| NUMBER THEORY SEMINAR |
Martin Olsson (UC BERKELEY) |
Local fundamental groups and reduction mod $p$ |
I will discuss various finiteness results for local fundamental groups, and how positive characteristic techniques can be used to deduce results in characteristic $0$. In particular, I will explain how to deduce a result of Xu on finiteness of local fundamental groups for klt singularities using positive characteristic methods. This is joint work with Bhargav Bhatt and Ofer Gabber" |
March 29, 2017, 3:00 pm at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Hannes Pichler (HARVARD UNIVERSITY) |
Photonic tensor networks produced by a single quantum emitter |
We discuss a protocol to generate two dimensional tensor network states using a single quantum system that sequentially interacts with a 1D string of qubits. This is accomplished by using parts of the string itself as a quantum queue memory. As a simple physical implementation, we consider a single atom or atom like system coupled to a 1D waveguide with a distant mirror, where guided photons represent the qubits while the mirror allows the implementation of the queue memory. We show that this allows for a realization of a universal quantum computer using a single atom coupled to light. To this end we first review the basic concepts of measurement based quantum computation, and then discuss an explicit protocol to deterministically create a 2D cluster state in a quantum nanophotonic experiment. We then classify the many-body quantum states that can be produced in this approach in terms of tensor network states" |
March 28, 2017, 2:45 pm at Jefferson 453 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Jordan Keller (COLUMBIA UNIVERSITY) |
Linear stability of Schwarzschild spacetime |
I will discuss recent work, joint with Pei-Ken Hung and Mu-Tao Wang, on the linear stability of the Schwarzschild spacetime. Our method employs Hodge decomposition to split linearized solutions into closed and co-closed portions, respectively identified with even-parity and odd-parity solutions in the physics literature. For each portion, we derive Regge-Wheeler type equations for decoupled, gauge-invariant quantities at the linearized connection level. With the choice of an appropriate gauge, decay estimates on these decoupled quantities are used to establish decay of the linearized metric coefficients of the solution" |
March 28, 2017, 3:00 - 4:00 PM at CMSA Building, 20 Garden St, G02 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
David Stapleton (STONY BROOK UNIVERSITY) |
Hilbert schemes of points on surfaces and their tautological bundles |
Fogarty showed in the 1970s that the Hilbert scheme of n points on a smooth surface is itself smooth. Interest in these Hilbert schemes has grown since it has been shown they arise in hyperkahler geometry, geometric representation theory, and algebraic combinatorics. In this talk we will explore the geometry of certain tautological bundles on the Hilbert scheme of points. In particular we will show that these tautological bundles are (almost always) stable vector bundles. We will also show that each sufficiently positive vector bundles on a curve C is the pull back of a tautological bundle from an embedding of C into the Hilbert scheme of the projective plane" |
March 28, 2017, 3:00 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Agnese Bissi (HARVARD UNIVERSITY) |
Loops in AdS from conformal symmetry |
In this talk I will discuss a new use for conformal field theory crossing equation in the context of AdS/CFT: the computation of loop amplitudes in AdS, dual to non-planar correlators in holographic CFTs. I will revisit this problem and the dual 1/N expansion of CFTs, in two independent ways. The first is to show how to explicitly solve the crossing equations to the first subleading order in 1/N^2, given a leading order solution. This is done as a systematic expansion in inverse powers of the spin, to all orders. These expansions can be resummed, leading to the CFT data for finite values of the spin. The second approach involves Mellin space. As an example, Iâll show how the polar part of the four-point, loop-level Mellin amplitudes can be fully reconstructed from the leading-order data. The anomalous dimensions computed with both methods agree. In the case of \phi^4 theory in AdS, the crossing solution reproduces a previous computation of the one-loop bubble diagram. I will end with a discussion on open problems and new developments" |
March 27, 2017, 12:00 pm at CMSA Building, 20 Garden St, G02 |
| JOINT DPT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Chiranjib Mukherjee (COURANT INSTITUTE ) |
Compactness and Large Deviations |
In a reasonable topological space, large deviation estimates essentially deal with probabilities of events that are asymptotically (exponentially) small, and in a certain sense, quantify the rate of these decaying probabilities. In such estimates, upper bounds for such small probabilities often require compactness of the ambient space, which is often absent in problems arising in statistical mechanics (for example, distributions of local times in Brownian motion in the full space Rd). Motivated by such a problem, we present a robust theory of âtranslation-invariant compactificationâ of probability measures in Rd. Thanks to an inherent shift-invariance of the underlying problem, we are able to apply this abstract theory painlessly and solve a long standing problem in statistical mechanics, the mean-field polaron problem. This talk is based on joint works with S. R. S. Varadhan (New York), as well as with Erwin Bolthausen (Zurich) and Wolfgang Koenig (Berlin)." |
March 24, 2017, 2:00 at Science Center Room 232 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Etale motivic cohomology |
" |
March 23, 2017, 3:00 - 5:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Peter Sarnak (PRINCETON UNIVERSITY) |
Integral points on Markoff type cubic surfaces |
Cubic surfaces in affine three space tend to have few integral points. Certain cubics such as x^3+y^3+z^3=m , may have many such points but very little is known about them. After a brief review of these questions we focus on Markoff type surfaces : x^2+y^2+z^2-x.y.z= m , for which a (nonlinear) descent is a starting point to investigate a Hasse Principle and strong approximation. Joint works with Ghosh and Bourgain/Gamburd" |
March 22, 2017, 3:00 pm at Science Center 507 |
| INFORMAL GEOMETRY & DYNAMICS SEMINAR |
Oleg Ivrii (CALIFORNIA INSTITUTE OF TECHNOLOGY) |
Differentiating Blaschke products |
" |
March 22, 2017, 4:00 pm at Science Center 507 |
| JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Alexander Fribergh (UNIVERSITĂ© DE MONTRĂ©AL) |
The ant in the labyrinth |
One of the most famous open problem in random walks in random environments is to understand the behavior of a simple random walk on a critical percolation cluster, a model known as the ant in the labyrinth. I will present new results on the scaling limit for the simple random walk on the critical branching random walk in high dimension. In the light of lace expansion, we believe that the limiting behavior of this model should be universal for simple random walks on critical structures in high dimensions" |
March 22, 2017, 3:00 PM at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SOCIAL SCIENCE APPLICATIONS FORUM |
Danielle Li (HARVARD UNIVERSITY) |
Financing Novel Drugs |
The process of drug discovery is expensive and highly uncertain. Because of this, risk-averse firms facing financial constraints may be less likely to invest in novel drugs than may be socially optimal. We examine this hypothesis by studying how resource constraints impact firmsâ decisions to invest in novel drug compounds. This paper has two contributions. First, we develop a new molecule-based measure of the chemical novelty of new drug candidates. Second, we use variation in the expansion of Medicare prescription drug coverage in the United States (which differentially benefited firms with more drugs targeted toward the elderly, as well as firms with more remaining market exclusivity on those drugs) to isolate exogenous variation in cash flow to firms. We find that firms which benefit more from the expansion of drug coverage develop more drug candidates as a result and, moreover, this increase is driven by an increase in the development of more chemically novel drug compounds" |
March 21, 2017, 4:30 - 5:30 PM at CMSA Building, 20 Garden St, G02 |
| MATHEMATICAL PHYSICS SEMINAR |
James Wootton (UNIVERSITY OF BASEL) |
Topological Error Correction |
Over the last decade there has been a great deal of interest in topologically ordered systems from the perspective of quantum computation. These typically have degenerate subspaces that cannot be accessed by local operations, but can be manipulated by the braiding of anyonic quasiparticles. This provides so-called âtopological protectionâ against local errors, and so forms an ideal basis for fault-tolerant quantum computation. In this talk I primarily review the surface codes, one of the most commonly considered systems for topological quantum computation. I will discuss the basics of anyons, how to do quantum computation with them and why you would want to. I ll also review the experimental progress that has been made in the last few years" |
March 21, 2017, 2:45 pm at Jefferson 453 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Brian Osserman (UC DAVIS) |
Limit linear series and the maximal rank conjecture |
The maximal rank conjecture addresses the degrees of equations cutting out suitably general curves in projective spaces. We describe an approach to this conjecture involving degenerating to a chain of genus-1 curves, and using ideas from limit linear series. More speculatively, we will describe the prospects for applications to related problems such as the strong maximal rank conjecture. This is joint work with Fu Liu, Montserrat Teixidor i Bigas, and Naizhen Zhan" |
March 21, 2017, 3:00 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Philippe Sosoe (CMSA) |
New bounds for the chemical distance in 2D critical percolation |
We consider the problem of estimating the length, in lattice spacings, of the shortest open connection between the two vertical sides of a square of side length N in critical percolation, when N tends to infinity. This is known as the chemical distance between the sides. Kesten and Zhang asked if this length is asymptotically negligible compared to the length of the âlowest crossingâ, whose length can be expressed in terms of arm exponents and thus calculated quite precisely on the hexagonal lattice. With M. Damron and J. Hanson, we answered this question in 2015. In this talk, we present improved estimates on the chemical distance, using a new iteration technique" |
March 20, 2017, 12:00 pm at CMSA Building, 20 Garden St, G10 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Aleksey Zinger (STONY BROOK UNIVERSITY) |
Enumerative geometry of curves: old and new |
I will present an overview of the (complex) Gromov-Witten invariants and their relation to curve counts provided by Pandharipande s version of Gopakumar-Vafa formula for Fano classes. I will then present a similar formula that transforms the real positive-genus GW-invariants of many real-orientable threefolds into signed counts of curves. These integer invariants provide lower bounds for counts of real curves of a given genus that pass through conjugate pairs of constraints. This talk is based on joint works with P. Georgieva and J. Niu" |
March 14, 2017, **CANCELED DUE TO WEATHER. to be rescheduled** at **CANCELED DUE TO WEATHER** |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL LECTURE SERIES ON DONALDSON-THOMAS AND GROMOV-WITTEN THEORIES |
Artan Sheshmani (THE QGM AARHUS AND CMSA HARVARD) |
Conifold Transitions and modularity of DT invariants on Nodal fibrations |
Following lectures I and II we continue the discussion on the moduli space of shaves with two dimensional support on K3-fibered threefolds, which can admit finitely many nodal (rational double point singularity at worst) fibers. We will use the conifold transitions and degeneration techniques in this case to relate the geometry of our moduli space and its enumerative invariants to the ones studied in lectures I, II over smooth K3-fibrations" |
March 10, 2017, 9:00 - 10:30 am at CMSA Building, 20 Garden St, G10 |
| CMSA SPECIAL LECTURE SERIES ON DONALDSON-THOMAS AND GROMOV-WITTEN THEORIES |
Artan Sheshmani (AARHUS UNIVERSITY/CMSA) |
Modularity of DT invariants on smooth K3 vibrations II |
Motivated by S-duality modularity conjectures in string theory, we study the Donaldson-Thomas invariants of 2-dimensional sheaves inside a nonsingular threefold X. Our main case of study is when X is given by a smooth surface fibration over a curve with the canonical bundle of X pulled back from the base curve. We study the Donaldson-Thomas invariants, as defined by Richard Thomas, of the 2-dimensional Gieseker stable sheaves in X supported on the fibers. In case where X is a K3 fibration, analogous to the Gromov-Witten theory formula established by Maulik-Pandharipande, we express these invariants in terms of the Euler characteristic of the Hilbert scheme of points on the fiber and the Noether-Lefschetz numbers of the fibration, and prove that the invariants have modular properties. We are intending to go through these lectures with a relatively slow speed, that is: Theorem-Proof style, (so we will be less hand-wavy!) and we intend to establish some of the required background, e.g Noether-Lefschetz theory, vector valued modular forms etc." |
March 08, 2017, 9:00 - 10:30 am at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Taylor Dupuy (VERMONT) |
On The Integers of CC(t)^{alg} |
We will discuss the first order theory of the ring of algebraic integers inside the algebraic closure of univariate rational functions over the complex numbers. It particular, this ring interprets the usual rational integers ZZ if we allow parameters. This is joint work in progress with Udi Hrushovski" |
March 08, 2017, 3:00 pm at Science Center 507 |
| INFORMAL GEOMETRY & DYNAMICS SEMINAR |
Dawei Chen (BOSTON COLLEGE & HARVARD UNIVERSITY) |
Extremal and rigid divisors on moduli spaces of curves |
" |
March 08, 2017, 4:00 pm at Science Center 530 |
| JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Xiaoqin Guo (STONY BROOK UNIVERSITY) |
Harnack inequality for a balanced random environment |
We consider a random walk in a balanced random environment on $Z^d$ which is allowed to be non-elliptic. This is a Markov chain generated by a discrete non-divergence form operator. In this talk, assuming that the environment is iid and âgenuinely d-dimensionalâ, we will present a Harnack inequality for discrete harmonic functions of the corresponding operator. The result is based on the analysis of the percolation structure of the (non-reversible) environment and renormalization arguments. Joint work with N. Berger, J.-D. Deuschel and M.Cohen" |
March 08, 2017, 3:00 pm at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Andreas Malmendier (UTAH STATE UNIVERSITY) |
Kummer surfaces, modular forms, and their roles in string dualities |
A smooth K3 surface obtained as the blow-up of the quotient of a four-torus by the involution automorphism at all 16 fixed points is called a Kummer surface. Kummer surface need not be algebraic, just as the original torus need not be. However, algebraic Kummer surfaces obtained from abelian varieties provide a fascinating arena for string compactification as they are not trivial spaces but are sufficiently simple for one to be able to analyze most of their properties in detail. In this talk, we give an explicit description for the relation between algebraic Kummer surfaces of Jacobians of genus-two curves with principal polarization and those associated to (1, 2)-polarized abelian surfaces from three different angles: the point of view of 1) the binational geometry of quartic surfaces in P^3 using even-eights, 2) elliptic fibrations on K3 surfaces of Picard-rank 17 over P^1 using Nikulin involutions, 3) theta-functions of genus-two using two-isogeny. Finally, we will explain how these (1,2)-polarized Kummer surfaces naturally allow for an identification of the complex gauge coupling in Seiberg-Witten gauge theory with the axion-dilaton modulus in string theory using an old idea of Sen. (This is joint work with Adrian Clingher." |
March 08, 2017, 11 am - 12 pm at CMSA Building, 20 Garden St, G10 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Bill Fulton (UNIVERSITY OF MICHIGAN) |
Degeneracy Loci with a Line Bundle |
In order to give formulas for classical as well as modern degeneracy loci, one needs to allow symplectic or quadratic forms on a vector bundle V with values in a line bundle L. If one has two flags of isotropic subbundles of V, one has a degeneracy locus for each signed permutation, specifying how they intersect. Finding formulas for their cohomology classes amounts to constructing double Schubert polynomials with a new parameter corresponding to the first Chern class of L. We construct these âtwisted double Schubert polynomialsâ and show they satisfy all the analogues of the type A polynomials, including positivity for their coefficients and their products. This is joint work with Dave Anderson, answering a question of Joe Harris from 1987" |
March 07, 2017, 3:00 pm at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Teng Fei (COLUMBIA UNIVERSITY) |
A construction of infinitely many solutions to the Strominger system |
The Strominger system is a system of PDEs describing the compactification of heterotic strings with torsion. Mathematically it can be thought of as a generalization of Ricci-flat metrics on non-KĂ€hler Calabi-Yau 3-folds. In this talk we present newly obtained smooth solutions to the Strominger system on infinitely many compact non-K" |
March 07, 2017, 4:15 pm at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Andreas Malmendier (UTAH STATE UNIVERSITY) |
Kummer surfaces, modular forms, and their roles in string dualities |
A smooth K3 surface obtained as the blow-up of the quotient of a four-torus by the involution automorphism at all 16 fixed points is called a Kummer surface. Kummer surface need not be algebraic, just as the original torus need not be. However, algebraic Kummer surfaces obtained from abelian varieties provide a fascinating arena for string compactification as they are not trivial spaces but are sufficiently simple for one to be able to analyze most of their properties in detail. In this talk, we give an explicit description for the relation between algebraic Kummer surfaces of Jacobians of genus-two curves with principal polarization and those associated to (1, 2)-polarized abelian surfaces from three different angles: the point of view of 1) the binational geometry of quartic surfaces in P^3 using even-eights, 2) elliptic fibrations on K3 surfaces of Picard-rank 17 over P^1 using Nikulin involutions, 3) theta-functions of genus-two using two-isogeny. Finally, we will explain how these (1,2)-polarized Kummer surfaces naturally allow for an identification of the complex gauge coupling in Seiberg-Witten gauge theory with the axion-dilaton modulus in string theory using an old idea of Sen. (This is joint work with Adrian Clingher.) " |
March 07, 2017, 2:45 pm at Jefferson 453 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SOCIAL SCIENCE APPLICATIONS FORUM |
Krishna Pendakur (HARVARD AND SIMON FRASER UNIVERSITY) |
Infant Mortality and the Repeal of Federal Prohibition |
Exploiting a newly constructed dataset on county-level variation in prohibition status, this paper asks two questions: what were the effects of the repeal of federal prohibition on infant mortality? And were there any significant externalities from the individual policy choices of counties and states on their neighbors? We find that dry counties with at least one wet neighbor saw baseline infant mortality increase by roughly 3%. We argue that such cross-border policy externalities are plausibly exogenous sources of variation in assessing the effects of prohibitionâs repeal and should be a key consideration in the contemporary policy debate on the prohibition of illicit substances." |
March 07, 2017, 4:30 - 5:30 PM at CMSA Building, 20 Garden St, G02 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Tom Rudelius (HARVARD PHYSICS) |
6D SCFTs and Group Theory |
We will explore the surprising connection between certain classes of homomorphisms and certain classes of non-compact Calabi-Yau manifolds using 6D superconformal field theories as an intermediate link" |
March 06, 2017, 12:00 pm at CMSA Building, 20 Garden St, G10 |
| THURSDAY SEMINAR |
Akhil Mathew (HARVARD UNIVERSITY) |
The Rost Motive |
" |
March 02, 2017, 3:00 - 5:00 PM at Science Center 507 |
| BRANDEIS, HARVARD, MIT, NORTHEASTERN JOINT MATHEMATICS COLLOQUIUM AT HARVARD |
Tony Yue Yu (UNIVERSITĂ© PARIS-SUD) |
Counting open curves via Berkovich geometry |
Motivated by mirror symmetry, we study the counting of open curves in log Calabi-Yau surfaces. Although we start with a complex surface, the counting is achieved by applying methods from Berkovich geometry (non-archimedean analytic geometry). This gives rise to new geometric invariants inaccessible by classical methods. These invariants satisfy a list of very nice properties and can be computed explicitly. If time permits, I will mention the conjectural wall-crossing formula, relations with the works of Gross-Hacking-Keel and applications towards mirror symmetry" |
March 02, 2017, 4:30 PM at Science Center Hall A |
| JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Shirshendu Gangly (UC BERKELEY ) |
Large deviation and counting problems in sparse settings |
The upper tail problem in the Erd Ìos-R Ìenyi random graph G ⌠Gn,p, where every edge is included independently with probability p, is to estimate the probability that the number of copies of a graph H in G exceeds its expectation by a factor 1 + ÎŽ. The arithmetic analog considers the count of arithmetic progressions in a random subset of Z/nZ, where every element is included independently with probability p. In this talk, I will describe some recent results regarding the solution of the upper tail problem in the sparse setting, i.e. where p decays to zero, as n grows to infinity. The solution relies on non-linear large deviation principles developed by Chatterjee and Dembo and more recently by Eldan and solutions to various extremal problems in additive combinatorics" |
March 01, 2017, 3:00 PM at CMSA Building, 20 Garden St, G10 |
| INFORMAL GEOMETRY & DYNAMICS SEMINAR |
Russell Lodge (STONY BROOK UNIVERSITY) |
Global dynamics of multi curves in complex dynamics |
" |
March 01, 2017, 4:00 pm at Science Center 530 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS COLLOQUIUM |
Jun Liu (HARVARD UNIVERSITY DEPARTMENT OF STATISTICS) |
Expansion of biological pathways by integrative Genomics |
The number of publicly available gene expression datasets has been growing dramatically. Various methods had been proposed to predict gene co-expression by integrating the publicly available datasets. These methods assume that the genes in the query gene set are homogeneously correlated and consider no gene-specific correlation tendencies, no background intra-experimental correlations, and no quality variations of different experiments. We propose a two-step algorithm called CLIC (CLustering by Inferred Co-expression) based on a coherent Bayesian model to overcome these limitations. CLIC first employs a Bayesian partition model with feature selection to partition the gene set into disjoint co-expression modules (CEMs), simultaneously assigning posterior probability of selection to each dataset. In the second step, CLIC expands each CEM by scanning the whole reference genome for candidate genes that were not in the input gene set but co-expressed with the genes in this CEM. CLIC is capable of integrating over thousands of gene expression datasets to achieve much higher coexpression prediction accuracy compared to traditional co-expression methods. Application of CLIC to ~1000 annotated human pathways and ~6000 poorly characterized human genes reveals new components of some well-studied pathways and provides strong functional predictions for some poorly characterized genes. We validated the predicted association between protein C7orf55 and ATP synthase assembly using CRISPR knock-out assays. Based on the joint work with Yang Li and the Vamsi Mootha lab" |
March 01, 2017, 4:30 PM at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
David Hansen (COLUMBIA UNIVERSITY) |
Some remarks on local Shimura varieties |
I ll give an introduction to local Shimura varieties and (more generally) moduli spaces of mixed-characteristic local shtukas as defined by Scholze. I ll also discuss some recent results and conjectures on their geometry and cohomology. This is partially joint work with Jared Weinstein" |
March 01, 2017, 3:00 pm at Science Center 507 |
| HARVARD MIT ALGEBRAIC GEOMETRY SEMINAR |
Daniel Litt (COLUMBIA UNIVERSITY) |
Arithmetic Restrictions on Geometric Monodromy |
Let X be an algebraic variety over a field k. Which representations of pi_1(X) arise from geometry, e.g. as monodromy representations on the cohomology of a family of varieties over X? We study this question by analyzing the action of the Galois group of k on the fundamental group of X. As a sample application of our techniques, we show that if X is a normal variety over a field of characteristic zero, and p is a prime, then there exists an integer N=N(X,p) satisfying the following: any irreducible, non-trivial p-adic representation of the fundamental group of X, which arises from geometry, is non-trivial mod p^N" |
February 28, 2017, 3:00 pm at MIT 4-153 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Nick Edelen (MIT) |
Quantitative Reifenberg for Measures |
In joint work with Aaron Naber and Daniele Valtorta, we demonstrate a quantitative structure theorem for measures in R^n under assumptions on the Jones \beta-numbers, which measure how close the support is to being contained in a subspace. Measures with this property have arisen in several interesting scenarios: in obtaining packing estimates on and rectifiability of the singular set of minimal surfaces; in characterizing L2-boundedness of Calderon-Zygmund operators; and as an âanalystâsâ formulation of the traveling salesman problem" |
February 28, 2017, 3:15 PM at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Wenbin Yan (CMSA) |
Argyres-Douglas Theories, Vertex Operator Algebras and Wild Hitchin Characters |
We discuss some interesting relations among 4d Argyles-Douglas (AD) theories, vertex operator algebras (VOA) and wild Hitchin system. We use the Coulomb branch index of AD theories to study geometric and topological data of moduli spaces of wild Hitchin system. These data show an one to one map between fixed points on the moduli space and irreducible modules of the VOA. Moreover, a limit of the Coulomb branch index of AD theories can be identified with matrix elements of the modular transform ST^kS in certain two-dimensional VOAs. The appearance of VOAs, which was known previously to be associated with Schur operators but not Coulomb branch operators, is somewhat surprising" |
February 27, 2017, 12:00 PM at CMSA Building, 20 Garden St, G10 |
| THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
Voevodsky's condition H90(n) |
" |
February 23, 2017, 3:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Steven Rayan (UNIVERSITY OF SASKATCHEWAN) |
Higgs bundles and the Hitchin system |
I will give an informal introduction to the Hitchin system, an object lying at the crossroads of geometry and physics. As a moduli space, the Hitchin system parametrizes semistable Higgs bundles on a Riemann surface up to equivalence. From this point of view, the Hitchin map and spectral curves emerge. We ll use these to form an impression of what the moduli space looks like. I will also outline the appearances of the Hitchin system in dynamics, hyperkaehler geometry, and mirror symmetry" |
February 22, 2017, 4:30 pm at CMSA Building, 20 Garden St, G10 |
| JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Bob Hough (STONY BROOK UNIVERSITY) |
Random walk on unipotent groups |
I will describe results of two recent papers from random walk on unipotent groups. In joint work with Diaconis (Stanford), we obtain a new local limit theorem on the real Heisenberg group, and determine the mixing time of coordinates for some random walks on finite unipotent groups. In joint work with Jerison and Levine (Cornell) we prove a cut-off phenomenon in sandpile dynamics on the torus $(\mathbb{Z}/m\mathbb{Z})^2$ and obtain a new upper bound on the critical exponent of sandpiles on $\mathbb{Z}^2$" |
February 22, 2017, 3:00 pm at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Yiwei She (IAS AND COLUMBIA UNIVERSITY) |
The (unpolarized) Shafarevich conjecture for K3 surfaces |
Let K be a number field, S a finite set of places of K, and g a positive integer. Shafarevich made the following conjecture for higher genus curves: the set of isomorphism classes of genus g curves defined over K and with good reduction outside of S is finite. Faltings proved this conjecture for curves and the analogous conjecture for polarized abelian surfaces and Zarhin removed the necessity of specifying a polarization. Building on the work of Faltings and Andre and using technical advances by Madapusi Pera, we prove the unpolarized Shafarevich conjecture for K3 surfaces." |
February 22, 2017, 3:00 pm at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Alex Waldron (SIMONS CENTER AT STONY BROOK) |
Long-time existence for Yang-Mills flow |
I ll describe the general picture of Yang-Mills flow on a four-dimensional Riemannian manifold, where curvature concentration is a subtle problem. Time permitting, I ll give an indication of my recent proof that bubbling occurs only at infinite time, which was conjectured in 1997" |
February 21, 2017, 3:15 - 4:15 PM at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SOCIAL SCIENCE APPLICATIONS FORUM |
Ravi Jagadeesan (HARVARD UNIVERSITY) |
Complementary inputs and the existence of stable outcomes in large trading networks |
This paper studies a model of large trading networks with bilateral contracts. The model allows income effects, unlike in parts of the matching literature, and imperfectly tradeable goods, unlike in the general equilibrium literature. In our setting, under standard continuity and convexity conditions, a stable outcome is guaranteed to exist in any acyclic network, as long as all firms regard sales as substitutes and the market is large. Thus, complementarities between inputs do not preclude the existence of stable outcomes in large markets. Even when there are complementarities between sales, this paper shows that tree stable outcomes are guaranteed to exist in large markets, under continuity and convexity conditions. The model presented in this paper generalizes and unifies versions of general equilibrium models with divisible and indivisible goods, matching models with continuously divisible contracts, models of large (two-sided) matching with complementarities, and club formation models. Additional results provide intuition for the role of uni-directional substitutability conditions and acyclicity in the main existence results, and explain what kinds of equilibria are guaranteed to exist even when these conditions are relaxed. Unlike in two-sided large-market settings, the sufficient conditions described in this paper pin down maximal domains for the existence of equilibria" |
February 21, 2017, 4:30 - 5:30 PM at CMSA Building, 20 Garden St, G02 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
David Hyeon (SEOUL NATIONAL UNIVERSITY) |
Commuting nilpotents modulo simultaneous conjugation and Hilbert scheme |
Pairs of commuting nilpotent matrices have been extensively studied, especially from the view point of quivers. But the space of commuting nilpotents modulo simultaneous conjugation has not received any attention at all although it has a definite moduli theory flavor. Unlike the case of commuting nilpotents paired with a cyclic vector, the GIT is not well behaved in this case. I will explain how a moduli space can be constructed as a homogeneous space, and show that it is isomorphic to an open subscheme of a punctual Hilbert scheme. Over the field of complex numbers, thus constructed space is diffeomorphic to a direct sum of twisted tangent bundles over a projective space. This is a joint work with W. Haboush" |
February 21, 2017, 3:00 pm at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Masahito Yamazaki (UNIVERSITY OF TOKYO) |
Integrable Lattice Models from Gauge Theory |
In a celebrated paper in 1989, E. Witten discovered a beautiful connection between knot invariants (such as the Jones polynomial) and three-dimensional Chern-Simons theory. Since there are similarities between knot theory and integrable models, it is natural to ask if there is also a gauge theory explanation for integrable models. The answer to this question was recently given by K. Costello in 2013. In this talk I will describe my ongoing work, which explains many results in integrable models from the standard quantum field theory analysis of Costello s theory" |
February 21, 2017, 2:45 pm at Jefferson 453 |
| GAUGE THEORY, TOPOLOGY AND SYMPLECTIC GEOMETRY SEMINAR |
Stefan Mueller (GEORGIA SOUTHERN) |
C^0-characterization and rigidity of symplectic and Lagrangian |
We prove that an embedding of a ball into a symplectic manifold is symplectic if and only if it preserves the shape invariant. The latter is, in brief, the set of all cohomology classes that can be represented by the pull-back of a fixed primitive one-form of the symplectic form by a Lagrangian embedding of a fixed manifold and of a given homotopy type. The proof is based on displacement information about (non)-Lagrangian submanifolds that comes from J-holomorphic curve methods. The definition of shape preserving does not involve derivatives and is preserved by uniform convergence (on compact subsets). In particular, we derive a new proof of C^0-rigidity of symplectic embeddings (and diffeomorphisms). We also discuss a similar characterization and rigidity for Lagrangian embeddings. As a consequence, we can make sense of the notions of symplectic and Lagrangian for homeomorphisms and topological submanifolds, respectively. An advantage of our techniques (over symplectic capacities) is that they avoid the cumbersome distinction between symplectic and anti-symplectic, and also work well in the contact setting" |
February 17, 2017, 3:30 - 4:30 pm at Science Center 507 |
| THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
Voevodsky's application of Steenrod operations to the Milnor conjecture II |
" |
February 16, 2017, 3:00 - 5:00 PM at Science Center 507 |
| JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Lisa Hartung (COURANT INSTITUTE) |
The Structure of Extreme Level Sets in Branching Brownian Motion |
Branching Brownian motion (BBM) is a classical process in probability, describing a population of particles performing independent Brownian motion and branching according to a Galton Watson process. Arguin et al.\ and A\\i{}d\ ekon et al.\ proved the convergence of the extremal process. In the talk we discuss how one can obtain finer results on the extremal level sets by using a random walk-like representation of the extremal particles. We establish among others the upper tail probabilities for the distance between the maximum and the second maximum (joint work with Aser Cortines and Oren Louder)" |
February 15, 2017, 3:00 PM at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS COLLOQUIUM |
Masahito Yamazaki (IMPU) |
Geometry of 3-manifolds and Complex Chern-Simons Theory |
The geometry of 3-manifolds has been a fascinating subject in mathematics. In this talk I discuss a quantization of 3-manifold geometry, in the language of complex Chern-Simons theory. This Chern-Simons theory in turn is related to the physics of 3-dimensional supersymmetric field theories through the so-called 3d/3d correspondence, whose origin can be traced back to a mysterious theory on the M5-branes. Along the way I will also comment on the connection with a number of related topics, such as knot theory, hyperbolic geometry, quantum dilogarithm and cluster algebras" |
February 15, 2017, 4:30-5:30 PM at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Michael Zieve (UNIVERSITY OF MICHIGAN) |
Uniform boundedness for maps between curves |
I will discuss the following conjecture: every rational map between curves over Q induces a map on rational points that is (<=32)-to-1 over all but finitely many values. In case the curves have genus one, this is a slightly weaker version of Mazur s uniform boundedness theorem. Progress towards the full result has relied on progress towards determining all possibilities for the monodromy group and ramification type of a complex rational function, contributing to problems originating in work of Zariski and Hurwitz" |
February 15, 2017, 3:00 PM at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Shamil Shakirov (HARVARD UNIVERSITY) |
Integrability of Refined Chern-Simons Theory |
We prove the recent conjecture by the speaker and Semeon Arthamonov that Reshetikhin-Turaev TQFT in genus 2 admits a q,t-deformation. The central role in the proof is played by an interesting integrable system on a genus 2 surface. This integrable system is a genus 2 generalization of the Rujsenaars-Schneider system, and its eigenfunctions are genus 2 analogues of Macdonald polynomials. Open questions, including generalization to higher genus, will be discussed" |
February 14, 2017, 2:45 pm at Jefferson 453 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Arnav Tripathy (HARVARD UNIVERSITY) |
Further counterexamples to the integral Hodge conjecture |
I ll briefly recall the history of counterexamples to the integral Hodge conjecture, starting with the topological motivations of Atiyah and Hirzebruch. I ll then transition to describing a new class of counterexamples to the integral Hodge and integral Tate conjectures that I show exist according to a conjecture of Ben Antieau" |
February 14, 2017, 3:00 pm at MIT 4-153 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SOCIAL SCIENCE APPLICATIONS FORUM |
Mauricio FernĂĄndez Duque (HARVARD UNIVERSITY) |
Pluralistic Ignorance and Preference Complementarities |
I develop a theory of group interaction with preference complementarities, in which individuals know that others privately judge whether their type matches that of the majority in the group. The model sheds light on situations of pluralistic ignorance -- a social situation where `a majority of group members privately reject a norm, but incorrectly assume that most others accept it, and therefore go along with it. (Katz and Allport, 1931). As opposed to past approaches, our model explains three stylized facts of pluralistic ignorance: that most individuals are acting reluctantly, that they think most others are not acting reluctantly, and that an inefficient equilibrium can be sustained in which most are reluctantly cooperating. We show some preliminary results suggesting that as the certainty over the population distribution of preferences grows, the probability of pluralistic ignorance increases when group size is small and decreases when group size is large" |
February 14, 2017, 4:30 - 5 :30pm at CMSA Building, 20 Garden St, G02 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Artan Sheshmani (AARHUS UNIVERSITY/CMSA) |
Nested Hilbert schemes and DT theory of local threefolds |
Following talk 1 we study the geometry of S which is projective simply connected complex surface and we let L be a line bundle on S. We study moduli space of stable compactly supported 2-dimensional sheaves on the total spaces of L. The moduli space admits a \C^*-action induced by scaling the fibers of L. We identify certain components of the fixed locus of the moduli space with the moduli space of torsion free sheaves on S and the nested Hilbert schemes on S. We define reduced Donaldson-Thomas invariants by virtual localization. When L is the canonical bundle of S these reduced DT invariants recover Vafa-Witten invariants defined by Tanaka-Thomas via the moduli space of Higgs pairs on S. Vafa-Witten invariants are expected to have modular properties predicted by S-duality. We further show that in this case, in combination with Mochizuki s formulas, we are able to express these equivariant Donaldson-Thomas invariants on the total space of canonical bundle of S in terms of our invariants of nested Hilbert schemes in talk 1, the Seiberg-Witten invariants of S, and the integrals over the products of Hilbert schemes of points on S" |
February 14, 2017, 4:15 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Artan Sheshmani (AARHUS UNIVERSITY/CMSA) |
The theory of Nested Hilbert schemes on surfaces |
In joint work with Amin Gholampour and Shing-Tung Yau we construct natural virtual fundamental classes for nested Hilbert schemes on a nonsingular projective surface S. This allows us to define new invariants of S that recover some of the known important cases such as Poincare invariants of D\{urr-Kabanov-Okonek and the stable pair invariants of Kool-Thomas. In the case of the nested Hilbert scheme of points, we can express these invariants in terms of integrals over the products of Hilbert scheme of points on S, and relate them to the vertex operator formulas found by Carlsson-Okounkov. The virtual fundamental classes of the nested Hilbert schemes play a crucial role in the local Donaldson-Thomas theory of threefolds that I will talk about, in talk " |
February 13, 2017, 12:00 pm at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Tom Luo (UNIVERSITY OF MINNESOTA) |
Semidefinite Relaxation of Nonconvex Quadratic Optimization |
Motivated by applications from wireless communication, we consider the NP-hard problem of finding a minimum norm vector in n-dimensional real or complex Euclidean space, subject to m concave homogeneous quadratic constraints. We show that a semidefinite programming (SDP) relaxation for this nonconvex quadratically constrained quadratic program (QP) provides an O(m^2) approximation in the real case, and an O(m) approximation in the complex case" |
February 09, 2017, 1:30 - 2:30 pm at CMSA Building, 20 Garden St, G10 |
| THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
Voevodsky's application of Steenrod operations to the Milnor conjecture |
" |
February 09, 2017, 3:00 pm at Science Center 507 |
| INFORMAL GEOMETRY & DYNAMICS SEMINAR |
Fabian Haiden (HARVARD UNIVERSITY) |
Flat surfaces and stability structures on categories |
" |
February 08, 2017, 4:00 pm at Science Center 530 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Matthew Headrick (BRANDEIS UNIVERSITY) |
Quantum entanglement, classical gravity, and convex programming: New connections |
In recent years, developments from the study of black holes and quantum gravity have revealed a surprising connection between quantum entanglement and classical general relativity. The theory of convex programming, applied in the differential-geometry setting, turns out to be useful for understanding what s behind this correspondence. We will describe these developments, giving the necessary background in quantum information theory and convex programming along the way" |
February 08, 2017, 4:30 pm at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Joël Bellaïche (BRANDEIS UNIVERSITY ) |
Lacunarity of modular forms |
Let $f = \sum a_n q^n$ be a modular form, either holomorphic or with poles at cusps, either of integral weight or of half-integral weight, either in characteristic zero or in positive characteristic. When is $f$ lacunary, that is, when does the set of integers $n$ such that $a_n \neq 0$ have density 0? More generally, how fast do the number of $n\leq x$ such that $a_n \neq 0$ grows when $x$ goes to infinity? There is an extremely vast literature about this family of questions. In this talk, I ll present a summary of what can be reasonably conjectured, what was previously known, and the proof of a recent result (joint work with Ben Green and Kannan Soundararajan) in positive characteristic" |
February 08, 2017, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Dan Mangoubi (HEWBREW UNIVERSITY OF JERUSALEM) |
Harmonic functions sharing the same zero set |
What can be said about the family of all harmonic functions sharing the same zero set in the unit ball of R^n? It turns out that an extension of the classical Harnack inequality gives the answer. This was recently stated and proved in two dimensions. Slightly later, A. Logunov and E. Malinnikova proved it in all dimensions. We describe these results and discuss the following problem: How can we construct interesting examples of such families in three dimensions? Do they really exist? This is a report on a joint work in progress with Adi Weller Weiser. Organized by Prof. Shing-Tung Ya" |
February 07, 2017, 4:15 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SOCIAL SCIENCE APPLICATIONS FORUM |
Nikhil Naik (MIT) |
Visual Urban Sensing: Understanding Cities with Computer Vision |
Street View services have documented the visual appearance of cities from more than a hundred countries across the world in the past decade. I design computer vision tools that harness Street View imagery to conduct computer-driven automated surveys of the built environment at street-level resolution and global scale. In this talk, I will describe two algorithms that computationally evaluate urban appearance from imagery. The first algorithm, Streetscore, quantifies the perceived safety of a street block, by harnessing data from a crowdsourced game. The second algorithm quantifies the growth or decay of cities from time-series Street View imagery obtained over several years. Finally, I will demonstrate the use of these algorithms for studying important questions in urban economics, sociology, and urban planning" |
February 07, 2017, 4:30 - 5:30 PM at CMSA Building, 20 Garden St, G02 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Aaron Bertram (UNIVERSITY OF UTAH) |
Counting finite quot schemes |
Grothendieck s quot scheme generalizes the Grassmannian (the variety of quotients of a vector space) to produce a projective scheme of quotients of a fixed coherent sheaf on a fixed variety. When the variety is a curve or del Pezzo surface, there are instances in which the quot scheme is both of expected dimension zero and actually of dimension zero, in which case we may ask for its cardinality. Over a curve, the cardinality of these quot schemes is the trace of a matrix, coming from a topological quantum field theory that contains both the quantum cohomology of the Grassmannian and the Verlinde formula. In the surface case, the cardinality is much more mysterious. This is work by my student Thomas Goller, and also joint work with with Thomas and Drew Johnson" |
February 07, 2017, 3:00 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Christophe Keller (HARVARD PAULSON SCHOOL OF ENGINEERING AND APPLIED SCIENCES) |
Mathieu Moonshine and Symmetry Surfing |
" |
February 06, 2017, 12:00 pm at CMSA Building, 20 Garden St, G10 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY ) |
Steenrod Operations in Motivic Cohomology |
" |
February 02, 2017, 3:00 - 5:00 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Philip Engel (HARVARD UNIVERSITY) |
The number of positively curved triangulations on the sphere |
" |
February 02, 2017, 4:00 pm at Science Center 530 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Sean Eddy (HARVARD DEPT OF MOLECULAR AND CELLULAR BIOLOGY) |
Biological sequence homology searches: the future of deciphering the past |
Computational recognition of distant common ancestry of biological sequences is a key to studying ancient events in molecular evolution. The better our sequence analysis methods are, the deeper in evolutionary time we can see. A major aim in the field is to improve the resolution of homology recognition methods by building increasingly realistic, complex, parameter-rich models. I will describe current and future research in homology search algorithms based on probabilistic inference methods, using hidden Markov models (HMMs) and stochastic context-free grammars (SCFGs). We make these methods available in the HMMER and Infernal software from my laboratory, in collaboration with database teams at the European Bioinformatics Institute in the UK" |
February 01, 2017, 4:30 pm at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Bjorn Poonen (MIT) |
Local arboreal representations |
Given a polynomial f(x) over a field K and an element a in K, if the solutions to f^n(x) = a in a separable closure K_s are distinct for all n, their union forms a tree, and we obtain a homomorphism from Gal(K_s/K) to the automorphism group of the tree. We study the image of Galois in the case where K is a local field. This is joint work with Jacqueline Anderson, Spencer Hamblen, and Laura Walton" |
February 01, 2017, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Yu Qiu (CHINESE UNIVERSITY OF HONG KONG) |
Stability conditions for quivers via exchange graphs |
Let Q be an acyclic quiver and D_N(Q) be the associated N-Calabi-Yau category. We (with Alastair King) show that the quotient graph of the exchange graph of hearts/t-structures in D_N(Q) by the spherical twists is isomorphic to the (N-1)-cluster exchange graph. In the case when Q is of Dynkin type, we (with Jon woolf) show that the spherical twist group is isomorphic to the braid group of Q and the corresponding (principal component of) space of stability conditions is contractible. Organized by Prof. Shing-Tung Ya" |
January 31, 2017, 4:15 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Yu Qiu (CHINESE UNIVERSITY OF HONG KONG) |
Spherical twists on 3-Calabi-Yau categories of quivers with potentials from surfaces and spaces of stability conditions |
We study the 3-Calabi-Yau category D(S) associated to a marked surface S. In the case when S is unpunctured, we show that the spherical twist group, which is a subgroup of auto-equivalence group of D(S), is isomorphic to a subgroup of the mapping class group of S_Delta--the decorated version of S. In the case when S is an annulus, we prove that the space Stab of stability conditions on D(S) is contractible. We also present working progress on proving the simply connectedness of Stab for any unpunctured case and on studying Stab for the punctured case" |
January 30, 2017, 12:00 pm at CMSA Building, 20 Garden St, G10 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Yong Lin (RENMIN UNIVERSITY) |
Heat kernel estimate and solution of semi linear heat equations on graphs |
We prove the heat kernel lower estimate on graphs under volume growth condition. By using this heat kernel estimate and curvature assumption, we prove the existence and nonexistence results of global solutions for the semilinear heat equation on graphs. --Organized by Professor Shing-Tung Ya" |
January 24, 2017, 4:15 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Anton Kapustin (CALIFORNIA INSTITUTE OF TECHNOLOGY) |
Fermionic state-sum models and topological field theory |
" |
January 12, 2017, 4:00 pm at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Gerard Ben Arous (COURANT INSTITUTE) |
Complexity of random functions of many variables: from geometry to statistical physics and deep learning algorithms |
Random functions of many variables tend to be very complex. I will survey recent work describing this phenomenon and its consequences, first from a geometric point of view. I will illustrate this phenomenon first in the case of random functions on the high-dimensional sphere. These random functions happen to be the energy landscapes of important models of statistical physics of disordered media, i.e spherical spin glasses. I will then show how this could be extended to the random landscapes of deep learning algorithms, which are at the heart of many of the recent progress in Data Science. The common mathematical tool underlying these different questions is given by Random Matrix Theory. The relevant work is joint with mathematical colleagues (Auffinger, Cerny, Subag, Zeitouni) or physicists (Biroli, Cammarota) and Computer Scientists (Yann Le Cun and his team at Facebook)" |
January 11, 2017, 4:00 pm at CMSA Building, 20 Garden St, G10 |
| JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Brian Rider (TEMPLE UNIVERSITY) |
Universality for the random matrix hard edge |
The hard edge refers to the distribution of the smallest singular value for certain ensembles of random matrices, or, and what is the same, that of the minimal point of a logarithmic gas constrained to the positive half line. For any inverse temperature and quadratic potential the possible limit laws (as the dimension, or number of particles, tends to infinity) was characterized by Jose Ramirez and myself in terms of the spectrum of a (random) diffusion generator. Here we show this picture persists for more general convex polynomial potentials. Joint work with Patrick Waters" |
December 14, 2016, 3:00 PM at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS HOMOLOGICAL MIRROR SYMMETRY SEMINAR |
Lino Campos Amorim (BOSTON UNIVERSITY) |
Fukaya category of a compact toric manifold |
In this talk I will discuss the Fukaya category of a toric manifold following the work of Fukaya-Oh-Ohta-Ono. I will start with an overview of the general structure of the Fukaya category of a compact symplectic manifold. Then I will consider toric manifolds in particular the Fano case and construct its mirror. References: arXiv:1011.4044 arXiv:0907.4219 arXiv:0802.170" |
December 08, 2016, 2:00 - 4:00 pm at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Andrew Sutherland (MIT) |
Sato-Tate in dimension 3 |
The Sato-Tate group of an abelian variety over a number field is a compact Lie group whose Haar measure is conjectured to govern the distribution of its Frobenius classes, and in particular, the limiting distribution of the normalized Euler factors that appear in its L-function. This conjecture has been proved in full generality only for abelian varieties of dimension 1, but there has been substantial progress in dimension 2, including a complete classification of the 52 Sato-Tate groups that arise and proofs of equidistribution for at least one example in all but the generic case. I will report on recent results and work in progress in dimension 3, including some remarkable new (and very recent) computations" |
December 07, 2016, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Valentino Tosatti (NORTHWESTERN UNIVERSITY) |
Metric limits of hyperkahler manifolds |
I will discuss a proof of a conjecture of Kontsevich-Soibelman and Gross-Wilson about the behavior of unit-diameter Ricci-flat Kahler metrics on hyperkahler manifolds (fibered by holomorphic Lagrangian tori) near a large complex structure limit. The collapsed Gromov-Hausdorff limit is a special Kahler metric on a half-dimensional complex projective space, away from a singular set of Hausdorff codimension at least 2. The resulting picture is also compatible with the Strominger-Yau-Zaslow mirror symmetry. This is joint work with Yuguang Zhang" |
December 07, 2016, 4:30 pm at CMSA Building, 20 Garden St, G10 |
| JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR: |
Dan Romik (UC DAVIS) |
A Pfaffian point process for Totally Symmetric Self Complementary Plane Partitions |
Totally Symmetric Self Complementary Plane Partitions (TSSCPPs) can be encoded as a family of nonintersecting lattice paths having fixed initial points and variable endpoints. The endpoints of the paths associated with a uniformly random TSSCPP of given order therefore induce a random point process, which turns out to be a Pfaffian point process. I will discuss conjectural formulas for the entries of the correlation kernel of this process, and a more general rationality phenomenon, which if true implies the existence of an interesting limiting process describing infinite TSSCPPs as well as conjectural probabilities for the occurrence of certain connectivity patterns in loop percolation (a.k.a. the dense O(1) loop model)" |
December 07, 2016, 3:00 pm at CMSA Building, 20 Garden St, G10 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Gabriele di Cerbo (COLUMBIA UNIVERSITY ) |
Log birational boundedness of Calabi-Yau pairs |
I will discuss a joint work with Roberto Svaldi on boundedness of Calabi-Yau pairs. Recent works in the minimal model program suggest that pairs with trivial log canonical class should satisfy some boundedness properties. I will show that Calabi-Yau pairs which are not birational to a product are indeed log birationally bounded. This result is the first step towards boundedness of elliptically fibered Calabi-Yau manifolds." |
December 6, 2016, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Mattias Jonsson (UNIVERSITY OF MICHIGAN) |
A variational approach to the Yau-Tian-Donaldson conjecture |
I will present joint work with Robert Berman and Sebastien Boucksom, on a new proof of a uniform version of the Yau-Tian-Donaldson conjecture for Fano manifolds with finite automorphism group. Our approach does not involve the continuity method or Cheeger-Colding-Tian theory. Instead, the proof is variational and uses pluripotential theory and certain non-Archimedean consideration" |
December 06, 2016, 4:15 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Hansol Hong (CMSA) |
Mirror construction via formal deformation of Lagrangians |
Iâll briefly review algebraic structures on categories that appear in homological mirror symmetry, and explain how the deformation of this algebraic structure on a Fukaya category can arise a mirror space" |
December 05, 2016, 12:00 pm at CMSA Building, 20 Garden St, G10 |
| GAUGE THEORY, TOPOLOGY AND SYMPLECTIC GEOMETRY SEMINAR |
Brendan McLellan (HARVARD UNIVERSITY) |
Some 1-loop results in contact Chern-Simons theory |
The 1-loop perturbative invariants for ordinary bosonic Chern-Simons theory are well known to be described in terms of the self-linking and linking invariants for knots and links. In this talk, some new results (joint w/ C. Beasley, R. Zhang) for the 1-loop invariants in contact Chern-Simons theory will be presented for Legendrian knots and links. Some interesting features enter the story, such as sublaplacians on the Heisenberg group, Folland-Stein operators, and a new realization of the well-known quantum shift in the Chern-Simons level." |
December 02, 2016, 3:30 - 4:30 pm at Science Center 507 |
| THURSDAY SEMINAR |
Dennis Gaitsgory (HARVARD UNIVERSITY ) |
Voevodsky's motives |
" |
December 01, 2016, 3:00 PM at Science Center 507 |
| JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
James Lee (UNIVERSITY OF WASHINGTON) |
Conformal growth rates, spectral geometry, and distributional limits of graphs |
Given a graph, one can deform its geometry according to a function that assigns non-negative weights to the vertices. We refer to this as a conformal deformation of the graph metric. For a finite graph, it makes sense to define the area of such a weight as the average of the squared weights of the vertices. One can similarly define the area of a conformal weight for a unimodular random graph. The conformal growth exponent is the smallest rate of volume growth of balls achievable by a conformal weight of unit area. We show that if a unimodular (rooted) random graph (G,x) has quadratic conformal growth (QCG) and the law of deg(x) is sufficiently well-behaved, then the random walk on G is almost surely recurrent. We also argue that our joint with Kelner, Price, and Teng (2011) can be used to show that every distributional limit of finite planar graphs has QCG. More generally, this holds for H-minor-free graphs, and other interesting families like string graphs (the intersection graph of continuous arcs in the plane). These methods do not rely on circle packings, and can instead be thought of as directly uniformizing the underlying graph metric. They yield a short proof of Benjamini and Schramm s result that a distributional limit of finite, bounded-degree planar graphs is almost surely recurrent, and provide a positive answer to their conjecture that the same should hold for H-minor-free graphs. Gurel-Gurevich and Nachmias recently solved a central open problem by showing that the uniform infinite planar triangulation (UIPT) and quadrangulation (UIPQ) are almost surely recurrent. By combining QCG with methods from spectral geometry, we present a new proof of this fact that follows from strong quantitative bounds on the heat kernel. A similar phenomenon holds beyond dimension two: Assuming the law of deg(x) has tails that decay faster than any inverse polynomial, the almost sure spectral dimension of a unimodular random graph (G,x) is equal to its conformal growth exponent. This has consequences for limits of graphs that can be sphere-packed in R^d for d > 2" |
November 30, 2016, 3:00 pm at CMSA Building, 20 Garden St, G02 |
| NUMBER THEORY SEMINAR |
Akshay Venkatesh (STANFORD) |
The action of the derived Hecke algebra on weight one forms |
I will explain how a derived version of the Hecke algebra acts on weight one forms. Conjecturally this action should encode information about certain Stark-type units, and we can test this conjecture numerically, using ideas of Merel and Mazur. Joint work with Michael Harris" |
November 30, 2016, 3:00 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Sharad Ramanathan (HARVARD MCB AND SEAS) |
Finding co-ordinate systemsd to monitor the development of mammalian embryos |
" |
November 30, 2016, 4:20 pm at CMSA Building, 20 Garden St, G10 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Kenny Ascher (COLUMBIA UNIVERSITY) |
Uniformity of integral points and the Lang-Vojta conjecture |
Caporaso, Harris, and Mazur showed, assuming Lang s conjecture, that the number of rational points on a smooth curve of genus greater than 1 is uniformly bounded by an integer depending solely on the genus and number field the curve is defined over. This theorem was proven by means of a purely algebro-geometric theorem known as a fibered power theorem. We discuss how this uniformity result follows from the fibered power theorem, and discuss recent extensions (joint with A. Turchet) aiming to, assuming the Lang-Vojta conjecture, study uniformity results for integral points on curves and surfaces of log general type" |
November 22, 2016, 3:00 PM at science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Xiangfeng Gu (STONYBROOK) |
Differential Geometric Methods for Engineering Applications |
With the development of virtual reality and augmented reality, many challenging problems raised in engineering fields. Most of them are with geometric nature, and can be explored by modern geometric means. In this talk, we introduce our approaches to solve several such kind of problems: including geometric compression, shape classification, surface registration, cancer detection, facial expression tracking and so on, based on surface Ricci flow and optimal mass transportation" |
November 22, 2016, 4:00 - 5:00 pm at CMSA Building, 20 Garden St, G10 |
| JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Jafar Jafarov (STANFORD UNIVERSITY) |
SU(N) Wilson loop expectations |
Lattice gauge theories are discrete approximations to quantum Yang-Mills theories. The main object of interest in lattice gauge theories are Wilson loop expectations. I will present 1/N expansion for SU(N) Wilson loop expectations in strongly coupled SU(N) lattice gauge theory in any dimension. I will show how to represented the coefficients of the expansion as absolutely convergent sums over trajectories in a string theory on the lattice, establishing a kind of gauge-string duality" |
November 22, 2016, 3:00 pm at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Hee Cheol Kim (HARVARD PHYSICS) |
Defects and instantons in 5d SCFTs |
In this talk I will discuss various BPS defects in 5d SUSY field theories. In the first part, I will talk about co-dimension 4 defects and their interaction with instanton particles. I will show that the partition function of this co-dimension 4 defect is related to Nekrasov s qq-character. In the second part, I will talk about co-dimension 2 defects and instanton partition functions. I will also explain that the partition functions of the co-dimension 2 defects give rise to eigenfunctions of associated integral Hamiltonians" |
November 21, 2016, 12:00 pm at CMSA Building, 20 Garden St, G10 |
| HARVARD, BRANDEIS, MIT, NORTHEASTERN JOINT COLLOQUIUM AT HARVARD |
Carlos Simpson (UNIVERSITE DE NICE) |
Calculating harmonic maps to buildings---a 2-dimensional combinatorial reduction calculus |
Over a Riemann surface, given a spectral curve for the group SL(3) we can look for harmonic maps to buildings whose differential is given by the associated triple of 1-forms. Gaiotto-Moore-Neitzke have introduced the spectral network associated to the spectral curve. We describe a combinatorial process, starting from the differentials, to construct the image of the harmonic map. A pre-theorem is that if the spectral network has no BPS states then the reduction process is well-defined, and we conjecture that it terminates. This will give information on WKB asymptotics. The reduction process may be viewed as a 2-dimensional generalization of the Stallings core graph construction. This is joint with Katzarkov, Noll and Pandit" |
November 17, 2016, Tea at 4:00 PM, the Austine & Chilton McDonnell Common Room, Science Center 4th Floor, Talk at 4:30 pm at Science Center Hall C |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MEMBERS' SEMINAR |
Henri Guenancia (STONY BROOK UNIVERSITY) |
Singular varieties with trivial canonical bundle |
If X is a smooth projective variety (or compact KÀhler manifold) with trivial first Chern class, then a famous result of Beauville and Bogomolov asserts that up to a finite étale cover, X is a product of varieties of three possible type: abelians varieties (or tori), Calabi-Yau varieties or HyperkÀhler varieties. These last two classes are defined using properties of the algebra of global holomorphic forms. If X is singular though (say with torsion canonical bundle and klt singularities) this result is not known and presumably very difficult. In this talk, we will explain that if in addition X is assumed to be strongly stable (which is an infinitesimal version of irreducibility) then X falls into one of the singular analogues of the two categories above (Calabi-Yau and HyperkÀhler varieties). This is ongoing joint work with Stefan Kebekus and Daniel Greb." |
November 17, 2016, 5:00 pm at CMSA Building, 20 Garden St, G10 |
| LOGIC COLLOQUIUM |
Haim Horowitz (HEWBREW UNIVERSITY OF JERUSALEM) |
On the non-existence and definability of mad families |
By an old result of Mathias, there are no mad families in the Solovay model constructed by the Levy collapse of a Mahlo cardinal. By a recent result of Törnquist, the same is true in the classical model of Solovay as well. In a recent paper, we show that ZF+DC+there are no mad families is actually equiconsistent with ZFC. I ll present the ideas behind the proof in the first part of the talk. In the second part of the talk, I ll discuss the definability of maximal eventually different families and maximal cofinitary groups. In sharp contrast with mad families, it turns out that Borel MED families and MCGs can be constructed in ZF. Finally, I ll present a general problem in Borel combinatorics whose solution should explain the above difference between mad and maximal eventually different families, and I ll show how large cardinals must be involved in such a solution. This is joint work with Saharon Shelah" |
November 17, 2016, 4:00 pm at 2 Arrow St, Rm 408 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
A^1 Homotopy Theory |
" |
November 17, 2016, 3:00 - 5:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Chao Li (COLUMBIA UNIVERSITY) |
Goldfeldâs conjecture and congruences between Heegner points |
Given an elliptic curve E over Q, a celebrated conjecture of Goldfeld asserts that a positive proportion of its quadratic twists should have analytic rank 0 (resp. 1). We show this conjecture holds whenever E has a rational 3-isogeny. We also prove the analogous result for the sextic twists of j-invariant 0 curves. For a more general elliptic curve E, we show that the number of quadratic twists of E up to twisting discriminant X of analytic rank 0 (resp. 1) is >>X/log^{5/6}X, improving the current best general bound towards Goldfeld s conjecture due to Ono--Skinner (resp. Perelli--Pomykala). We prove these results by establishing a congruence formula between p-adic logarithms of Heegner points based on Coleman s integration. This is joint work with Daniel Kriz" |
November 16, 2016, 3:00 pm at Science Center 507 |
| JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Yu Gu (STANFORD) |
Local vs global random fluctuations in stochastic homogenization |
We will discuss stochastic homogenization of elliptic equations in divergence form, of which the probabilistic counterpart is the random conductance model. I will try to explain some probabilistic and analytic approaches we use to obtain the first and higher order random fluctuations. It turns out that in high dimensions, a formal two-scale expansion only leads to the correct" |
November 16, 2016, 2:30 pm *note change in time* at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Tristan Collins (HARVARD UNIVERSITY) |
Restricted volumes and finite time singularities of the Kahler-Ricci flow |
I will discuss the relationship between restricted volumes, as defined algebraically or analytically, and the finite time singularities of the Kahler-Ricci flow. This is joint work with Valentino Tosatti" |
November 16, 2016, 3:30 pm *Special time* at CMSA Building, 20 Garden St, G10 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Sebastien Picard (COLUMBIA UNIVERSITY) |
Geometric Flows and Strominger systems |
The anomaly flow is a geometric flow which implements the Green-Schwarz anomaly cancellation mechanism originating from superstring theory, while preserving the conformally balanced condition of Hermitian metrics. I will discuss criteria for long time existence and convergence of the flow on toric fibrations with the Fu-Yau ansatz. This is joint work with D.H. Phong and X.W. Zhang" |
November 15, 2016, 4:15 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SOCIAL SCIENCE APPLICATIONS FORUM |
Ben Roth (MIT) |
Keeping the Little Guy Down: A Debt Trap for Informal Lending |
Microcredit and other forms of informal finance have so far failed to catalyze business growth among small scale entrepreneurs in the developing world, despite their high return to capital. This prompts a re-examination of the special features of informal credit markets that cause them to operate inefficiently. We present a theory of informal lending that highlights two of these features. First, borrowers and lenders bargain not only over division of surplus but also over contractual flexibility (the ease with which the borrower can invest to grow her business). Second, when the borrower s business becomes sufficiently large she exits the informal lending relationship and enters the formal sector â an undesirable event for her informal lender. We show that in Stationary Markov Perfect Equilibrium these two features lead to a poverty trap and study its properties. The theory facilitates reinterpretation of a number of empirical facts about microcredit: business growth resulting from microfinance is low on average but high for businesses that are already relatively large, and microlenders have experienced low demand for credit. The theory features nuanced comparative statics which provide a testable prediction and for which we establish novel empirical support. Using the Townsend Thai data and plausibly exogenous variation to the level of competition Thai money lenders face, we show that as predicted by our theory, money lenders in high competition environments impose fewer contractual restrictions on their borrowers. We discuss robustness and policy implications." |
November 15, 2016, 4:30 - 5:30 PM at CMSA Building, 20 Garden St, G02 |
| RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Boaz Barak (HARVARD PAULSON SCHOOL ) |
Computational Bayesianism, sums of squares, cliques, and unicorns |
Can we make sense of quantities such as the probability that 2^81712357 - 1 is prime or the probability that statement X is a logical contradiction? More generally, can we use probabilities to quantify our computational uncertainty in cases where all the relevant information is given but in a computationally hard-to-extract form? In this talk we will discuss how such pseudo probabilities can arise from the Sum of Squares (SOS) semidefinite program (Parrilo 00, Lasserre 01). We will show how this yields an approach for showing both positive and negative results for the SOS algorithms. In particular we will present better algorithms for the tensor decomposition problem from data analysis, and stronger lower bounds for the planted clique problem. The talk will be partially based on joint works with Sam Hopkins, Jon Kelner, Pravesh Kothari, Ankur Moitra, Aaron Potechin and David Steurer. I will not assume any prior knowledge on the sum of squares algorithm or semidefinite programming." |
November 09, 2016, 3:00 PM at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Norden E. Huang (NATIONAL CENTRAL UNIVERSITY) |
On Holo-Hilbert Spectral Analysis |
Traditionally, spectral analysis is defined as transform the time domain data to frequency domain. It is achieved through integral transforms based on additive expansions of a priori determined basis, under linear and stationary assumptions. For nonlinear processes, the data can have both amplitude and frequency modulations generated by intra-wave and inter-wave interactions involving both additive and nonlinear multiplicative processes. Under such conditions, the additive expansion could not fully represent the physical processes resulting from multiplicative interactions. Unfortunately, all existing spectral analysis methods are based on additive expansions, based either on a priori or adaptive bases. While the adaptive Hilbert spectral analysis could accommodate the intra-wave nonlinearity, the inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase lock modulations are left untreated. To resolve the multiplicative processes, we propose a full informational spectral representation: The Holo-Hilbert Spectral Analysis (HHSA), which would accommodate all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions, through additional dimensions in the spectrum to account for both the variations in frequency and amplitude modulations (FM and AM) simultaneously. Applications to wave-turbulence interactions and other data will be presented to demonstrate the usefulness of this new spectral representation" |
November 09, 2016, 4:30 pm at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Jared Weinstein (BOSTON UNIVERSITY ) |
The cohomology of local Shimura varieties |
This is joint work with Tasho Kaletha. The local Langlands correspondence predicts that representations of a reductive group G over a p-adic field are related to Galois representations into the Langlands dual of G. A conjecture of Kottwitz (as generalized by Rapoport and Viehmann) asserts that this relationship appears in a precise way in the cohomology of local Shimura varieties, which were shown to exist by Scholze. We don t know how Galois acts on this cohomology yet, but we can verify much of the rest of the conjecture, in a large degree of generality, using a Lefschetz-Verdier fixed point formula" |
November 09, 2016, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SOCIAL SCIENCE APPLICATIONS FORUM |
Sifan Zhou (CMSA) |
Non-Compete Agreements and the Career of PhDs |
Non-compete agreements are legal contracts that employers use to restrain ex-employees from joining another firm or starting a new business in competition against them. While non-compete agreements protect employersâ investments in R&D and human capital, such protection may come at the costs of employees. I study the effects of non-compete agreements on doctorate recipients by analyzing the time-series and cross-sectional variations in the enforceability of these contracts in the United States. Using a difference-in-difference approach, I find that, for PhDs who work in the for-profit sector, tougher enforcement decreases their within-state job mobility. The reduced within-state job mobility is in part compensated by an increase in job changing across state borders, in line with the situation that non-compete agreements are more difficult to enforce across jurisdictions. Tougher enforcement also slows down the salary growths of these PhDs, consistent with a model in which general human capital is turned into firm-specific human capital and workers lose bargaining power as they cannot threaten to leave for an outside offer. What is more, freshly minted PhDs are less likely to stay working in the state from which they received their degrees if the state has tougher enforcement. All these effects are consistently strong for engineering majors and less so for life sciences majors" |
November 08, 2016, 4:30 PM - 5:30 PM at CMSA Building, 20 Garden St, G02 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Francois Greer (UNIVERSITY OF NOTRE DAME) |
Noether-Lefschetz Theory and Elliptic Calabi-Yau Threefolds |
The Hodge theory of surfaces provides a link between enumerative geometry and modular forms. I will introduce a general approach to studying the Gromov-Witten theory of elliptically fibered CY3 s using the cohomological theta correspondence. As an application, we will examine the Weierstrass model overP2, proving part of the modularity statement predicted by Huang-Katz-Klemm using the topological string partition function" |
November 08, 2016, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Nicolaos Kapouleas (BROWN UNIVERSITY) |
Gluing constructions for minimal surfaes and other geometric objects |
" |
November 08, 2016, 4:15 pm at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Seung-Joo Lee (VIRGINIA TECH) |
Multiple Fibrations in Calabi-Yau Geometry and String Dualities |
We study the ubiquity of multiple fibration structures in known constructions of Calabi-Yau manifolds and explore the role they play for string dualities. Upon introducing new tools for resolved Calabi-Yau varieties, we analyze a set of F-theory effective theories associated to the different elliptic fibrations and relate them via the M-/F-theory correspondence. Explicit geometric examples will include higher-rank Mordell-Weil groups and non-flat fibrations. In addition, in the context of heterotic/F-theory duality, we also investigate the role played by multiple nested structures of K3- and elliptic fibrations in known and novel string dualities in various dimensions" |
November 07, 2016, 12:00 PM at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
An Huang (HARVARD UNIVERSITY ) |
Tautological Systems |
This is a continuation of Bong Lian s talk on 10/28, and more details will be discussed." |
November 04, 2016, 2:00 - 3:00 pm at CMSA Building, 20 Garden St, G10 |
| LOGIC COLLOQUIUM |
Theodore A. Slaman (UC BERKELEY) |
Recursion Theory and Diophantine Approximation |
Recursion Theory deals with the definability of sets, especially sets of natural numbers or equivalently real numbers. Diophantine Approximation deals with the approximation of real numbers by rational numbers, which can be viewed as a number theoretic form of definability. We will discuss connections between these areas" |
November 03, 2016, 4:00 pm at 2 Arrow St, Rm 420 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS HOMOLOGICAL MIRROR SYMMETRY |
Yusuf Baris Kartal (MIT) |
HMS for Del Pezzo surfaces |
I will present Auroux-Katzarkov-Orlov s proof of one side of the homological mirror symmetry for Del Pezzo surfaces. Namely I will prove their derived categories are equivalent to the categories of vanishing cycles for certain LG-models together with B-fields. I plan to show how the general B-field corresponds to non-commutative Del Pezzo surfaces and time allowing may mention HMS for simple degenerations of Del Pezzo surfaces. The tools include exceptional collections( and mutations for degenerate case), explicit description of NC deformations, etc" |
November 03, 2016, 2:00 PM - 4:00 PM at CMSA Building, 20 Garden St, G10 |
| THURSDAY SEMINAR |
Marc Hoyols (MIT) |
The Nesterenko-Suslin-Totaro theorem |
" |
November 03, 2016, 3:00 - 5:00 PM at Science Center 507 |
| JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Ramon van Handel (PRINCETON UNIVERSITY) |
Inhomogeneous random matrices |
How do random matrices behave when the entries can have an arbitrary variance pattern? New problems arise in this setting that are almost completely orthogonal to classical random matrix theory. I will illustrate such problems by describing one of my favorite conjectures on this topic due to R. Latala, and the various mathematical techniques and questions that are emerging from its investigation" |
November 02, 2016, 3:00 pm at CMSA Building, 20 Garden St, G10 |
| SPECIAL SEMINAR |
Henry Cohn (MICROSOFT) |
Sphere packing problem in 8 and 24 dimensions |
" |
November 02, 2016, 10:30 AM - 12:00 PM at Science Center 530 |
| NUMBER THEORY SEMINAR |
() |
No seminar this week |
No seminar this week due to Fields Medal Symposium" |
November 02, 2016, at |
| INFORMAL GEOMETRY AND DYNAMICS SEMINAR |
Simion Filip (HARVARD UNIVERSITY ) |
From Teichmueller curves to higher-dimensional invariant subvarieties |
" |
November 02, 2016, 4:00 PM at Science Center 530 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Robert Haslhofer (UNIVERSITY OF TORONTO) |
The moduli space of 2-convex embedded spheres |
We investigate the topology of the space of smoothly embedded n-spheres in R^{n+1}, i.e. the quotient space M_n:=Emb(S^n,R^{n+1})/Diff(S^n). By Hatcherâs proof of the Smale conjecture M_2 is contractible, but the topology of M_n for n\geq 3 is highly nontrivial. In this talk, I will explain how geometric analysis can be used to study the topology of M_n respectively some of its variants. I will start by explaining the topological background and sketching a geometric analytic proof of Smaleâs theorem that M_1 is contractible. In the second half of my talk, Iâll describe recent work on space of smoothly embedded spheres in the 2-convex case, i.e. when the sum of the two smallest principal curvatures is positive. Our main theorem (joint with Buzano and Hershkovits) proves that this space is path-connected, for every n. The proof uses mean curvature flow with surgery. *Organized by Prof. S.T. Yau" |
November 01, 2016, 3:00 - 4:00 PM *Special Time* at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Joseph Minahan (UPPSALA UNIVERSITY) |
Supersymmetric gauge theories on $d$-dimensional spheres |
In this talk I discuss localizing super Yang-Mills theories on spheres in various dimensions. Our results can be continued to non-integer dimensions, at least perturbatively, and can thus be used to regulate UV divergences. I will also show how this can provide a way to localize theories with less supersymmetry" |
October 31, 2016, 12:00 pm at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Bong Lian (BRANDEIS UNIVERSITY) |
Tautological systems |
I will give an introduction to this class of D-modules whose construction is inspired by the B-model side of mirror symmetry. This theory has led to solutions to a number of old problems on period integrals and mirror symmetry. In this talk, I will review the construction and explain some of the basic properties of the D-modules" |
October 28, 2016, 12:45 pm at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS HOMOLOGICAL MIRROR SYMMETRY SEMINAR |
Philip Engel (HARVARD UNIVERSITY) |
Mirror symmetry in the complement of an anticanonical divisor |
According to the SYZ conjecture, the mirror of a Calabi-Yau variety can be constructed by dualizing the fibers of a special Lagrangian fibration. Following Auroux, we consider this rubric for an open Calabi-Yau variety X-D given as the complement of a normal crossings anticanonical divisor D in X. In this talk, we first define the moduli space of special Lagrangian submanfiolds L with a flat U(1) connection in X-D, and note that it locally has the structure of a Calabi-Yau variety. The Fukaya category of such Lagrangians is obstructed, and the degree 0 part of the obstruction on L defines a holomorphic function on the mirror. This âsuperpotential depends on counts of holomorphic discs of Maslov index 2 bounded by L. We then restrict to the surface case, where there are codimension 1 âwallsâ consisting of Lagrangians which bound a disc of Maslov index 0. We examine how the superpotential changes when crossing a wall and discuss how one ought to âquantum correctâ the complex structure on the moduli space to undo the discontinuity introduced by these discs" |
October 27, 2016, 2:00 - 4:00 pm at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Henry Cohn (MICROSOFT) |
Sums of squares, correlation functions, and exceptional geometric structures |
Some exceptional structures such as the icosahedron or E_8 root system have remarkable optimality properties in settings such as packing, energy minimization, or coding. How can we understand and prove their optimality? In this talk, I ll interweave this story with two other developments in recent mathematics (without assuming familiarity with either): how semidefinite optimization and sums of squares have expanded the scope of optimization, and how representation theory has shed light on higher correlation functions for particle systems" |
October 26, 2016, 4:30 pm at CMSA Building, 20 Garden St, G10 |
| JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Wei Wu (NEW YORK UNIVERSITY) |
Extremal and local statistics for gradient field models |
The gradient field models with uniformly convex potential (also known as the Ginzburg-Landau field) is believed to be in the Gaussian universality class, and has been applied to study different lattice models. Previous work by Naddaf-Spencer and by Miller proved the macroscopic averages of the field converge to a continuum Gaussian free field. In this talk we will describe recent progresses to understand the maximum and local statistics of the field, that indicates the Gaussian universality holds in a strong sense" |
October 26, 2016, 3:00 PM at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Ananth Shankar (HARVARD UNIVERSITY) |
Abelian varieties isogenous to Jacobians |
Chai and Oort have asked the following question: For any algebraically closed field $k$, and for $g \geq 4$, does there exist an abelian variety over $k$ of dimension $g$ not isogenous to a Jacobian? The answer in characteristic 0 is now known to be yes. We present a heuristic which suggests that for certain $g \geq 4$, the answer in characteristic $p$ is no. We will also construct a proper subvariety of $X(1)^n$ which intersects every isogeny class, thereby answering a related question, also asked by Chai and Oort. This is joint work with Jacob Tsimerman" |
October 26, 2016, 3:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Ian Shipman (HARVARD UNIVERSITY) |
Ulrich bundles and a generalization |
Let (X,L) be a smooth, polarized variety. A vector bundle E on X is called an Ulrich bundle if all cohomology of the bundles E(-L),...,E( -dim(X) L ) vanishes. I will give an introduction to Ulrich bundles, highlighting their connection to several elementary problems of interest. Then I will describe some of my work (joint with Y. Mustopa & R. Kulkarni) on a generalization of Ulrich bundles and on the connection between Ulrich bundles and (higher rank) Brill-Noether theory" |
October 25, 2016, 3:00 pm at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Jonathan Zhu (HARVARD UNIVERSITY) |
Entropy and self-shrinkers of the mean curvature flow |
The Colding-Minicozzi entropy is an important tool for understanding the mean curvature flow (MCF), and is a measure of the complexity of a submanifold. Together with Ilmanen and White, they conjectured that the round sphere minimises entropy amongst all closed hypersurfaces. We will review the basics of MCF and their theory of generic MCF, then describe the resolution of the above conjecture, due to J. Bernstein and L. Wang for dimensions up to six and recently claimed by the speaker for all remaining dimensions. A key ingredient in the latter is the classification of entropy-stable self-shrinkers that may have a small singular set. -- Organized by Prof. Shing-Tung Ya" |
October 25, 2016, 3:00 - 4:00 pm *special time at CMSA Building, 20 Garden St, G10 *different location |
| SPECIAL SEMINAR SERIES, JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS |
Masaki Kashiwara (RIMS, KYOTO UNIVERSITY) |
Indsheaves and Riemann-Hilbert correspondence of holonomic D-modules, Part 2 |
" |
October 25, 2016, 4:15 - 5:15 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Arnav Tripathy (HARVARD UNIVERSITY) |
Spinning BPS states and motivic Donaldson-Thomas invariants |
I ll describe a new chapter in the enumerative geometry of the K3 surface and its product with an elliptic curve in a long line of extensions starting from the classic Yau-Zaslow formula for counts of rational nodal curves. In particular, I ll give a string-theoretic derivation of the threefold s motivic Donaldson-Thomas invariants given the Hodge-elliptic genus of the K3, a new quantity interpolating between the Hodge polynomial and the elliptic genus" |
October 24, 2016, 12:00 pm at CMSA Building, 20 Garden St, G10 |
| GAUGE THEORY AND SYMPLECTIC GEOMETRY SEMINAR |
Colin Adams (WILLIAMS COLLEGE) |
Volume and volume density for hyperbolic knots and links |
We use combinatorial decompositions of knot and link complements to determine volume bounds for hyperbolic knots and links. We use this to consider the volume density of a hyperbolic link, which is its hyperbolic volume divided by its crossing number, and how that is related to the determinant density. Then we generalize to so-called multi-crossing projections. This is when the combinatorics becomes interesting" |
October 21, 2016, 3:30 - 4:30 pm at Science Center 507 |
| LOGIC COLLOQUIUM |
Joel David Hamkins (CITY UNIVERSITY OF NEW YORK) |
Recent advances in set-theoretic geology |
Set-theoretic geology is the study of the set-theoretic universe V in the context of all its ground models and those of its forcing extensions. For example, a bedrock of the universe is a minimal ground model of it and the mantle is the intersection of all grounds. In this talk, I shall explain some recent advances, including especially the breakthrough result of Toshimichi Usuba, who proved the strong downward directed grounds hypothesis: for any set-indexed family of grounds, there is a deeper common ground below them all. This settles a large number of formerly open questions in set-theoretic geology, while also leading to new questions. It follows, for example, that the mantle is a model of ZFC and provably the largest forcing-invariant definable class. Strong downward directedness has also led to an unexpected connection between large cardinals and forcing: if there is a hyper-huge cardinal Îș, then the universe indeed has a bedrock and all grounds use only Îș-small forcing. (Post questions and commentary on my blog at http://jdh.hamkins.org/recent-advances-in-set-theoretic-geology-harvard-logic-colloquium-october-2016/." |
October 20, 2016, 4:00 pm at 2 Arrow St, Rm 420 |
| MATHEMATICAL PHYSICS SEMINAR |
Vaughan Jones (VANDERBILT UNIVERSITY) |
Scale Invariant Transfer Matrix and Hamiltonian for Quantum Spin Chains Pt. II |
On examples of quantum spin chains we calculate transfer matrices that are strictly invariant under block spin renormalisation. They are necessarily highly spatially inhomogeneous. But we are able to construct spatially homogeneous ones which are not scale invariant as operators but are as quadratic forms" |
October 20, 2016, 1:15 pm at Jefferson 256 |
| THURSDAY SEMINAR |
Marc Hoyois (MIT) |
Weight one motivic cohomology |
" |
October 20, 2016, 3:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS HOMOLOGICAL MIRROR SYMMETRY SEMINAR |
Tim Large (MIT) |
Symplectic cohomology and wrapped Fukaya categories |
While mirror symmetry was originally conjectured for compact manifolds, the phenomenon applies to non-compact manifolds as well. In the setting of Liouville domains, a class of open symplectic manifolds including affine varieties, cotangent bundles and Stein manifolds, there is an A-infinity category called the wrapped Fukaya category, which is easier to define and often more amenable to computation than the original Fukaya category. In this talk I will construct it, along with symplectic cohomology (its closed-string counterpart), and compute some examples. We will then discuss how compactifying a symplectic manifold corresponds, on the B-side of mirror symmetry, to turning on a Landau-Ginzburg potential" |
October 20, 2016, 2:00 - 4:00 pm at CMSA Building, 20 Garden St, G10 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Bena Tshishiku (HARVARD UNIVERSITY) |
Moduli space, surface bundles, and the Atiyah-Kodaira examples |
" |
October 19, 2016, 4:00 pm at Science Center 530 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Vaughan Jones (VANDERBILT UNIVERSITY) |
Are the Thompson groups any good as a model for Diff(S^1)? |
The Thompson groups are by definition groups of piecewise linear diffeomorphisms of the circle. A result of Ghys-Sergiescu says that a Thompson group can be conjugated to a group of smooth diffeomorphisms. Thatâs the good news. The bad news is that there is an important central extension of Diff(S^1) which requires a certain amount of smoothness for its definition. And Ghys-Sergiescu show that, no matter how the Thompson groups are embedded in Diff(S^1), the restriction of the central extension splits. Is it possible to obtain central extensions of the Thompson groups by any procedure analogous to the constructions of the central extension of Diff(S^1)? I will define all the players in this game, expain this question in detail, and present some failed attempts to answer it." |
October 19, 2016, 4:30 pm at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Rong Zhou (HARVARD UNIVERSITY ) |
Mod p isogeny classes on Shimura varieties with parahoric level structure. |
The Langlands-Rapoport conjecture gives a description of the mod p points of suitable integral models for Shimura varieties. Such results are of use, for example, in computing the local factor of the (semi-simple) Hasse-Weil zeta function of the Shimura variety. In this talk, we show the mod p isogeny classes on the integral models of Shimura varieties with parahoric level constructed by Kisin and Pappas have the form predicted by the conjecture, when the group is residually split at p. Along the way, we verify some of the He-Rapoport axioms which allow us to deduce the non-emptiness of Newton strata for these models" |
October 19, 2016, 3:00 PM at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Vaughan Jones (VANDERBILT UNIVERSITY) |
Scale Invariant Transfer Matrix and Hamiltonian for Quantum Spin Chains |
On examples of quantum spin chains we calculate transfer matrices that are strictly invariant under block spin renormalisation. They are necessarily highly spatially inhomogeneous. But we are able to construct spatially homogeneous ones which are not scale invariant as operators but are as quadratic forms." |
October 18, 2016, 2:45 pm at Jefferson 453 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Jian Xiao (NORTHWESTERN UNIVERSITY) |
Positivity in the convergence of the inverse $\sigma_k$ flow |
By relating the existence of special K\ahler metrics with with algebro-geometric stability conditions, such as the Yau-Tian-Donaldson conjecture on the existence of constant scalar curvature, Lejmi and Sz ekelyhidi proposed a conjectural numerical criterion for the solvability of the inverse $\sigma_k$ equation, or equivalently, for the convergence of the inverse $\sigma_k$ flow. Their conjecture looks like a non-linear version of Demailly-Paun s numerical characterization of the K\ ahler cone. In this talk, we discuss the positivity aspects, partially verifying their conjecture for the case k=n-1" |
October 18, 2016, 3:00 - 4:00 PM *Special Time* at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Claudiu Raicu (UNIVERSITY OF NOTRE DAME) |
Cohomology of determinantal thickenings |
I will explain how to determine the cohomology groups of arbitrary equivariant thickenings of generic determinantal ideals, as well as the ranks of the maps in cohomology induced by inclusions of such thickenings. One application of this work is a concrete description of the linear functions that describe the Castelnuovo-Mumford regularity of sufficiently large powers and symbolic powers of determinantal ideals" |
October 18, 2016, 3:00 pm at MIT 4-153 |
| SPECIAL SEMINAR SERIES, JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS |
Masaki Kashiwara (RIMS, KYOTO UNIVERSITY) |
Indsheaves and Riemann-Hilbert correspondence of holonomic D-modules, Part 1 |
" |
October 18, 2016, 4:15 - 5:15 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Fabian Haiden (HARVARD UNIVERSITY) |
Balanced filtrations and asymptotics for semistable objects |
I will discuss some recent results which came out of the study of the flow on metrized quiver representations. This flow is a finite-dimensional toy model for non-linear heat-type flows. In joint work with Katzarkov, Kontsevich, and Pantev, we find that the asymptotics of the flow on a given quiver representation define a filtration (indexed by R^\infty) which has a purely algebraic interpretation. A novel feature is the existence of non-linear walls, on which asymptotics of the metric are described by nested logarithms." |
October 17, 2016, 12:00 pm at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MEMBERS' SEMINAR |
Vaughan Jones (VANDERBILT UNIVERSITY) |
The Thompson groups as scaling symmetries of quantum spin chains |
The âblock spinâ renormalisation procedure consists of replacing a lattice by a coarser one by replacing a block of spins by a single spin. This is particularly transparent for a chain of spins in one dimension. We can form a âsemicontinous limitâ Hilbert space by reversing the block spin procedure and we will see that Thompsonâs groups F and T act on this Hilbert space via unitary transformations with interesting coefficients" |
October 14, 2016, 5:00 pm at CMSA Building, 20 Garden St, G10 |
| THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
Statement of the Milnor conjectures |
I will discuss the orginal forms of Milnor s conjectures as described in his paper, Algebraic K-theory and Quadratic Forms." |
October 13, 2016, 3:00 - 5:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Yihang Zhu (HARVARD UNIVERSITY) |
The Hasse-Weil zeta functions of the intersection cohomology of minimally compactified orthogonal Shimura varieties |
Initiated by Langlands, the problem of computing the Hasse-Weil zeta functions of Shimura varieties in terms of automorphic L-functions has received continual study. We will discuss how recent progress in various aspects of the field, made by many people, has allowed the extension of the project to some Shimura varieties not treated before. In the particular case of the minimally compactified orthogonal Shimura varieties, we discuss the computation of the local zeta factor of the intersection cohomology, and the comparison to the Arthur-Selberg trace formula via the process of stabilization. Key ingredients include comparing Harish Chandra character formulas to Kostant s Theorem on Lie algebra cohomology, and a comparison between different normalizations of the transfer factors for real endoscopy to get all the signs right." |
October 12, 2016, 3:00 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Conan Leung (CHINESE UNIVERSITY OF HONG KONG) |
Coisotropic A-branes and their SYZ transform |
Kapustin introduced coisotropic A-branes as the natural boundary condition for strings in A-model, generalizing Lagrangian branes and argued that they are indeed needed to for homological mirror symmetry. I will explain in the semiflat case that the Nahm transformation along SYZ fibration will transform fiberwise Yang-Mills holomorphic bundles to coisotropic A-branes. This explains SYZ mirror symmetry away from the large complex structure limit" |
October 12, 2016, 4:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Michael Damron (GEORGIA INSTITUTE OF TECHNOLOGY ) |
Bigeodesics in first-passage percolation |
Abstract: In first-passage percolation, we place i.i.d. continuous weights at the edges of Z^2 and consider the weighted graph metric. A distance minimizing path between points x and y is called a geodesic, and a bigeodesic is a doubly-infinite path whose segments are geodesics. It is a famous conjecture that almost surely, there are no bigeodesics. In the `90s, Licea and Newman showed that, under a curvature assumption on the ``asymptotic shape, all infinite geodesics have asymptotic directions and there are no bigeodesics with both ends directed in some deterministic subset D of [0,2pi) with countable complement. I will discuss recent work with Jack Hanson in which we show that there are no bigeodesics with one end directed in any deterministic direction, assuming the shape boundary is differentiable. This rules out existence of ground state pairs for the related disordered ferromagnet whose interface has a deterministic direction. Furthermore it resolved the Benjamini-Kalai-Schramm ``midpoint problem under the additional assumption of differentiability" |
October 12, 2016, 3:00 PM at CMSA Building, 20 Garden St, G10 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Mark Stern (DUKE UNIVERSITY) |
Instantons on ALF spaces |
I will discuss progress on establishing Cherkis s Nahm transform for multi center Taub NUT spaces. This is joint work with Sergey Cherkis and Andres Larrain. Organized by Prof. S.T. Ya" |
October 11, 2016, 4:15 pm at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Yasuyuki Kawahigashi (UNIVERSITY OF TOKYO) |
Gapped Domain Walls Between Topological Phases and Subfactors |
We study anyon condensation and gapped domain walls from a viewpoint of subfactors. We present a mathematical realization of composition of gapped domain walls and show how a general gapped domain wall between topological phases is realized as a composition of the ones arising from anyon condensation. The mathematical structure is closely related to rational heterotic full conformal field theor" |
October 11, 2016, 2:45 PM at Jefferson 453 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Robert Friedman (COLUMBIA UNIVERSITY) |
Deformations of cusp singularities |
Cusp singularities are a class of normal surface singularities with a rich geometry and deformation theory. In particular their smoothing components are very closely connected to the moduli of certain rational surfaces. In 1981, Looijenga gave a necessary condition for a cusp singularity to be smoothable and conjectured that this condition was also sufficient, a conjecture recently proved by Gross-Hacking-Keel and P. Engel. This talk describes recent joint work with Engel. We define an invariant λ for every semi-stable K-trivial model of a one parameter smoothing of a cusp singularity and show that all possible values of the invariant arise. Using this result, we characterize those rational double point singularities which are adjacent to cusp singularities" |
October 11, 2016, 3:00 pm at Science Center 507 |
| SPECIAL SEMINAR |
Nike Sun (UC BERKELEY) |
Phase transitions in random constraint satisfaction problems |
I will discuss a class of random constraint satisfaction problems (CSPs), in particular the boolean k-satisfiability (k-SAT) problem. For many random CSP models, heuristic methods from statistical physics yield detailed predictions on phase transitions and other phenomena. This includes the presence of a so-called replica symmetry breaking phenomenon, the mathematical understanding of which remains lacking. I will survey some of these heuristics, and describe some progress in the development of mathematical theory for these models. This talk is based on joint works with Jian Ding, Allan Sly, and Yumeng Zhang" |
October 07, 2016, 3:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
K-Theory of Henselian Rings II |
" |
October 06, 2016, 3:00 - 5:00 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS HOMOLOGICAL MIRROR SYMMETRY SEMINAR |
Hansol Hong (CMSA) |
Homological mirror symmetry for elliptic curves |
We survey the proof of homological mirror symmetry by Polishchuk and Zaslow. Some of more recent methods to prove HMS for elliptic curves will be discussed also, which use homological algebra techniques and formal deformation theory of Lagrangians etc" |
October 06, 2016, 2:00 - 4:00 pm at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
William Yun Chen (INSTITUTE FOR ADVANCED STUDY) |
Moduli Interpretations for Noncongruence Modular Curves |
Let G be a finite 2-generated group, then we define the notion of a G-structure for elliptic curves, which generalize the classical congruence level structures over Z[1/|G|]. The resulting moduli stacks of elliptic curves with G-structures over C is a union of modular curves, often noncongruence if G is nonabelian. Using the congruence subgroup property of SL(2,Z), we deduce that every (non)congruence modular curve is a moduli space of elliptic curves with G-structure. If time permits we will discuss connections with the Inverse Galois Problem and the Unbounded Denominators Conjecture" |
October 05, 2016, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Alexander Logunov (TEL AVIV UNIVERSITY) |
Zeroes of harmonic functions and Laplace eigenfunctions |
Nadirashvili conjectured that for any non-constant harmonic function in R^3 its zero set has infinite area. This question was motivated by the Yau conjecture on zero sets of Laplace eigenfunctions. Both conjectures can be treated as an attempt to control the zero set of a solution of elliptic PDE in terms of growth of the solution. For holomorhpic functions such kind of control is possible only from one side: there is a plenty of holomorphic functions that have no zeros. While for a real-valued harmonic function on a plane the length of the zero set can be estimated (locally) from above and below by the frequency, which is a characteristic of growth of the harmonic function. We will discuss the notion of frequency, its properties and applications to zero sets in the higher dimensional case, where the understanding is far from being complete" |
October 05, 2016, 4:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| JOINT DEPARTMENT OF MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Edgar Dobriban (STANFORD UNIVERSITY) |
Computation, statistics and random matrix theory |
Random matrices are useful models for large datasets. The Marchenko-Pastur (1967) ensemble for general covariance matrices is an increasingly used modeling framework that captures the effects of correlations in the data, with numerous statistical applications. In this talk we discuss the fruitful interactions between computation, statistics and random matrix theory in this area. We explain a fundamental computational problem in RMT: computing the limit empirical spectral distribution (ESD) of general covariance matrices. Our recent Spectrode method solves this problem efficiently. As an application, we solve a challenging problem in theoretical statistics. We construct optimal statistical tests based on linear spectral statistics to detect principal components below the phase transition. We also describe the software we are building for working with large random matrices, which we hope will broaden reach of RMT" |
October 05, 2016, 3:00 pm at CMSA Building, 20 Garden St, G10 |
| MATHEMATICAL PHYSICS SEMINAR |
Dietmar Bisch (VANDERBILT UNIVERSITY) |
Single Generated Planar Algebras |
Jones and I discovered the Fuss-Catalan algebras as the fundamental symmetry of subfactors that have an intermediate subfactor. As a planar algebra, they are singly generated, and can be viewed as a colored version of the Temperley-Lieb algebras. Their canonical generator satisfies a Yang-Baxter-type equation. We discuss these ideas and will try to keep the talk as accessible to non-experts as possible" |
October 04, 2016, 2:45 pm at Jefferson 453 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Alexander Logunov (ST. PETERSBURG & TEL-AVIV) |
Zero set of a non-constant harmonic function in R^3 has infinite surface area |
Nadirashvili conjectured that for any non-constant harmonic function in R^3 its zero set has infinite surface area. This question was motivated by the Yau conjecture on zero sets of Laplace eigenfunctions. We will give a sketch of the proof of Nadirashvili s conjecture. -- Organized by Prof. Shing-Tung Ya" |
October 04, 2016, 4:15 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Masahito Yamazaki (IMPU) |
Conformal Blocks and Verma Modules |
(for physicists) I will discuss analytic structures of the conformal block as a function of the scaling dimension. This will lead us torecursion relations for conformal blocks, which are also efficient for numerics. (for mathematicians) I will discuss representation theory of parabolic Verma modules for basic Lie superalgebras. In particular I will introduce a new determinant formula for the contravariant form" |
October 03, 2016, 12:00 pm at CMSA Building, 20 Garden St, G10 |
| GAUGE THEORY, TOPOLOGY, AND SYMPLECTIC GEOMETRY SEMINAR |
Vladimir Chernov (DARTMOUTH UNIVERSITY) |
Minimizing intersection points of loops on a surface and the Andersen-Mattes-Reshetikhin Poisson bracket. (based on a joint work with Patricia Cahn) |
Given two free homotopy classes α1,α2 of loops on an oriented surface, it is natural to ask how to compute the minimum number of intersection points m(α1,α2) of loops in these two classes. We show that for α1â α2 the number of terms in the Andersen-Mattes-Reshetikhin Poisson bracket of α1 and α2 is equal to m(α1,α2). Chas found examples showing that a similar statement does not, in general, hold for the Goldman Lie bracket of α1 and α2. If time permits we will also discuss the following. Turaev conjectured that his cobracket of a loop is zero if and only if the loop is homotopic to a simple loop. Counterexamples to this conjecture were found by Chas. Cahn modified the Turae v operation so that the conjecture is true for the modified operation" |
September 30, 2016, 3:30 - 4:30 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS HOMOLOGICAL MIRROR SYMMETRY SEMINAR |
Netanel Blaier (BRANDEIS UNIVERSITY) |
Intro to HMS 2 |
In the second talk, we review (some) of the nitty-gritty details needed to construct a Fukaya categories. This include basic Floer theory, the analytic properties of J-holomorphic curves and cylinders, Gromov compactness and its relation to metric topology on the compactified moduli space, and Banach setup and perturbation schemes commonly used in geometric regularization. We then proceed to recall the notion of an operad, Fukaya s differentiable correspondences, and how to perform the previous constructions coherently in order to obtain $A_\infty$-structures. We will try to demonstrate all concepts in the Morse theory toy model . Time providing, we also discuss orientations." |
September 29, 2016, 2:00 - 4:00 pm at CMSA Building, 20 Garden St, G10 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
K-Theory of Henselian Rings |
" |
September 29, 2016, 3:00 - 5:00 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Hong Liu (MIT) |
A new theory of fluctuating hydrodynamics |
Despite its long and glorious history, hydrodynamics has so far been formulated mostly at the level of equations of motion, which is inadequate for capturing fluctuations. In a fluid, however, fluctuations occur spontaneously and continuously, at both the quantum and statistical levels, the understanding of which is important for a wide variety of physical problems. Another unsatisfactory aspect of the current formulation of hydrodynamics is that the equations of motion are constrained by various phenomenological conditions on the solutions, which need to be imposed by hand. One of such constraints is the local second law of thermodynamics, which plays a crucial role, yet whose physical origin has been obscure. We present a new theory of fluctuating hydrodynamics which incorporates fluctuations systematically and reproduces all the phenomenological constraints from an underlying Z_2 symmetry. In particular, the local second law of thermodynamics is derived. The theory also predicts new constraints which can be considered as nonlinear generalizations of Onsager relations. When truncated to Gaussian noises, the theory recovers various nonlinear stochastic equations. Curiously, to describe thermal fluctuations of a classical fluid consistently one needs to introduce anti-commuting variables and the theory exhibits an emergent supersymmetry." |
September 28, 2016, 4:30 PM at Science Center 507 |
| INFORMAL GEOMETRY AND DYNAMICS SEMINAR |
Curtis McMullen (HARVARD UNIVERSITY) |
Introduction to Teichmueller curves in genus 2 |
" |
September 28, 2016, 4:00 pm at Science Center 530 |
| NUMBER THEORY SEMINAR |
Min Ru (UNIVERSITY OF HOUSTON) |
Height inequalities in Diophantine approximation |
In this talk, I ll discuss the recent established height inequality, in terms of an (ample) line bundle, for a sum of subschemes located in l-subgeneral position in an algebraic variety. It extends, as well as gives an alternative short and simpler proof of, the recent result of McKinnon and Roth. The inequality obtained connects the result of McKinnon and Roth (the case when the subschemes are points) and the results of Corvarja-Zannier, Evertse-Ferretti, Ru, and Ru-Vojta (the case when the subschmes are divisors). Part of the work was done with P. Vojta and with Julie Wang" |
September 28, 2016, 3:00 PM at Science Center 507 |
| JOINT HARVARD MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Antonio Auffinger (NORTHWESTERN UNIVERSITY) |
Parisi formula for the ground state energy of the Sherrington-Kirkpatrick model |
Spin glasses are disordered spin systems originated from the desire of understanding strange magnetic behaviors of certain alloys in physics. As mathematical objects, they are often cited as examples of complex systems and have provided several fascinating structures and conjectures. In this talk, we will focus on the Sherrington-Kirkpatrick spin glass model. We will present the Parisi formula and some properties for the maximum energy. In addition, we will discuss some representations of the Parisi Formula in terms of stochastic optimal control problems. This talk is based on recent joint works with Wei-Kuo Chen" |
September 28, 2016, 3:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Junliang Shen (ETH ZURICH) |
Elliptic Calabi-Yau 3-folds, Jacobi forms, and derived categories |
By physical considerations, Huang, Katz and Klemm conjectured in 2015 that topological string partition functions for elliptic Calabi-Yau 3-folds are governed by certain Jacobi forms. This gives strong structure results for curve counting invariants of elliptic CY 3-folds. I will explain a mathematical approach to proving (part of) the HKK Conjecture. Our method is to construct an involution on the derived category and use wall-crossing techniques. If time permits, I will also discuss the connection to the Oberdieck-Pandharipande Conjecture concerning K3 surfaces. The talk is based on joint work with Georg Oberdieck" |
September 27, 2016, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Tian-Jun Li (UNIVERSITY OF MINNESOTA) |
Symplectic divisor compactifications in dimension 4 |
We investigate the notion of symplectic divisorial compactification for symplectic 4-manifolds with either convex or concave type boundary. This is motivated by the notion of compactifying divisors for open algebraic surfaces. We give a sufficient and necessary criterion, which is simple and also works in higher dimensions, to determine whether an arbitrarily small concave/convex neighborhood exist for an Ï-orthogonal symplectic divisor (a symplectic plumbing). If deformation of symplectic form is allowed, we show that a symplectic divisor has either a concave or convex neighborhood whenever the symplectic form is exact on the boundary of its plumbing. We also observe that, up to Stein cobordisms, every contact 3-manifold admits a divisor cap. Joint work with Cheuk Yu Mak. âOrganized by S.T. Yau " |
September 27, 2016, 4:15 pm at Science Center 507 |
| HARVARD MATHEMATICAL PHYSICS SEMINAR |
Zhengwei Liu (HARVARD UNIVERSITY) |
A New Diagrammatic Approach to Quantum Information--the four string model |
We introduce a new diagrammatic approach to quantum information, that we call holographic software. Our new approach is a small modification of previous diagrammatic approaches, yet our small change leads to a great deal of new understanding and to a large number of new insights and motivation. Its application leads us to new protocols, designed in a topological way" |
September 27, 2016, 2:45 pm at Jefferson 453 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Can Kozcaz (CMSA) |
Cheshire Cat Resurgence |
We explore a one parameter ζ-deformation of the quantum-mechanical Sine-Gordon and Double-Well potentials which we call the Double Sine-Gordon (DSG) and the Tilted Double Well (TDW), respectively. In these systems, for positive integer values of ζ, the lowest ζ states turn out to be exactly solvable for DSG â a feature known as Quasi-Exact-Solvability (QES) â and solvable to all orders in perturbation theory for TDW. For DSG such states do not show any instanton-like depen- dence on the coupling constant, although the action has real saddles. On the other hand, although it has no real saddles, the TDW admits all-orders perturbative states that are not normalizable, and hence, requires a non-perturbative energy shift. Both of these puzzles are solved by including complex saddles." |
September 26, 2016, 12:00 PM at CMSA Building, 20 Garden St, G10 |
| GAUGE THEORY, TOPOLOGY, AND SYMPLECTIC GEOMETRY SEMINAR |
Paul Feehan (RUTGERS UNIVERSITY) |
The Lojasiewicz-Simon gradient inequality and applications to energy discreteness and gradient flows in gauge theory |
The Lojasiewicz-Simon gradient inequality is a generalization, due to Leon Simon (1983), to analytic or Morse-Bott functionals on Banach manifolds of the finite-dimensional gradient inequality, due to Stanislaw Lojasiewicz (1963), for analytic functions on Euclidean space. We shall discuss several recent generalizations of the Lojasiewicz-Simon gradient inequality and a selection of their applications, such as global existence and convergence of Yang-Mills gradient flow over four-dimensional manifolds and discreteness of the energy spectrum for harmonic maps from Riemann surfaces into analytic Riemannian manifolds" |
September 23, 2016, 3:30 - 4:30 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS HOMOLOGICAL MIRROR SYMMETRY SEMINAR |
Netanel Blaier (BRANDEIS UNIVERSITY) |
Intro to HMS |
This is the first talk of the seminar series. We survey the statement of Homological Mirror Symmetry (introduced by Kontsevich in 1994) and some known results, as well as briefly discussing its importance, and the connection to other formulations of Mirror Symmetry and the SYZ conjecture. Following that, we will begin to review the definition of the A-side (namely, the Fukaya category) in some depth. No background is assumed! Also, in the last half hour, we will divide papers and topics among participants" |
September 22, 2016, 2:00 - 4:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| THURSDAY SEMINAR |
Akhil Mathew (HARVARD UNIVERSITY) |
Thomason's \'etale descent theorem in algebraic K-theory |
I will explain some of the ingredients in the statement and proof of Thomason s theorem that algebraic K-theory, after inversion of the Bott element, satisfies \ etale descent and admits a local-to-global spectral sequence" |
September 22, 2016, 3:00 - 5:00 PM at Science Center 507 |
| JOINT HARVARD MATHEMATICS AND CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Stephane Benoist (MIT) |
Near critical spanning forests |
We study random spanning forests in the plane, which are slight perturbations of a uniformly chosen spanning tree (UST) and come with a natural fragmentation dynamics. We show how to relate the scaling limit of these forests to the stationary distribution of a natural Markov process on a state space of abstract graphs with edge-weights. This abstract graph setup could be fruitful for using renormalization ideas. In this point of view, our dynamics on forest corresponds to a repulsive direction around the UST fixed point. This is a joint work with Laure Dumaz (CNRS, Paris-Dauphine) and Wendelin Werner (ETH ZĂŒrich)" |
September 21, 2016, 3:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| NUMBER THEORY SEMINAR |
Alexandra Shlapentokh (EAST CAROLINA UNIVERSITY) |
On first-order definability and decidability problems over number fields and their infinite algebraic extensions |
We will discuss some recent developments connected to several problems of definability and decidability over number fields and infinite algebraic extensions of Q. In particular, we will address the results concerning the big subrings of number fields and so-called p-bounded extensions of Q" |
September 21, 2016, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
L. Mahadevan (SEAS, DEPT OF PHYSICS AND DEPT OF ORGANISMAL AND EVOLUTIONARY BIOLOGY, HARVARD UNIVERSITY) |
Morphogenesis: Biology, Physics and Mathematics |
A century since the publication of Darcy Thompson s classic âOn growth and form, his vision has finally begun to permeate into the fabric of modern biology. Within this backdrop, I will discuss some simple questions inspired by the onset of form in biology wherein mathematical models and computations, in close connection with experiments allow us to begin unraveling the physical basis for morphogenesis in the context of examples such as tendrils, leaves, guts and brains. I will also try and indicate how these problems enrich their roots, creating new questions in mathematics, physics and biology" |
September 21, 2016, 4:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Gao Chen (STONY BROOK) |
Classification of gravitational instantons |
A gravitational instanton is a complete non-compact Calabi-Yau surface, i.e. hyperk\ahler 4-manifold with an appropriate curvature decay condition on the end. In this talk, I will discuss the classification of gravitational instantons with faster than quadratic curvature decay condition. It s a joint work with Xiuxiong Chen" |
September 20, 2016, 4:15 PM at Science Center 507 |
| SPECIAL SEMINAR |
Maryna Viazovska (HUMBOLDT UNIVERSITY OF BERLIN) |
The sphere packing problem in dimensions 8 and 24 |
The sphere packing problem is to find an arrangement of non-overlapping unit spheres in the $d$-dimensional Euclidean space in which the spheres fill as large a proportion of the space as possible. In this talk we will present a solution of the sphere packing problem in dimensions 8 and 24. In 2003 N. Elkies and H. Cohn proved that the existence of a real function satisfying certain constrains leads to an upper bound for the sphere packing constant. Using this method they obtained almost sharp estimates in dimensions 8 and 24. We will show that functions providing exact bounds can be constructed explicitly as certain integral transforms of modular forms. Therefore, the sphere packing problem in dimensions 8 and 24 is solved by a linear programming method" |
September 19, 2016, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Johannes Kleiner (UNIVERSITY OF REGENSBURG) |
A New Candidate for a Unified Physical Theory |
The CFS theory is a new approach to describe fundamental physics. Giving quantum mechanics, general relativity and quantum field theory as limiting cases, it is a candidate for a unified physical theory. The goal of my talk is to explain the basic concepts and the general physical picture behind the approach. In particular, I will focus on the connection to contemporary physics" |
September 19, 2016, 12:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| GAUGE THEORY, TOPOLOGY, AND SYMPLECTIC GEOMETRY SEMINAR |
Eli Grigsby (BOSTON COLLEGE) |
Annular Khovanov-Lee homology, Braids, and Cobordisms |
Khovanov homology associates to a knot K in the three-sphere a bigraded vector space arising as the homology groups of an abstract chain complex. Using a deformation of Khovanov s complex, due to Lee, Rasmussen defined an integer-valued knot invariant he called s(K) that gives a lower bound on the 4-ball genus of knots, sharp for knots that can be realized as quasipositive braid closures. On the other hand, when K is a braid closure, its Khovanov complex can itself be realized in a natural way as a deformation of a triply-graded complex, defined by Asaeda-Przytycki-Sikora, further studied by L. Roberts, and now known as the (sutured) annular Khovanov complex. In this talk, I will describe joint work with Tony Licata and Stephan Wehrli aimed at understanding an annular version of Lee s deformation of the Khovanov complex. In particular, we obtain a family of real-valued braid conjugacy class invariants generalizing Rasmussen s s invariant that give bounds on the Euler characteristic of smoothly-imbedded surfaces in the thickened solid torus as well as information about the associated mapping class of the punctured disk. The algebraic model for this construction is the recently-defined Upsilon invariant of Ozsvath-Stipsicz-Szabo" |
September 16, 2016, 3:30 - 4:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
The Lichtenbaum-Quillen conjectures |
This talk will focus on the statement of the Lichtenbaum-Quillen conjectures and Suslin s rigidity theorem" |
September 15, 2016, 3:00 - 5:00 PM at Science Center 507 |
| HARVARD, BRANDEIS, MIT, NORTHEASTERN JOINT COLLOQUIUM AT HARVARD |
Ziv Ran (UC RIVERSIDE) |
Generic Projections |
A geometric object X is fully described or embedded via a vector space V of functions. How much information is lost in replacing V by a randomly chosen subspace of given dimension ? We try to shed ( project ) some light on a special case of this problem occurring in complex Algebraic Geometry" |
September 15, 2016, Tea at 4:00 PM, the Austine & Chilton McDonnell Common Room, Science Center 4th Floor, Talk at 4:30 pm at Science Center Hall A |
| NUMBER THEORY SEMINAR |
Jennifer Balakrishnan (BOSTON UNIVERSITY) |
Iterated p-adic integrals and rational points on curves |
I will discuss some new relationships between iterated p-adic line integrals (Coleman integrals), motivated by the problem of explicitly finding rational points on curves. In particular, I will describe the link between p-adic heights and double integrals and give a few classes of hyperelliptic curves where ``quadratic Chabauty gives us a finite set of p-adic points containing all rational points. I will also briefly discuss new identities between triple Coleman integrals. This is joint work with Netan Dogra" |
September 14, 2016, 3:00 - 4:00 PM at Science Center 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
Curtis McMullen (HARVARD UNIVERSITY) |
Almost simple geodesics on the triply-punctured sphere |
" |
September 14, 2016, 4:00 PM at Science Center 530 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Sze-Man Ngai (GEORGIA SOUTHERN UNIVERSITY) |
The multifractal formalism and spectral asymptotics of self-similar measures with overlaps |
Self-similar measures form a fundamental class of fractal measures, and is much less understood if they have overlaps. The multifractal formalism, if valid, allows us to compute the Hausdorff dimension of the multifractal components of the measure through its Lq-spectrum. The asymptotic behavior of the eigenvalue counting function for the associated Laplacians is closely related to the multifractal structure of the measure. Throughout this talk, the infinite Bernoulli convolution associated with the golden ratio will be used as a basic example to describe some of the results" |
September 14, 2016, 4:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Aruna Kesavan (PENN STATE/CMSA) |
Asymptotic structure of space-time with a positive cosmological constant |
Cosmological observations suggest that our universe is best described on large scales by Einstein s equations with a positive cosmological constant. In this talk, we discuss the implications of this fact for the asymptotic structure of space-time, symmetries and conservation laws. This is joint work with Abhay Ashtekar and Beatrice Bonga" |
September 13, 2016, 4:15 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Brooke Ullery (HARVARD UNIVERSITY) |
Measures of irrationality for hypersurfaces of large degree |
The gonality of a smooth projective curve is the smallest degree of a map from the curve to the projective line. There are a few different definitions that attempt to generalize the notion of gonality to higher dimensional varieties. The intuition is that the higher these numbers, the further the variety is from being rational. I will discuss some of these definitions, and present joint work with Lawrence Ein and Rob Lazarsfeld. Our main result is that if X is an n-dimensional hypersurface of degree d at least (5/2)n, then any dominant rational map from X to Pn must have degree at least d-1" |
September 13, 2016, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Chong Wang (HARVARD UNIVERSITY) |
A duality web in 2+1 dimensions |
I will discuss a web of field theory dualities in 2+1 dimensions that generalize the known particle/vortex duality. Some of these dualities relate theories of fermions to theories of bosons. Others relate different theories of fermions. Assuming some of these dualities, other dualities can be derived. I will present several consistency checks of the dualities and relate them to S-dualities in 3+1 dimensions." |
September 12, 2016, 12:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| GAUGE THEORY, TOPOLOGY, AND SYMPLECTIC GEOMETRY SEMINAR |
Daniel Cristofaro-Gardiner (HARVARD UNIVERSITY) |
Symplectic embeddings and the Fibonacci numbers |
It can be subtle to determine whether or not one symplectic manifold can be embedded into another, even for simple domains in C^n. For example, McDuff and Schlenk computed when a four-dimensional ellipsoid can be symplectically embedded into a ball, and found that if the ellipsoid is close to round, the answer is given by an ``infinite staircase determined by the odd-index Fibonacci numbers and the Golden Mean. McDuff was later able to find a purely combinatorial criteria for determining when one four-dimensional ellipsoid can be symplectically embedded into another, but ellipsoid embeddings in higher dimensions are still poorly understood. I will explain ongoing work with Hind and McDuff concerning our attempts to better understand the higher-dimensional situation. The focus of the talk will be recent work showing that a version of the McDuff-Schlenk result holds in all dimensions" |
September 09, 2016, 3:30 - 4:30 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Bong Lian (BRANDEIS UNIVERSITY) |
Riemann-Hilbert Problem and Period Integrals |
Period integrals of an algebraic manifolds are certain special functions that describe, among other things, deformations of the variety. They were originally studied by Euler, Gauss and Riemann, who were interested in analytic continuation of these objects. In this lecture, we will discuss a number of long-standing problems on period integrals in connection with mirror symmetry and Calabi-Yau geometry. We will see how the theory of D-modules have led us to solutions and insights into some of these problems" |
September 09, 2016, 3:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Comparing Algebraic and Topological K-Theory |
This semester the Thursday Seminar will be devoted to motivic homotopy theory, with an emphasis on Voevodsky s proof of the Bloch Kato conjecture. This first talk will be an overview of some of the ideas we plan to cover" |
September 08, 2016, 3:00 - 5:00 PM at Science Center 507 |
| CMSA CHINESE ECONOMY SEMINAR |
Lintong Li & Jian Wang (BEJING UNIV. & UNIV. OF LEUVEN) |
|
" |
July 26, 2016, 1:30 - 3:00 pm at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS CHINESE ECONOMY SEMINAR |
Wei Huang (HARVARD UNIVERSITY ECONOMICS) |
What do Social Pensions do for China's Rural Poor Elderly Citizens? |
This paper examines the impact of social pensions. We first show that the introduction of social pensions leads to a 1.7-2.2 percent decrease in mortality among the age-eligible elderly using the aggregate-level data from 10 countries. Utilizing the county-by-county rollout of the New Rural Pension Scheme in rural China, we find that, for the pension-eligible people, the scheme provision leads to a 17.6 and 9.6 percent increase in household income and food expenditure, a 6.2 percent decrease in labor supply, and an 11.4, 11.3 and 14.1 percent reduction in disability, underweight and mortality, respectively. In addition, we also find the social pensions increase the proportion of pre-school boys cared by their grandparents, and the rates of having pocket money, self-reported health, and being in school. (JEL classifications: E21, H55, I38, O22" |
July 19, 2016, 1:30 - 3:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Paul Bourgade (NYU) |
Extremes of random matrices and log-correlated fields |
Abstract: I will review recent progress on the connection between branching processes and random matrices, together with Arguin and Belius. For example, we will calculate the maximum eigenvalues displacement for random unitary matrices." |
June 08, 2016, 3:00 pm at CMSA Building, 20 Garden St, G02 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Jun Yin (UNIVERSITY OF WISCONSIN) |
Generalized Circular Law |
It is well known that for an i.i.d random matrix, the eigenvalue density satisfies the so called circular law, up to the optimal scale. In this talk, we will introduce our new work on the local law of the product of deterministic matrix $T$ and an i.i.d. random matrix" |
June 01, 2016, 3:00 PM at CMSA Building, 20 Garden Street, Room G02 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GENERAL RELATIVITY SEMINAR |
Scott Hughes (MIT) |
The gravitational-wave event GW150914: What we learned, and how we learned it |
After about two decade of construction and initial operation, the recently upgraded LIGO detectors announced the direct observation of gravitational waves on February 11th 2016. Â This event appears to be associated with the merger of two black holes at a distance of about 400 megaparsecs from our solar system. Â In this talk, I will describe this discovery, focusing on the methods used to determine the source characteristics and why we are confident that the waves LIGO measured originate in the merger of two black holes" |
May 25, 2016, 12:00 - 1:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GENERAL RELATIVITY SEMINAR |
Achilleas Porfyriadis (HARVARD UNIVERSITY PHYSICS) |
Gravitational waves from the Kerr/CFT correspondence |
Properties of diffeomorphisms imply that gravitational dynamics of the near-horizon region of near-extreme Kerr are governed by an infinite-dimensional conformal symmetry. This symmetry may be exploited to analytically, rather than numerically, compute a variety of potentially observable processes. In this talk I will show how we compute the gravitational radiation due to a geodesic particle that orbits in the near-horizon region and plunges into the horizon of such a near-extreme black hole." |
May 18, 2016, 12:00 - 1:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL MATHEMATICAL PHYSICS SEMINAR |
Tomoyuki Arakawa (RIMS, KYOTO UNIVERSITY) |
Vertex algebras and symplectic varieties |
There is a natural functor form the category of vertex algebras to the category of affine Poisson varieties that sends a vertex algebra V to its associated variety X_V. Although X_V is merely a Poisson variety in general, the recent study of four dimensions N=2 superconformal field theories predicts the existence of a large number of interesting vertex algebras whose associated varieties are symplectic (in fact, hyperKahler). In this talk I will discuss these vertex algebras in relations with Feigin-Frenkel conjecture on Kac-Wakimoto admissible representations, the Deligne exceptional series, and W-algebras" |
May 13, 2016, 4:00 - 5:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Laure Saint-Raymond (ĂCOLE NORMALE SUPĂ©RIEURE ) |
Fluctuating dynamics for a 2D rarified gas of hard disks  (joint work with T. Bodineau and I. Gallagher) |
Consider the fluctuating dynamics of a large system of hard disks close to equilibrium in the low density limit. By symmetry arguments combined with a suitable pruning procedure of collision trees, one can control the collision process and prove the propagation of chaos on a time scale much larger than the mean free time. Then one can establish a long time convergence result to the linearized Boltzmann equation, and eventually derive the acoustic and incompressible Stokes-Fourier equations" |
May 11, 2016, 2:30 -3:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GENERAL RELATIVITY SEMINAR |
Piotr T. Chrusciel (UNIVERSITY OF VIENNA) |
Gluing things in general relativity |
I will review the existing constructions of vacuum general relativistic initial data sets, with emphasis on gluing methods" |
May 11, 2016, 12:00 - 1:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Juerg Froehlich (ETH AND IAS) |
Implications of the Chiral Anomaly - From the Quantum Hall Effect to Topological Insulators and Out to Space |
Starting with an analysis of chiral edge currents in 2D electron gases exhibiting the quantum Hall effect, I will discuss the role of anomalous chiral edge currents and of anomaly inflow in 2D insulators with explicitly broken parity and time-reversal and in time-reversal invariant 2D topological insulators exhibiting edge spin-currents. I will derive the topological Chern-Simons theories that yield the correct response equations for the 2D bulk of such materials. After an excursion into the theory of 3D topological insulators, including âaxionic insulatorsâ, I discuss a model of Dark Matter and Dark Energy involving an axion coupled to the instanton density of a gauge field" |
May 11, 2016, 4:00 - 5:00 PM *please note change in time* at CMSA Building, 20 Garden Street, Room G10 |
| NUMBER THEORY SEMINAR |
Shai Haran (TECHNION, ISRAEL) |
New Foundations for Arithmetical Geometry, Pt 1 (Follow up talk at MIT on 5/5/16) |
We shall give a simple generalization of commutative rings. The category GR of such generalized rings contains ordinary commutative rings (fully, faithfully), but also the integers and the residue field at a real or complex place of a number field ; the field with one element F1 (the initial object of GR) ; the Arithmetical Surface (the categorical sum of the integers Z with them self). We shall show this geometry sees the real and complex places of a number field K : the valuation sub GR of K correspond to the finite and infinite primes of K, and there is a compactification of the spectrum of the integers of K. One can develope algebraic geometry using generalized rings following Grothendieck s paradigm, with Quillen s homotopical algebra replacing homological algebra. There is a theory of differentials which satisfy all the usual properties, as well as an analogue of Quillen s cotangent complex. We compute the differentials of the integers Z over F1. We associate with any compact topologi" |
May 04, 2016, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Hirosi Ooguri (CALIFORNIA INSTITUTE OF TECHNOLOGY) |
String Theory And Its Applications in Mathematics and Physics |
In the past few decades, we have discovered several new connections between mathematics and physics via study of string theory. In this talk, I will review some of these connections, focusing on topological string theory, the mirror symmetry, the large N duality, and the Mathieu moonshine. I will also discuss a new perspective that is emerging at the interface between information theory and geometry. The talk is aimed at a general audience in mathematics and physics" |
May 04, 2016, 4:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GENERAL RELATIVITY SEMINAR |
Robert Penna (MIT) |
BMS Invariance and the membrane paradigm |
The Bondi-van der Burg-Metzner-Sachs (BMS) group is the asymptotic symmetry group of asymptotically flat spacetime. It is infinite dimensional and entails an infinite number of conservation laws. According to the black hole membrane paradigm, null infinity (in asymptotically flat spacetime) and black hole event horizons behave like fluid membranes. Membrane fluid dynamics is governed by an infinite set of symmetries and conservation laws. Our main result is to point out that the infinite set of symmetries and conserved charges of the BMS group and the membrane paradigm are the same. This relationship sheds light on the physical interpretation of BMS conservation laws, generalizes the BMS conservation laws to arbitrary subregions of arbitrary null surfaces, and clarifies the identification of the superrotation subgroup of the BMS group" |
May 04, 2016, 12:00 - 1:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| SPECIAL PRESENTATION |
Manjul Bhargava (Princeon), Barry Mazur (Harvard), Matt Brown (Writer and Director), Stephen Wolfram (CEO, Wolfram Research), Robert Kanigel (Author) () |
The Man Who Knew Infinity: Bringing Mathematics to the Silver Screen |
3:30-4:00PM Manjul Bhargava (R. Brandon Fradd Professor of Mathematics, Princeton University) Title: Gems of Ramanujan and their lasting impact on Mathematics 4:00-4:45PM Panel discussion moderated by Barry Mazur (Gerhard Gade University Professor, Harvard University), with participants Matt Brown (Writer and Director), Manjul Bhargava (Associate Producer), Stephen Wolfram (CEO, Wolfram Research) and Robert Kanigel (author of the biography The Man Who Knew Infinity." |
April 30, 2016, 3:30 - 4:45 pm at Science Center Hall D |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Sijue Wu (UNIVERSITY OF MICHIGAN) |
Mathematical analysis of the water waves and some related problems |
In this talk, I will describe the main ideas in our recent work on water waves. If time permits, I will also discuss some of the main ideas of our results on self-gravitating fluid bodies" |
April 29, 2016, 10:30 AM at Science Center 530 |
| LOGIC COLLOQUIUM |
Andrew Marks (UCLA) |
Martin measure and strong ergodicity |
Assuming the axiom of determinacy, Martin has shown that any set of Turing degrees either contains a Turing cone, or is disjoint from a Turing cone. Thus, the collection of sets of Turing degrees which contain a cone forms a countably complete measure which is called Martin s measure. It is an open problem to characterize the additivity of Martin measure, in the general sense of for what (not necessarily well-orderable) sets X can the Turing degrees be partitioned into |X| many Martin measure 0 sets. We will describe an approach to this problem which is based on the ergodic-theoretic ideas of cocycle superrigidity and strong ergodicity. This leads to some new problems in recursion theory (related to the study of never continuously random reals) and descriptive set theory (in Borel combinatorics). This is joint work with Adam Day. " |
April 28, 2016, 2:00 - 4:00 PM at 2 Arrow Street, Room #420 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Mihalis Dafermos (PRINCETON UNIVERSITY) |
The linear stability of the Schwarzschild solution to gravitational perturbations |
I will discuss our recent proof of the full linear stability of the Schwarzschild solution in general relativity to gravitational perturbations. This is joint work with Gustav Holzegel (Imperial) and Igor Rodnianski (Princeton). Reference: http://arxiv.org/abs/1601.06467" |
April 28, 2016, 9:50 - 10:50 am at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Fraydoun Rezakhanlou (UC BERKELEY) |
Diffusions with Rough Drifts and Navier-Stokes Equation |
" |
April 28, 2016, 3:00 - 4:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS GENERAL RELATIVITY SEMINAR |
Andy Strominger and Milhalis Dafermos (HARVARD PHYSICS AND PRINCETON UNIVERSITY ) |
The Scattering Problem in General Relativity |
" |
April 27, 2016, 12:00 - 1:00 PM at CMSA Building, 20 Garden St, G10 |
| NUMBER THEORY SEMINAR |
Xinwen Zhu (CALIFORNIA INSTITUTE OF TECHNOLOGY) |
On some Tate cycles on Shimura varieties mod p |
I will first describe a large class of conjectural Tate classes in the middle dimensional etale cohomology of many Shimura varieties mod p (e.g. Hilbert and Picard modular surfaces at inert primes). According to the Tate conjecture, there should exist corresponding algebraic cycles. Then I will explain a uniform construction of these cycles by the geometric Satake (for p-adic groups). This is based on a joint work with Liang Xiao" |
April 27, 2016, 3:00 - 4:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS COLLOQUIUM |
Paul Seidel (MIT) |
Topological quantum field theory and the Gauss-Manin connection |
The Gauss-Manin connection on the cohomology of a fibration is a classical object in algebraic geometry. Getzler gave an interpretation and generalization in terms of noncommutative geometry. In this talk, we will explain how such a connection arises in any suitable two-dmensional topological field theory. This only depends on the formalism of such theories (i.e. on your ability to draw surfaces, in this case spheres with holes)" |
April 27, 2016, 4:30 PM at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Marek Biskup (UCLA) |
Local limit theory for extreme values of 2D Discrete Gaussian Free Field |
The 2D Discrete Gaussian Free Field (DGFF) is a centered Gaussian process on a finite subset of the square lattice with covariance given by the Green function of the simple random walk killed upon first exit from the set. The prime interest in this object stems from the existence of a conformally-invariant scaling limit and numerous consequences thereof -- e.g., the coupling to SLE_4, conformal loop ensemble, etc. In my talk I will focus on the behavior of the DGFF at and near points where it has a nearly-maximal local maximum. In particular, I will show that the extremal process of the DGFF scales to a cluster-process and also prove a local limit theorem for the maximum (both position and value) of the DGFF in scaled-up lattice versions of nice continuum domains. Based on joint work with Oren Louidor" |
April 27, 2016, 2:15 - 3:30 pm at CMSA Building, 20 Garden St, G02 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Xinwen Zhu (CALIFORNIA INSTITUTE OF TECHNOLOGY) |
Towards a p-adic non-abelian Hodge Theory |
I will first give a brief review the non-abelian Hodge theory for complex manifolds and describe a conjectural p-adic analogue. Then I will discuss what we know so far and the following consequence of (the known part of) the theory: Let L be a p-adic local system on a (geometrically) connected algebraic variety over a number field. If itâs stalk at one point, regarded as a p-adic Galois representation, is geometric in the sense of Fontaine-Mazur, then the stalk at every point is geometric. This is based on a joint work with Ruochuan Liu" |
April 26, 2016, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR |
Andre Neves (IMPERIAL COLLEGE LONDON) |
A path to Yau's conjecture |
I will talk about my ongoing work Fernando Marques and explain a program based on Almgren-Pitts Min-max theory to show that any closed manifold admits an infinite number of distinct minimal hypersurfaces (Yau s conjecture). I will also mention some new developments due to Liokumovich and ourselves" |
April 26, 2016, 9:50 - 10:50 am at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Georg Oberdieck (MIT) |
Counting curves in K3xP1 and quasi Jacobi forms |
I will report on some recent calculations (in special cases) of Gromov-Witten invariants of two classes of Calabi-Yau threefolds, namely Abelian threefolds and the product of a K3 surface with an elliptic curve. Our method is by degeneration to the product K3xP1 and exploiting various formal properties of the generating series. This leads to conjectures relating invariants of K3xP1 to quasi Jacobi forms" |
April 25, 2016, 12:00 - 2:00 PM at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Stefano Bianchini (SISSA) |
Quadratic interaction functional for system of conservation laws |
The theory of hyperbolic systems of conservation laws in 1-d depends on the existence of some interaction Lyapunov functionals, which control the growth of the BV norm of the solution. Depending on the structure of the system, these functionals have different forms: the original Glimm functional (which works for particular systems) is stronger that the Lyapunov functional used in the general case. We show that for some problems an interaction functional as strong as the Glimm one is needed, and we give its natural extension to the general case, as well as some application of this stronger estimate" |
April 21, 2016, 9:50 - 10:50 am at CMSA Building, 20 Garden Street, Room G10 |
| THURSDAY SEMINAR |
Jared Weinstein (BOSTON UNIVERSITY) |
The Fargues-Fontaine curve |
" |
April 21, 2016, 3:00 - 5:00 PM at Science Center 507 |
| HARVARD, BRANDEIS, MIT, NORTHEASTERN JOINT COLLOQUIUM AT HARVARD |
Alex Eskin (UNIVERSITY OF CHICAGO) |
Polygonal Billiards and Dynamics on Moduli Spaces |
Billiards in polygons can exhibit some bizarre behavior, some of which can be explained by deep connections to several seemingly unrelated branches of mathematics. These include algebraic geometry (and in particular Hodge theory), Teichmuller theory and ergodic theory on homogeneous spaces. I will attempt to explain some of these connections, and to survey some recent progress in the area." |
April 21, 2016, Tea at 4:00 PM, the Austine & Chilton McDonnell Common Room, Science Center 4th Floor, Talk at 4:30 pm at Science Center Hall E |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Mark Rudelson (UNIVERSITY OF MICHIGAN) |
Delocalization of eigenvectors of random matrices |
Heuristically, delocalization for a random matrix means that its normalized eigenvectors look like the vectors uniformly distributed over the unit sphere. This can be made precise in a number of different ways. We will consider two complimentary approaches to delocalization. For a matrix with independent entries, we show that with high probability, the largest coordinate of a normalized eigenvector is of the same order as for a uniform random unit vector. This means that the Euclidean norm of an eigenvector cannot be concentrated on a few coordinates. On the other hand, we show that with high probability, any sufficiently large set of coordinates of an eigenvector carries a non-negligible portion of its Euclidean norm. The latter result pertains to a large class of random matrices including the ones with independent entries, symmetric, skew-symmetric matrices, as well as more general ensembles" |
April 20, 2016, 3:00 PM at CMSA Building, 20 Garden Street, Room G02 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GENERAL RELATIVITY SEMINAR |
Paul Chesler (HARVARD UNIVERSITY PHYSICS) |
Numerical relativity in asymptotically anti-de Sitter spacetime |
Via holographic duality, numerical relativity in asymptotically anti-de Sitter (AdS) spacetime can be employed to study dynamics in a variety of interesting strongly interacting quantum field theories. However, traditional numerical relativity methods are ill-suited for AdS spacetime due to the existence of its boundary. I will describe a remarkably efficient characteristic evolution scheme which is well-suited for a diverse set of gravitational problems in AdS spacetime, and will showcase results for both gravitational turbulence and the creation of microscopically small droplets of quark-gluon plasma" |
April 20, 2016, 12:00 - 1:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| NUMBER THEORY SEMINAR |
Nicolas Templier (CORNELL UNIVERSITY) |
Kloosterman families, Quantum cohomology and geometric Langlands |
We prove cases of Rietsch mirror conjecture that the Dubrovin quantum connection for projective homogeneous varieties is isomorphic to the pushforward D-module attached to Berenstein-Kazhdan geometric crystals. The idea is to recognize the quantum connection as Galois and the geometric crystal as automorphic. We reveal surprising relations with the works of Frenkel-Gross, Heinloth-Ngo-Yun and Zhu on Kloosterman sheaves. The isomorphism comes from global rigidity results where Hecke eigensheaves are determined by their local ramification. It implies combinatorial identities for the counts of rational curves and the Peterson variety presentation as corollary. Work with Thomas Lam" |
April 20, 2016, 3:00 PM at Science Center 507 |
| LOGIC COLLOQUIUM |
Scott Cramer (RUTGERS UNIVERSITY) |
Woodin's AD-conjecture for I0 |
We will discuss Woodin s AD-conjecture, which gives a deep relationship between very large cardinals and determined sets of reals. In particular we will show that the AD-conjecture holds for the axiom I0 and that there are many interesting consequences of this fact. We will also discuss variations of the AD-conjecture and their consequences, including generic absoluteness properties for I0." |
April 20, 2016, 2:00 - 4:00 PM at 2 Arrow Street, Room #420 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Sijue Wu (UNIVERSITY OF MICHIGAN) |
On two dimensional gravity water waves with angled crests |
In this talk, I will survey the recent understandings on the motion of water waves obtained via rigorous mathematical tools, this includes the evolution of smooth initial data and some typical singular behaviors. In particular, I will present our recently results on gravity water waves with angled crests" |
April 20, 2016, 4:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR |
Xu-jia Wang (AUSTRALIAN NATIONAL UNIVERSITY) |
Boundary behavior of solutions to singular elliptic equations |
We study regularity and singularity profile of solutions to a number of singular elliptic equations arising in geometric and physical applications. By careful construction of barrier functions we establish the optimal regularity for these equations. Beyond the optimal regularity we can furthermore express the solution as a combination of logarithm and power functions, which gives precise information on the singularity of the solution." |
April 19, 2016, 9:50 - 10:50 am at Science Center 232 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Jonathan Wise (UNIVERSITY OF COLORADO, BOULDER) |
Compactifying the Abel map with logarithmic geometry |
" |
April 19, 2016, 3:00 PM at MIT 2-131 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Dmitry Jakobson (MCGILL UNIVERSITY) |
Nodal Sets in Conformal Geometry |
We study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal geometry of Courant s Nodal Domain Theorem. We also show that on any manifold of dimension $n \geq 3$, there exist many metrics for which our invariants are nontrivial. We prove that the Yamabe operator can have an arbitrarily large number of negative eigenvalues on any manifold of dimension $n \geq 3$, and that 0 is generically not an eigenvalue of that operator. We obtain related results for some higher order GJMS operators on some Einstein and Heisenberg manifolds. This is joint work with Yaiza Canzani, Rod Gover, Raphael Ponge, Asma Hassannezhad and Michael Levitin. If time permits, we shall discuss related results for operators on graphs" |
April 19, 2016, 4:15 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Carlos Shahbazi (INSTITUTE FOR THEORETICAL PHYSICS, SACLAY, FRANCE) |
Geometric U-folds and the twisted Strominger system |
I will describe the geometry and topology of a general class of U-folds compatible with the global formulation of four-dimensional extended supergravity on a differentiable spin manifold. We have named these U-folds as âgeometric U-foldsâ. The topology of geometric U-folds depends on certain fiber bundles which twist the local string theory fields and which we fully characterize. Smooth non-trivial U-folds of this type can exist only in theories where both the scalar and the space-time manifolds have non-trivial fundamental group and the scalar map is homotopically non-trivial. Requiring consistency with global Supergravity implies that geometric U-folds must be globally glued by using discrete subgrups of the continuous U-duality group, in agreement with String Theory requirements. Finally, I will briefly discuss twisted version of the Strominger system inspired in non-geometry, and which contains solutions with remarkably interesting properties. In particular, they avoid the Maldacena-Nunez no-go theorem. This is work done in collaboration with Calin Lazaroiu and Mario Garcia-Fernandez" |
April 18, 2016, 12:00 - 2:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SOCIAL SCIENCE APPLICATIONS FORUM |
Annie Liang ( HARVARD UNIVERSITY ECONOMICS) |
The Theory is Predictive, but is it Complete? An Application to Human Perception of Randomness (with Jon Kleinberg and Sendhil Mullainathan) |
When we test a theory using data, it is common to focus on correctness: do the predictions of the theory match what we see in the data? But we also care about completeness: how much of the predictable variation in the data is captured by the theory? Â This question is difficult to answer, because in general we do not know how much âpredictable variationâ there is in the problem. In this paper, we propose the use of machine learning algorithms as a means of constructing a benchmark level for the best attainable level of prediction. We illustrate this approach on the task of prediction of human-generated random sequences. Relative to an atheoretical machine learning algorithm benchmark, we find that existing behavioral models explain roughly 10 to 15 % of the predictable variation in this problem. This fraction is robust across several datasets, suggesting that (1) there is a significant amount of structure in this problem that our models have yet to capture and (2) machine learning may provide a generally viable approach to testing completeness." |
April 18, 2016, 5:30 PM *note change in time at CMSA Building, 20 Garden Street, Room G10 |
| BASIC NOTIONS SEMINAR |
Camillo DeLellis (UNIVERSITY OF ZURICH AND CMSA) |
Singularity and regularity of area minimizing surfaces |
The Plateau s problem, named after the Belgian physicist J. Plateau, is a classic in the calculus of variations and regards minimizing the area among all surfaces spanning a given contour. The notion of surface has been generalized in several ways in the past century in order to give far-reaching existence theories for the Plateau s problem. The corresponding minimizers are not always regular and the problem of describing their singularities is still widely open" |
April 18, 2016, 3:00 - 3:55 pm at Science Center 507 |
| GAUGE THEORY, TOPOLOGY, AND SYMPLECTIC GEOMETRY SEMINAR |
Felix Schlenk (NEUCHATEL) |
Complexity of Reeb flows via Floer homology |
The topological entropy of a self-map of a compact metric space is a numerical invariant that gives a measure for the orbit complexity of the mapping. For instance, isometries and gradient flows have vanishing topological entropy, and expanding maps and geodesic flows of negative curvature metrics have positive topological entropy. Various Floer homologies (Lagrangian Floer homology, Rabinowitz-Floer homology, Legendrian contact homology) have been used to prove positivity of topological entropy for all Reeb flows on certain classes of contact manifolds. I ll explain these results and the idea of their proofs. This is joint work with Urs Frauenfelder, Leonardo Macarini, Clémence Labrousse, and new work by Marcelo Alves" |
April 15, 2016, 3:30 - 4:30 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Tai-peng Tsai (UNIVERSITY OF BRITISH COLUMBIA) |
Stability of periodic waves of the 1D nonlinear Schr\ |
We consider the stability of periodic waves of the 1D cubic Schr" |
April 14, 2016, 9:50 - 10:50 am at CMSA Building, 20 Garden Street, Room G10 |
| NUMBER THEORY SEMINAR |
Ali Altug (COLUMBIA UNIVERSITY) |
Functoriality, trace formula, and related problems |
The Arthur-Selberg trace formula is a vast generalization of the classical Poisson summation formula to the non-abelian setting of a reductive algebraic group. It is one of the most prominent tools in number theory and the modern theory of automorphic forms and has found spectacular, but so far limited, applications to the functoriality conjectures. In his recent article âProblems Beyond Endoscopyâ, Arthur posed several problems, mostly about the trace formula, motivated by considerations related to beyond endoscopy. In this talk I will first timeintroduce strategy of beyond endoscopy and the role of the trace formula therein. I will then talk about certain problems that arise when one tries to execute this strategy and discuss several results for the group GL(2). In the last part of the talk I will discuss a particular problem raised by Arthur, regarding the isolation of certain distributions that appear the discrete part of the trace formula in the geometric side, which is essential to beyond endoscopy as well as other applications of the trace formula" |
April 13, 2016, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GENERAL RELATIVITY SEMINAR |
Felix Finster (UNIVERSITY OF REGENSBURG) |
Linear stability of Kerr black holes |
After a brief historical review of the linear stability problem for Schwarzschild and non-extreme Kerr black holes, I will explain how to attack the problem in the Teukolsky framework" |
April 13, 2016, 12:00 - 1:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Jun Zhang (UNIVERSITY OF MICHIGAN, ANN ARBOR - DEPARTMENT OF PSYCHOLOGY & DEPARTMENT OF MATHEMATICS) |
Kahler and Para-Kahler Structure in Information Geometry |
*In Collaboration with Teng-Fei, MIT Mathematics* Information Geometry is the differential geometric study of the manifold of probability models, and promises to be a unifying geometric framework for statistical inference, information theory, machine learning, etc. Instead of using metric for measuring distances on such manifolds, these applications often use âdivergence functionsâ for measuring proximity of two points (that do not impose symmetry and triangular inequality), for instance Kullback-Leibler divergence, Bregman divergence, f-divergence, etc. Divergence functions induce what is called âstatistical structureâ on a manifold: a Riemannian metric g together with a pair of torsion-free affine connections D, D*, such that D and D* are both Codazzi coupled to g while being conjugate to each other. Divergence functions also induce a natural symplectic structure w on the product manifold. This talk will report our recent research investigating the interaction of D with g, w, and a tangent-bundle isomorphism L, two special cases being L= J (almost complex structure, J^2 = -id) and L=K (almost para-complex structure, K^2 = id). We show that Codazzi coupling of D with any two of the compatible triple (g, w, L) will lead to its coupling with the remainder, which further gives rise to a (para-)Kahler structure on the manifold. We call this Codazzi-(para-)Kahler structure, generalizing the special (para-)Kahler geometry known in mathematical physics, without requiring D to be flat. In fact, we prove a general result that g-conjugate, w-conjugate, and L-gauge transformations of D, along with the identity transform, form a 4-element Klein group. This leads a Codazzi-(para-)Kahler manifold to admit a pair of torsion-free connections compatible with the (g, w, L). Finally, we discuss implications of the rich geometric structures we reveal for statistical inference, information, and machine learning" |
April 13, 2016, 4:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR |
Connor Mooney (UNIVERSITY OF TEXAS AT AUSTIN) |
Finite time blowup for parabolic systems in the plane |
Abstract: We will discuss an example of finite time blowup from smooth data for a linear uniformly parabolic system in two dimensions." |
April 12, 2016, 9:50 - 10:50 am at CMSA Building, 20 Garden Street, Room G10 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Alex Isaev (MSI / AUSTRALIAN NATIONAL UNIVERSITY) |
Isolated hypersurface singularities and associated forms |
In our recent articles joint with M. Eastwood and J. Alper, it was conjectured that all rational GLn-invariant functions of homogeneous forms of degree d>2 on complex space Cn can be extracted, in a canonical way, from those of forms of degree n(d-2) by means of assigning to every form with nonvanishing discriminant the so-called associated form. While this surprising statement is interesting from the point of view of classical invariant theory, its original motivation was the reconstruction problem for isolated hypersurface singularities, which is the problem of finding a constructive proof of the well-known Mather-Yau theorem. Settling the conjecture is part of our program to solve the reconstruction problem for quasihomogeneous isolated hypersurface singularities. In my talk, I will give an overview of the recent progress on the conjecture. If time permits, I will further discuss the morphism that assigns to a nondegenerate form its associated form. This morphism is rather natural and deserves attention regardless of the conjecture. In particular, it leads to a natural contravariant" |
April 12, 2016, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Igor Wigman (KING'S COLLEGE LONDON) |
On the number of nodal domains of toral eigenfunctions |
We study the number of nodal domains of toral Laplace eigenfunctions. Following Nazarov-Sodin s results for random fields and Bourgain s de-randomisation procedure we establish a precise asymptotic result for generic eigenfunctions. Our main results in particular imply an optimal lower bound for the number of nodal domains of generic toral eigenfunctions. This work is joint with Jerry Buckley" |
April 12, 2016, 4:15 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Milton D. Jara (IMPA) |
Around the strong KPZ universality conjecture |
The strong KPZ universality conjecture states that there exists a universal process (the so-called KPZ fixed point) which is the scaling limit of fluctuations of currents in conservative, one-dimensional systems near a flat stationary state. We conjecture that at stationarity, the KPZ fixed point is an energy solution of a nonlocal version of the KPZ equation. We give support to this conjecture by showing how such nonlocal equations may arise as the scaling limit of interacting particle systems. Based on joint works with P. Gonçalves (Lisbon), M. Gubinelli (Bonn), C. Bernardin (Nice), S. Olla (Paris) and T. Komorowski (Warsaw)" |
April 11, 2016, 2:15 PM at Science Center 530 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Orlando Alvarez (UNIVERSITY OF MIAMI) |
Effective Actions, Lovelock Lagrangians and Lipschitz-Killing Curvatures |
We show that there is a universal perturbative expansion for the effective action of certain classes of field theories where the support of the action is localized near a submanifold. The first terms of a multipole-like expansion for the effective action are closely related to the Lovelock gravitational lagrangians constructed using the Lipschitz-Killing curvatures. Higher order multipole-like corrections are also explicitly written down but they involve more complicated curvature combinations" |
April 11, 2016, 3:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Luis Haug (MIT) |
Lagrangian antisurgery and cobordisms |
What Lagrangian submanifolds occur in a symplectic manifold is a central question in symplectic geometry. I will talk about an implementation of surgery for Lagrangian submanifolds, which can be used to produce new Lagrangians from given ones. I will also explain the construction of corresponding Lagrangian cobordisms in the sense of Biran-Cornea, whose existence sometimes has interesting Floer theoretical and Fukaya categorical implications" |
April 08, 2016, 3:30 - 4:30 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Stefano Bianchini (SISSA) |
Concentration of entropy dissipation for scalar conservation laws |
Let $u(t,x)$ be an entropy $L^\infty$-solution of the scalar conservation laws $$ u_t + f(u)_x = 0. $$ Under no assumptions on the flux function $f$ the solution is in general only $L^\infty$, and thus questions regarding the regularity of the dissipation measure were open. We will show that the entropy dissipation is actually concentrated on a $1$-rectifiable set: there is a countable set of Lipschitz curves $\gamma_i(t)$ such that for all entropies $\eta$, entropy flux $q$ it holds $$ \eta_t + q_x = \sum_i c_{\eta,i}(t) \mathcal H1 \llcorner_{\gamma_i}. $$ Corollaries of this results are regularity estimates for the original solution $u$: the existence of a Lagrangian representation, the structure of Young solutions, the BV regularity of $f (u)$, the strong continuity in time" |
April 07, 2016, 10:00 AM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS COLLOQUIUM |
Lars Hernquist (HARVARD UNIVERSITY ) |
Next-Generation Cosmological Simulations: Galaxy Assembly and Evolution |
A predictive theory of galaxy formation remains elusive, even after more than 50 years of dedicated effort by many renowned astrophysicists. The problem of galaxy formation is made difficult by the large range in scales involved and the many non-linear physical processes at play. This talk describes a new generation of numerical models that are designed to overcome these difficulties based on novel schemes for solving the fluid equations on a moving mesh. Initial results from this study provide insight into many aspects of galaxy assembly and the relationship between galaxies and cosmologically-distributed baryons" |
April 06, 2016, 4:30 PM at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS SEMINAR ON GENERAL RELATIVITY |
Milhalis Dafermos (PRINCETON UNIVERSITY) |
The black hole stability problem: the inside story |
" |
April 06, 2016, 12:00 - 1:00 PM at CMSA Building, 20 Garden St, G02 |
| NUMBER THEORY SEMINAR |
Ari Shnidman (BOSTON COLLEGE) |
Heights of generalized Heegner cycles |
I ll present a pair of Gross-Zagier type formulas, one p-adic and the other archimedean, for the central derivative of a Rankin-Selberg L-function attached to a cuspform and a Hecke character of smaller weight. I ll also give some applications towards conjectures connecting algebraic cycles and special values of L-functions, due to Bloch, Beilinson, Kato, and Perrin-Riou." |
April 06, 2016, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Timo Seppalainen (UNIVERSITY OF WISCONSIN, MADISON) |
Variational formulas and Busemann functions for random paths in a random medium |
The directed polymer model describes a random walk in a random potential. It was introduced by Huse and Henley in the statistical physics literature in 1985. This model is a member of the KPZ (Kardar-Parisi-Zhang) universality class and has been an object of much study in both the statistical physics and probability communities. This talk begins by deriving variational formulas for the limiting free energy of the polymer model and for the time constant of the related last-passage percolation model. Minimizers of the variational formulas come from microscopic gradients called Busemann functions. The existence of Busemann functions can be proved for exactly solvable models such as the log-gamma polymer. Busemann functions also serve as boundary conditions for a stationary polymer process, which in turn can be used to derive fluctuation exponents. This talk is partly based on joint works with Nicos Georgiou, Firas Rassoul-Agha and Atilla Yilmaz." |
April 06, 2016, 3:00 PM at CMSA Building, 20 Garden Street, Room G02 |
| DIFFERENTIAL GEOMETRY SEMINAR |
John Toth (MCGILL UNIVERSITY) |
Nodal Length of Steklov Eigenfunctions on Real-Analytic Riemannian Surfaces |
We prove sharp upper and lower bounds for the nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces with boundary. The argument involves frequency function methods for harmonic functions in the interior of the surface as well as the construction of exponentially accurate approximations for the Steklov eigenfunctions near the boundary (joint with David Sher and Iosif Polterovich)" |
April 05, 2016, 4:15 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR |
Niky Kamran (MCGILL UNIVERSITY) |
Non-uniqueness results for the anisotropic Calderon problem with data measured on disjoint sets |
We will present some simple counterexamples to uniqueness for the Calderon problem on Riemannian manifolds with boundary when the Dirichlet and Neumann data are measured on disjoint sets of the boundary. The counterexamples are in the case of two and three dimensional Riemannian manifolds with boundary having the topology of circular cylinders in dimension two and toric cylinders in dimension three. The construction could be easily extended to higher-dimensional Riemannian manifolds. This is joint work with Thierry Daude (Cergy-Pontoise) and Francois Nicoleau (Nantes)" |
April 05, 2016, 9:50 - 10:50 am at Science Center 232 *please note change of location this week* |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SOCIAL SCIENCE APPLICATIONS FORUM |
Lauren Cohen (HARVARD BUSINESS SCHOOL AND NBER) |
Playing Favorites: How Firms Prevent the Revelation of Bad News |
We explore a subtle but important mechanism through which firms manipulate their information environments. We show that firms control information flow to the market through their specific organization and choreographing of earnings conference calls. Firms that âcastâ their conference calls by disproportionately calling on bullish analysts tend to underperform in the future. Firms that call on more favorable analysts experience more negative future earnings surprises and more future earnings restatements. A long-short portfolio that exploits this differential firm behavior earns abnormal returns of up to 182 basis points per month, or over 21 percent per year. Further, firms that cast their calls have higher accruals leading up to the call, barely exceed/meet earnings forecasts on the call that they cast, and in the quarter directly following their casting tend to issue equity and have significantly more insider selling and stock option exercises." |
April 04, 2016, 5:00 - 6:00 PM at CMSA Building, 20 Garden Street, Room G02 |
| BASIC NOTIONS SEMINAR |
Barry Mazur (HARVARD UNIVERSITY) |
How many rational points are there? |
Algebraic varieties tend to have few rational points that aren t forced by some geo- metric structure. In my Basic Notions Seminar lecture I will give a survey of recent work, computations, heuristics, and open problems on this topic. I will also mention some work-in-progress joint with Karl Rubin" |
April 04, 2016, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Bei Jia (UNIVERSITY OF TEXAS AT AUSTIN) |
Topological String Theory Revisited |
In this talk we will revisit the formulation of topological string theory. We will start with $\mathcal{N}=2$ super Riemann surfaces and define topological twists in terms of geometry. The outcome will be called semirigid super Riemann surfaces, which for us will serve as worldsheets for defining topological strings. Both topological sigma models and topological gravity can be put on these worldsheets. We then define our version of topological string amplitudes as integrals over the supermoduli spaces associated with these semirigid super Riemann surfaces. We will discuss some consequences of this definition and try to relate to some known results in the literature" |
April 04, 2016, 12:00 - 2:00 PM at CMSA Building, 20 Garden Street, Room G02 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
David Xianfeng Gu (STONY BROOK UNIVERSITY) |
A Discrete Variational Approach for Solving Monge-Ampere Equation |
Both Optimal mass transportation problem and Alexandrov problem can be converted to solve Monge-Ampere equation. A discrete varational approach is presented, which convert the problem to optimizing a convex energy with geometric meaning. The method can be easily converted to computing power Voronoi diagram and Delaunay triangulation in conventional computational geometry. The method has been applied for area-preserving mesh parameterization in computer graphics, shape classification based on Wasserstein distance in geometric data analaysis and medical imaging." |
April 04, 2016, 1:00 - 2:00 PM at Science Center Hall A |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Ana Rita Pires (FORDHAM UNIVERSITY) |
Symplectic embeddings and infinite staircases |
McDuff and Schlenk determined when a four-dimensional symplectic ellipsoid can be symplectically embedded into a four-dimensional ball, and found that if the ellipsoid is close to round, the answer is given by an ``infinite staircase determined by the odd index Fibonacci numbers, while if the ellipsoid is sufficiently stretched, all obstructions vanish except for the volume obstruction. Infinite staircases have also been found when embedding ellipsoids into polydisks (Frenkel--Muller) and into the ellipsoid E(2,3) (Cristofaro-Gardiner--Kleinman). In this talk, we will see how the sharpness of ECH capacities for embedding of ellipsoids implies the existence of infinite staircases for these and three other domains. This is joint work with Dan Cristofaro-Gardiner, Tara Holm, and Alessia Mandini" |
April 01, 2016, 3:30 - 4:30 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Felix Finster (UNIVERSITY OF REGENSBURG) |
Lorentzian spectral geometry and the fermionic signature operator |
In certain globally hyperbolic space-times, one can introduce the fermionic signature operator as a self-adjoint operator on the Hilbert space of solutions of the Dirac equation. Its spectrum encodes geometric information on the space-time. After a brief introduction to globally hyperbolic space-times and spinors, I will introduce the basic concepts, outline a few general results and give the connection to quantum field theory. In the second part of the talk, I will focus on the analysis of the spectrum of the fermionic signature operator for Lorentzian surfaces. This is joint work with Moritz Reintjes and Olaf MĂŒller" |
March 31, 2016, 9:50 - 10:50 am at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
David Garfinkle (OAKLAND UNIVERSITY) |
Gravitational Wave Memory |
Gravitational waves are detected by the stretching and squeezing that they induce in gigantic laser interferometers. Even after the wave has passed, there is a residual stretch and squeeze, which is known as gravitational wave memory. This talk will cover various aspects of this phenomenon" |
March 30, 2016, 4:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Nikolai Makarov (CALIFORNIA INSTITUTE OF TECHNOLOGY) |
Random normal matrices with hard edge spectrum |
We will discuss the problems of existence and universality of the scaling limits for the eigenvalues of a random normal matrix, in particular near the hard edge of the spectrum. Our approaches uses rescaled Ward s equation and analyticity properties of the correlation kernels. This is a joint work with Y. Ameur and N.-G. Kan" |
March 30, 2016, 2:15 PM at CMSA Building, 20 Garden Street, Room G02 |
| NUMBER THEORY SEMINAR |
John Bergdall (BOSTON UNIVERSITY) |
Slopes of modular forms and the ghost conjecture |
In this talk we will discuss the so-called p-adic slopes of modular forms. We will present an explicit two variable power series that we conjecture, in the so-called regular case , is a slight deformation of the Fredholm series for the U_p operator acting on the p-adic Banach spaces of p-adic modular forms. Then we will discuss the consequences of our conjecture, possibly including an attempt to understand an old conjecture of GouvĂȘa and Mazur. This is joint work with Robert Pollack" |
March 30, 2016, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Yi Zhang (HARVARD UNIVERSITY) |
Hyperbolic problems for families of algebraic manifolds |
In this talk, we report some progress on the hyperbolic problem for any smooth quasi-projective manifold $S$ which effectively parameterizes polarized projective manifolds. This is a joint work with K.F Liu and S.T. Yau. We set up a weak type of relative Bertini s theorem for the family and construct a locally injective period map on an open dense subset $U$ of $S$ by the technique of cyclic covering. We then discuss the Viehweg s positivity problems on $S." |
March 29, 2016, 4:15 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Ben Davison (ĂCOLE POLYTECHNIQUE FĂ©DĂ©RALE DE LAUSANNE) |
Beyond the Kontsevich Soibelman integrality conjecture |
I will discuss recent work with Sven Meinhardt, starting by explaining what the integrality conjecture is, before explaining the categorified analog of this conjecture, stated in terms of Hall algebras. The proofs of these conjectures makes concrete the link between Donaldson-Thomas theory and quantum groups (specifically, Yangians)" |
March 29, 2016, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR |
Piotr Chrusciel (UNIVERSITY OF VIENNA) |
Mass oc characteristic surfaces |
I will discuss various notions of mass in general relativity, and will present an elementary proof of positivity of mass of globally smooth light-cones" |
March 29, 2016, 9:50 - 10:50 am at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Dan Xie (CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS) |
New N=2 dualitites |
We will discuss new type of N=2 dualities. These N=2 SCFTs have the fractional Coulomb branch operators and exact marginal deformations. Different duality frames are found using different decompositions of the 3d mirror of these theories" |
March 28, 2016, 12:00 - 2:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| BASIC NOTIONS SEMINAR / FACULTY COLLOQUIUM |
Shing-Tung Yau (HARVARD UNIVERSITY) |
Quasilocal conserved quantities in general relativity and gravitational radiation |
In this talk , I shall discuss my work with Mu-Tao Wang and Po-Ning Chen on defining and proving properties of various important quantities of spacetime in general relativity. Some relation with questions in gravitational radiation will be discussed" |
March 28, 2016, 3:00 PM at Science Center 507 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Perfectoid Spaces III |
" |
March 24, 2016, 3:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Michael Eichmair (UNIVERSITY OF VIENNA) |
Minimal surfaces, isoperimetry, and non-negative scalar curvature in asymptotically flat manifolds |
We start with an overview of the known results on the global effects of non-negative scalar curvature on the large-scale isoperimetric structure of asymptotically flat manifolds. I will then discuss my recent proof with O. Chodosh of the following theorem that was conjectured by R. Schoen: The only asymptotically flat Riemannian three-manifold with non-negative scalar curvature that admits an unbounded complete surface of locally least area is flat Euclidean space" |
March 24, 2016, 9:50 - 10:50 am at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Richard Freeman (HARVARD UNIVERSITY ECONOMICS) |
Pulling Apart of Wages and Productivity: why "identical" workers have increasingly different pay and productivity |
Competition is supposed to produce a single price or wage for identical products/workers.. But big data on product and labor markets finds large dispersion of prices/wages for similar workers or even identical products. Most of the increase in inequality of earnings is attributable to the pay of similar workers moving apart, depending on the establishment/firm that employs them. And the productivity of those establishments/firms has also moved apart. Why have earnings and producivity grown further apart like astronomical objects in the expanding universe? What does it mean for your future earnings" |
March 23, 2016, 4:30 - 5:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| NUMBER THEORY SEMINAR |
Jacob Tsimerman (UNIVERSITY OF TORONTO) |
Bounding 2-torsion in class groups |
(Joint with Bhargava, Shankar, Taniguchi, Thorne, and Zhao) Zhangâs conjecture asserts that for fixed positive integers m,n, the size of the m-torsion in the class group of a degree n number field is smaller than any power of the discriminant. In all but a handful of cases, the best known result towards this conjecture is the ``convexâ bound given by the Brauer-Siegel Theorem. We make progress on this conjecture by giving a âsubconvexâ bound on the size of the 2-torsion of the class group of a number field in terms of its discriminant, for any value of n. The proof is surprisingly elementary, and we give several applications of this result stemming from the case of cubic fields, including improved bounds on the number of A4 fields, and on the number of integer points an elliptic curve can have. Along the way, we prove a a surprising result on the shape of the lattice of the ring of integers of a number field. Namely, we show that such a lattice is very limited in how âskewâ it can be" |
March 23, 2016, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Zeev Rudnick (TEL AVIV UNIVERSITY & IAS) |
Quantum chaos, eigenvalue statistics and the Fibonacci sequence |
One of the outstanding insights obtained by physicists working on Quantum Chaos is a conjectural description of local statistics of the spectrum of the Laplacian on a Riemannian surface according to crude properties of the dynamics of the geodesic flow, such as hyperbolicity versus integrability. I will describe in general terms what these conjectures say and discuss recent joint work with Valentin Blomer and with Jean Bourgain in which we study the size of the minimal gap between the first N eigenvalues of the Laplacian on a rectangular billiard having irrational squared aspect ratio. For certain quadratic irrationalities, such as the golden ratio, we show that the minimal gap is about 1=N, consistent with Poisson statistics. In the case of the golden ratio, the argument involves some curious properties of the Fibonacci sequence" |
March 23, 2016, 3:00 PM at CMSA Building, 20 Garden Street, Room G02 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Albert Chau (UNIVERSITY OF BRITISH COLUMBIA) |
An existence time estimate for Kahler Ricci flow and applications |
In the talk I will discuss an existence time estimate for Kahler Ricci flow on non-compact manifolds, and related a priori estimates. I will discuss applications to the flow of unbounded curvature metrics in general, and also non-negatively curved Kahler metrics on Cn. Connections will be drawn to Yau s uniformization conjecture which states that a complete non-compact Kahler manifold with positive bisectional curvature is biholomorphic to Cn. The talk will is based on joint work with Luen Fai Tam and Ka Fai Li" |
March 22, 2016, 4:15 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
HĂ©lĂšne Esnault (FREIE UNIVERSITĂ€T BERLIN) |
Various aspects of Lefschetz theorems |
We review various forms of Lefschetz theorems, in particular for l-adic sheaves, explain what one hopes on the crystalline side" |
March 22, 2016, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Jose Juan Fernandez Melgarejo (HARVARD UNIVERSITY) |
Gauged SUGRAS and duality symmetric theories |
We will review the main features of gauged SUGRAs and the embedding tensor formalism. We will motivate the construction of duality symmetric theories and study some of them: Generalized Geometry and Double Field Theory (DFT). In particular, we will show how DFT provides a criterion to distinguish geometric and non-geometric gaugings. This test will allow us to circumvent the no-go theorems on the existence of dS solutions and, as an example, we will show the first stable dS solutions in half-maximal SUGRAs" |
March 21, 2016, 12:00 - 2:00 PM at CMSA Building, 20 Garden Street, Room G02 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Hao Shen (COLUMBIA UNIVERSITY) |
The Sine-Gordon stochastic PDE and regularity structures |
We discuss the dynamical sine-Gordon equation in two space dimension with parameter $\beta$. This is a heat equation perturbed by space-time white noise and a trigonometric nonlinearity, which is the natural dynamics associated to the sine-Gordon model in quantum field theory. We show that when $\beta^2 < 16\pi /3$, the Wick renormalized equation is locally well-posed on torus, and depending on different ranges of $\beta$ we apply the Da Prato-Debussche method or Hairer s theory of regularity structures. One of the interesting aspects is that certain moment estimates in the proof rely on an interpretation of the model as a space-time Coulomb gas system. Based on joint work with Martin Hairer" |
March 11, 2016, 1:30 - 3:00 PM *note special time at Science Center 232 *note different location |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Nikhil Savale (NOTRE DAME) |
Koszul complexes, Birkhoff normal form and the magnetic Dirac operator |
We consider the semi-classical Dirac operator coupled to a magnetic potential on a large class of manifolds including all metric contact manifolds. We prove a sharp local Weyl law and a bound on its eta invariant. The bound on the eta invariant is a sharp form of the results in Taubes s work on the Weinstein conjecture via Seiberg-Witten theory. In the absence of a Fourier integral parametrix, the method relies on the use of almost analytic continuations combined with the Birkhoff normal form and local index theory" |
March 11, 2016, 3:30 - 4:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Perfectoid Spaces II |
" |
March 10, 2016, 3:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Feimin Huang (CHINESE ACADEMY OF SCIENCES) |
Isometric immersion of complete surface with slowly decaying negative Gauss curvature |
The isometric immersion of Riemannian manifold is a fundamental problem in differential geometry. When the manifold is two dimension and its Gauss curvature is negative, the isometric immersion problem is considered through the Gauss-Codazzi system. It is shown that if the Gauss curvature satisfies an integrable condition, then the manifold has a global isometric immersion in $R^3$ even the Gauss curvature decays very slowly at infinity." |
March 10, 2016, 9:50 - 10:50 am at CMSA Building, 20 Garden Street, Room G02 |
| NUMBER THEORY SEMINAR |
Tasho Kaletha (HARVARD UNIVERSITY) |
On the local and global Arthur-Langlands conjectures |
Until recently, precise statements of the local and global Arthur\-Langlands conjectures were available only for quasi-split groups. We will discuss an extension of these conjectures to general connected reductive groups, which is obtained by introducing a new kind of Galois cohomology theory for affine algebraic groups over local and global fields. Afterwards, we will discuss recent progress towards the proof of the local conjectures, based on results on the classification of supercuspidal representations of p-adic groups and their character formulas. Time permitting, we will also mention results on the global conjectures" |
March 09, 2016, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Adam W. Marcus (MATHEMATICS AND PACM, PRINCETON UNIVERSITY) |
Polynomials and (finite) free probability |
In this talk, I will introduce a new theory of ``finite free probability that reveals an intimate connection between free probability and the use of polynomials in previous work with Dan Spielman and Nikhil Srivastava. In particular, I will discuss the two basic operations in free probability theory (the free additive and free multiplicative convolutions), and how they relate to the asymptotic eigenvalue distributions of random matrices. I will then show how certain binary operations on polynomials act as finite analogues of the free convolutions and how this can be used to effectively transfer the asymptotic bounds obtained in free probability to bounds in this new theory (which can then be applied to finite scenarios). If time permits, I will show how one can use such ideas to prove tight bounds on Restricted Invertibility, and discuss a conjectured relationship to low temperature $\beta$-ensembles" |
March 09, 2016, 3:00 PM at CMSA Building, 20 Garden Street, Room G02 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Piotr Chrusciel (UNIVERSITY OF VIENNA) |
The mathematics of gravitation |
I will present a survey of mathematical topics of current interest in Einstein s gravitation theor" |
March 09, 2016, 4:25 PM at CMSA Building, 20 Garden Street, Room G10 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Herman Gluck (UNIVERSITY OF PENNYSLVANIA) |
Germs of fibrations of spheres by great circles always extend to the whole sphere |
We prove that every germ of a smooth great circle fibration of  S^(2n+1) extends to such a fibration of all of S^(2n+1) , a result previously known only for S^3 " |
March 08, 2016, 4:15 PM at Science Center 507 |
| GEOMETRIC ANALYSIS |
Albert Chau (UNIVERSITY OF BRITISH COLUMBIA) |
Survey on Kahler Ricci flow on non-negatively curved non-compact mainfolds |
I will survey results on the Kahler Ricci flow on non-negatively cur the flow of bounded curvature metrics will first reviewed, then recent results for the flow of unbounded curvature metrics and metrics on C^n will be discussed. This is partly based on joint work with Ka Fai Li and Luen-Fai Tam.ved non-compact Kahler manifolds, and their application to Yau s uniformization conjecture in Kahler geometry. Earlier results and techniques fo" |
March 08, 2016, 9:50 - 10:50 am at CMSA Building, 20 Garden St, G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Michele Del Zotto (HARVARD UNIVERSITY PHYSICS) |
Little String Theories in F-theory |
I am going to discuss some consequences of the geometric engineering of 6D little-string-theories in F-theory. Several of their physical properties are geometrized in interesting ways. In particular, T-duality of LSTs is related to 3-CYs with double elliptic structures, which can be realized either via flop transitions or directly in the same Kaehler cone. Based on joint works with Bhardwaj, Heckman, Morrison, Rudelius, Tomasiello, and Vafa" |
March 07, 2016, 12:00 - 2:00 PM at CMSA Building, 20 Garden Street, Room G02 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Perfectoid Spaces |
" |
March 03, 2016, 3:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Piotr Chrusciel (UNIVERSITY OF VIENNA) |
Singularities in general relativity |
I will review the singularities that arise in Einstein equations, and present a recent construction with Paul Klinger of a class of vacuum space-times with controlled behaviour of the singularity and without symmetries" |
March 03, 2016, 9:50 - 10:50 am at CMSA Building, 20 Garden Street, Room G02 |
| HARVARD, BRANDEIS, MIT, NORTHEASTERN JOINT COLLOQUIUM AT HARVARD |
Wei Ho (UNIVERSITY OF MICHIGAN) |
Ranks of elliptic curves: heuristics, theorems, and data (revisited!) |
In 2007, Bektemirov, Mazur, Stein, and Watkins published a beautiful paper (Average ranks of elliptic curves: tension between data and conjecture) that described the state of the art in the study of the distribution of ranks of elliptic curves over Q. The last decade has seen progress on these questions in many directions, perhaps the most surprising being genuine theorems giving upper bounds on the average ranks of elliptic curves over Q (led by work of Bhargava-Shankar). In these theorems, the set of elliptic curves over Q are ordered by height, which is a measure of the size of the coefficients defining each curve, as opposed to by conductor, a more arithmetic invariant used to order curves in most previous work. In this talk, we will discuss the updated heuristics and conjectures in this field as well as some of these theorems and the main ideas behind their proofs. We will compare the expected behavior with data from a new database of elliptic curves over Q ordered by height (joint work with Balakrishnan, Kaplan, Spicer, Stein, and Weigandt); perhaps the new data resolves some of the old tension" |
March 03, 2016, Tea at 4:00 PM, the Austine & Chilton McDonnell Common Room, Science Center 4th Floor, Talk at 4:30 pm at Science Center Hall A |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Lydia Bieri (UNIVERSITY OF MICHIGAN) |
Mathematical General Relativity |
General Relativity (GR) Theory celebrated its 100th anniversary last year. In this talk, I shall highlight some of the main mathematical breakthroughs in GR. I will also discuss new questions and some recent research. This will include the question of Kerr stability, the notion of quasi-local mass as well as some of my work with collaborators that relates to gravitational waves and LIGO." |
March 02, 2016, 4:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| NUMBER THEORY SEMINAR |
Noam Elkies (HARVARD UNIVERSITY) |
Some elliptic curves and surfaces of j-invariant zero |
We describe a family of rational elliptic surfaces of j-invariant 0 and Q-rank 4 that is closely related with a 4-dimensional complex reflection group and with two moduli spaces proved isomorphic by van Geemen. Â Specializations of this family yield several new Diophantine records: j=0 curves over Q with rank as large as 17, quadratic fields whose class groups have 3-rank as large as 8, and pure cubic fields whose class groups have 2-rank as large as 15" |
March 02, 2016, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Yong Lin (RENMIN UNIVERSITY OF CHINA) |
Some PDE's on graphs |
We will talk about the compact solutions of some variational inequalities on graphs, and the existence of solutions to some nonlinear elliptic equations on graphs" |
March 01, 2016, 4:15 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR |
Ben Weinkove (NORTHWESTERN UNIVERSITY) |
Monge-Ampere equations and metrics on complex manifolds |
Yau s Theorem shows that one can prescribe the volume form of a Kahler metric within a given cohomology class, and this is equivalent to solving a complex Monge-Ampere equation. I will describe some joint work with Tosatti and Szekelyhidi-Tosatti on Monge-Ampere type equations on non-Kahler complex manifolds, and the existence of special metrics with prescribed volume form. My talk will focus on the analytic aspects of these problems" |
March 01, 2016, 9:50 - 10:50 am at CMSA Building, 20 Garden Street, Room G02 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SOCIAL SCIENCE APPLICATIONS FORUM |
Scott Kominers (HARVARD SOCIETY OF FELLOWS) |
Patent Trolls: Evidence from Targeted Firms (joint work with Lauren Cohen and Umit G. Gurun) |
We develop a theoretical model of, and provide the first large-sample evidence on, the behavior and impact of non-practicing entities (NPEs) in the intellectual property space. Our model shows that NPE litigation can reduce infringement and support small inventors. However, the model also shows that as NPEs become effective at bringing frivolous lawsuits, the resulting defense costs inefficiently crowd out some firms that, absent NPEs, would produce welfare-enhancing innovations without engaging in infringement. Our empirical analysis shows that on average, NPEs appear to behave as opportunistic patent trolls. NPEs sue cash-rich firms â a one standard deviation increase in cash holdings increases a firm s chance of being targeted by NPE litigation more than fourfold. We find moreover that NPEs target cash unrelated to the alleged infringement at essentially the same frequency as they target cash related to the alleged infringement. By contrast, cash is neither a key driver of intellectual property lawsuits by practicing entities (e.g., IBM and Intel), nor of any other type of litigation against firms. The cash-targeting behavior we observe is driven by large aggregator NPEs, and is not the behavior of small innovators. We find further suggestive evidence of NPE opportunism, such as forum shopping and targeting of firms that may have reduced ability to defend themselves against litigation. Finally, we find that NPE litigation has a real negative impact on innovation at targeted firms: firms substantially reduce their innovative activity after settling with NPEs (or losing to them in court)" |
February 29, 2016, 5:00 - 6:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Can Kozcas (CMSA) |
Elliptic Virasoro conformal blocks |
We study certain six dimensional theories arising on (p,q) brane webs living on R Ă S1. These brane webs are dual to toric elliptically fibered Calabi-Yau threefolds. The compactification of the space on which the brane web lives leads to a deformation of the partition functions equivalent to the elliptic deformation of the Ding-Iohara algebra. We compute the elliptic version Dotsenko-Fateev integrals and show that they reproduce the instanton counting of the six dimensional theory" |
February 29, 2016, 12:00 - 2:00 PM at CMSA Building, 20 Garden Street, Room G02 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Tilting, ctd. |
" |
February 25, 2016, 3:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Chunpeng Wang (JILIN UNIVERSITY) |
Smooth Transonic Flows of Meyer Type in De Laval Nozzles |
This talk concerns smooth transonic steady potential flows of Meyer type in two-dimensional de Laval nozzles, which are governed by an equation of mixed type with degeneracy at the sonic state. We seek a smooth transonic flow of Meyer type which satisfies physical boundary condition and whose sonic points are exceptional in a de Laval nozzle. For such a flow, its sonic curve must be located at the throat of the nozzle and the governing equation is strongly degenerate in the sense that the sonic curve is a characteristic degenerate boundary in the subsonic-sonic region, while in the sonic-supersonic region all characteristics from sonic points coincide, which are the sonic curve and never approach the supersonic region. It is proved that there exists uniquely such a smooth transonic flow near the throat of the nozzle, whose acceleration is Lipschitz continuous, if the wall of the nozzle is sufficiently flat. The works are jointed with Professor Zhouping Xin" |
February 25, 2016, 9:50 - 10:50 am at CMSA Building, 20 Garden Street, Room G02 |
| NUMBER THEORY SEMINAR |
Jerry Wang (PRINCETON UNIVERSITY) |
Density of polynomials with squarefree discriminant |
The problem of the density of squarefree discriminant polynomials is an old one, being considered by many people, and the density being conjectured by Lenstra. A proof has been out of question for a long time. The reason it was desired is that a squarefree discriminant polynomial f immediately gives the ring of integers of Q[x]/f(x) and its Galois group. In recent joint work with Manjul Bhargava and Arul Shankar, we counted the number of odd degree polynomials with squarefree discriminant and proved the conjecture of Lenstra. In this talk, I will explain the general strategy of the squarefree sieve and the specific strategy to deal with discriminants which in turn leads to counting integral orbits for a representation of a non-reductive group" |
February 24, 2016, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Aukosh Jagannath (COURANT INSTITUTE) |
The Parisi Variational Problem |
The Parisi Variational Problem is a challenging non-local, strictly convex variational problem over the space of probability measures whose analysis is of great interest to the study of mean field spin glasses. In this talk, I will present a conceptually simple approach to the study of this problem using techniques from PDEs, stochastic optimal control, and convex optimization. We will begin with a new characterization of the minimizers of this problem whose origin lies in the first order optimality conditions for this functional. As a demonstration of the power of this new approach, we will study a prediction of de Almeida and Thouless regarding the validity of the 1 atomic anzatz. We will generalize their conjecture to all mixed p-spin glasses and prove that their condition is correct in the entire temperature-external field plane except for a compact set whose phase is unknown at this level of generality. A key element of this analysis is a new class of estimates regarding Gaussian integrals in the large noise limit called âDispersive Estimates of Gaussians.â This is joint work with Ian Tobasco (NYU Courant)" |
February 24, 2016, 3:00 PM at CMSA Building, 20 Garden Street, Room G02 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Dan Xie (CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS) |
Singularity theory and supersymmetric field theory |
I will discuss the use of singularity theory to study supersymmetric field theory in various dimensions. Many objects studied in singularity theory, such as the Milnor fibration, mini-versal deformation, resolution, etc., have interesting applications to physics." |
February 24, 2016, 4:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| HARVARD LOGIC SEMINAR |
John Baldwin (UNIVERSITY OF ILLINOIS AT CHICAGO) |
The divorce of set theory and first order model theory |
Around 1970 there seemed to be inevitable ties between axiomatic set theory and even first order model theory. The advent of stability theory erased this impression, by showing that while cardinality is deeply entangled with first order model theory, the niceties of cardinal arithmetic are not. We describe the types of entanglement as oracular (consistency inspires a ZFC proof), transitory (the hypothesis is eliminable), and full (there is an equivalence with an independent set theoretic proposition). In the last case, set theoretic pluralism entails model theoretic pluralism." |
February 24, 2016, 4:00 - 6:00 PM at 2 Arrow Street, Room #420 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Damin Wu (UNIVERSITY OF CONNECTICUT) |
On negatively pinched complete Kahler manifold |
We prove that a complete Kahler manifold with holomorphic curvature bounded between two negative constants admits a complete Kahler-Einstein metric. This is a joint work with S. T. Yau" |
February 23, 2016, 4:15 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Marc Hoyois (MIT) |
A1-homotopical classification of principal G-bundles |
Let k be an infinite field and G an isotropic reductive k-group. If X is a smooth affine k-variety, then locally trivial G-torsors over X are classified by maps X â BG in the A1-homotopy category. I will discuss the proof of this statement and some applications. This is joint work with Aravind Asok and Matthias Wendt" |
February 23, 2016, 3:00 PM at MIT 2-131 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Burkhard Schwab (CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS) |
BMS, Soft Theorems and String Theory |
From the worldsheet theory point of view, diffeomorphisms of the target space are not (gauge) symmetries but rather examples of (trivial) dualities between string models. Different types of target space transformations (small diffeomorphisms, large diffeomorphisms, Killing vectors) have a different effect on the action. Unilke Killing vectors, large and small diffeomorphisms deform the action due to the insertion of new operators. I will discuss when these operators have a non-trivial effect on correlation functions of vertex operators and show that the operator inserted by a large diffeomorphism is a vertex operator of a graviton with no energy -- a soft graviton. Based on 1506.0578" |
February 22, 2016, 12:00 - 2:00 PM at CMSA Building, 20 Garden Street, Room G02 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Jo Nelson (COLUMBIA/IAS) |
An integral lift of contact homology |
Cylindrical contact homology is arguably one of the more notorious Floer-theoretic constructions. The past decade has been less than kind to this theory, as the growing knowledge of gaps in its foundations has tarnished its claim to being a well-defined contact invariant. However, jointly with Hutchings we have managed to redeem this theory in dimension 3 for dynamically convex contact manifolds. This talk will highlight our implementation of non-equivariant constructions, domain dependent almost complex structures, automatic transversality, and obstruction bundle gluing, yielding a homological contact invariant which is expected to be isomorphic to SH^+ under suitable assumptions, though it does not require a filling of the contact manifold. By making use of family Floer theory we obtain an S^1-equivariant theory defined over Z coefficients, which when tensored with Q yields cylindrical contact homology, now with the guarantee of well-definedness and invariance" |
February 19, 2016, 3:30 - 4:30 PM at Science Center 507 |
| EVOLUTION EQUATIONS SEMINAR |
Zouqiang Shi (TSINGHUA UNIVERSITY ) |
Low dimensional manifold model for image processing |
In this talk, I will present a novel low dimensional manifold model for image processing problems. This model is based on the observation that for many natural images, the patch manifold usually has low dimension structure. Then, we use the dimension of the patch manifold as a regularization to recover the original image. Using some formula in differential geometry, this problem is reduced to solve Laplace-Beltrami equation on manifold. The Laplace-Beltrami equation is solved by the point integral method. Numerical tests show that this method gives very good results in image inpainting, denoising and super-resolution problem" |
February 18, 2016, 9:50 - 10:50 am at CMSA Building, 20 Garden St, G02 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Tilting |
" |
February 18, 2016, 3:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Florent Bekerman (MIT) |
Transport Methods and Universality for beta-matrix models |
We use transport methods to show universality of local statistics for non-critical beta-matrix models. We construct an approximate transport map between the densities of the eigenvalues under two different potentials , obtained as the flow of an approximate solution of a linearized Monge-AmpĂšre equation. The transport map enjoys accurate estimates in the dimension and can be used to show some universality results in the bulk and at the edge. This is based on a work with A. Figalli and A. Guionnet" |
February 17, 2016, 2:50 PM at CMSA Building, 20 Garden Street, Room G02 |
| NUMBER THEORY SEMINAR |
Ila Varma (HARVARD UNIVERSITY) |
Galois representations associated to regular algebraic cuspidal automorphic representations of GLn are de Rham |
I will discuss local-global compatibility at p for the p-adic Galois representations constructed by Harris- Lan-Taylor-Thorne and Scholze. More precisely, let rp (Ï) denote an n-dimensional p-adic representation of the absolute Galois group of a CM field F attached to a regular algebraic cuspidal automorphic representation Ï of GLn (AF ). For any prime v | p of F , we show that rp (Ï)|Gal(F v /Fv ) is de Rham. To prove the above, we use the fact that the representations rp (Ï) can be constructed as a subrepre- sentation of a p-adic Galois representation Rp (Î ) associated to an overconvergent GU (n, n)-automorphic representation Î . We can then construct a certain âtwistedâ one-parameter family containing Î and a Zariski-dense set of points whose associated Galois representations are already known to be de Rham. Using results of R. Liu and S. Shah, we can show that each specialization within this family has n periods, and conclude the result by proving that the resulting n periods of Rp (Î ) are all distinct periods of rp (Ï)" |
February 17, 2016, 3:00 - 4:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Samuel Kou (HARVARD UNIVERSITY STATISTICS) |
Big data, Google and disease detection: the statistical story |
Big data collected from the internet have generated significant interest in not only the academic community but also industry and government agencies. They bring great potential in tracking and predicting massive social activities. We focus on tracking disease epidemics in this talk. We will discuss the applications, in particular Google Flu Trends, some of the fallacy and the statistical implications. We will propose a new model that utilizes publicly available online data to estimate disease epidemics. Our model outperforms all previous real-time tracking models for influenza epidemics at the national level of the US. We will also draw some lessons for big data applications" |
February 17, 2016, 4:30 - 5:30 PM at CMSA Building, 20 Garden Street, Room G10 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Lydia Bieri (UNIVERSITY OF MICHIGAN) |
The Shape of the Universe |
In General Relativity, a major branch of research is devoted to the study of the geometric properties of solutions to the Einstein equations. Gravitational waves, which are predicted by the theory of General Relativity and expected to be detected in the near future, are fluctuations of the spacetime curvature. These waves leave a footprint in the spacetime regions they travelled through. We investigate the geometric-analytic properties of various spacetimes with gravitational radiation" |
February 16, 2016, 4:15 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Dhruv Ranganathan (YALE UNIVERSITY) |
Non-archimedean geometry, logarithmic structures, and spaces of curves in toric varieties |
I will discuss the relationship between moduli spaces of logarithmic stable maps to toric varieties and the polyhedral geometry of their Birkovich skeletons. In genus 0, the latter can be interpreted as a parameter space for tropical curves, and this gives explicit control on the geometry of logarithmic stable maps. Concerning higher genus, I will discuss some recent ideas, building on work of Abramovich-Wise, Olsson, and Ulirsch, that point to a relationship between the virtual fundamental class and the tropical realizability problem" |
February 16, 2016, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR |
Camillo DeLellis (INSTITUT FĂŒR MATHEMATIK UNIVERSITĂ€T ZĂŒRICH) |
Approaching Plateau's problem with minimizing sequences of sets |
In a joint paper with Francesco Ghiraldin and Francesco Maggi we provide a compactness principle which is applicable to different formulations of Plateau s problem in codimension one and which is exclusively based on the theory of Radon measures and elementary comparison arguments. Exploiting some additional techniques in geometric measure theory, we can use this principle to give a different proof of a theorem by Harrison and Pugh and to answer a question raised by Guy David." |
February 16, 2016, 9:50 - 10:50 am at CMSA Building, 20 Garden Street, Room G02 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Artan Sheshmani (MIT) |
Counting curves on surfaces in Calabi-Yau threefolds and proof of S-duality modularity conjecture |
I will talk about an algebraic-geometric proof of the S-duality conjecture in superstring theory, made formerly by physicists Gaiotto, Strominger, Yin, regarding the modularity of DT invariants of sheaves supported on hyperplane sections of the quintic Calabi-Yau threefold. Together with Amin Gholampour we use degeneration and localization techniques to reduce the threefold theory to a certain intersection theory over the relative Hilbert scheme of points on surfaces and then prove modularity; More precisely, we have proven that the generating series, associated to the top intersection numbers of the Hilbert scheme of points, relative to an effective divisor, on a smooth quasi-projective surface is a modular form. This is a generalization of the result of Okounkov-Carlsson, where they used representation theory and the machinery of vertex operators to prove this statement for absolute Hilbert schemes. These intersection numbers eventually, together with the generating series of Noether-Lefschetz numbers as I will explain, will provide the ingredients to achieve an algebraic-geometric proof of S-duality modularity conjecture. Our work is based on our earlier results with Richard Thomas and Yukinobu Toda, which I will also discuss as further ingredients, needed for the final proof" |
February 15, 2016, 12:00 pm at CMSA Building 20 Garden St G02 |
| THURSDAY SEMINAR |
Bhargav Bhatt (UNIVERSITY OF MICHIGAN) |
Overview of the perfectoid construction of A\Omega |
" |
February 11, 2016, 3:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Lydia Bieri (UNIVERSITY OF MICHIGAN) |
Einstein's Equations, Energy and Gravitational Radiation |
The Einstein equations of General Relativity (GR) govern the laws of the universe. They can be written as a set of constraints on the initial data and a set of evolution equations. A major goal in the study of these equations is to investigate the analytic properties and geometries of the solution spacetimes.In particular, fluctuations of the curvature of the space time, known as gravitational waves, have been a highly active research topic, as we are believed to be on the verge of their detection. Understanding gravitational radiation is tightly interwoven with the study of the Cauchy problem in GR. I will address recent work with David Garfinkle on gravitational radiation in asymptotically flat as well as cosmological spacetimes" |
February 11, 2016, 9:50 - 10:50 am at CMSA Building, 20 Garden Street, Room G02 |
| NUMBER THEORY SEMINAR |
Paul Frank Baum (PENNSYLVANIA STATE UNIVERSITY) |
Geometric Structure in Smooth Dual |
Let G be a connected split reductive p-adic group. Examples are GL(n, F) , SL(n, F) , SO(n, F), and Sp(n, F) where n can be any positive integer and F can be any finite extension of the field Qp of p-adic numbers. The smooth (or admissible) dual of G is the set of equivalence classes of smooth irreducible representations of G. The smooth dual of G is the disjoint union of subsets known as the Bernstein components. The talk will explain the ABPS (Aubert-Baum-Plymen-Solleveld) conjecture which states that each Bernstein component is a complex affine variety. Each of these complex affine varieties is explicitly identified as the extended quotient associated to the given Bernstein component. The ABPS conjecture has been proved for GL(n, F ), SL(n, F ), SO(n, F ), and Sp(n, F ). The talk will conclude with an exposition of the connection between ABPS and the local Langlands conjecture. The above is joint work with Anne-Marie Aubert, Roger Plymen, and Maarten Solleveld." |
February 10, 2016, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Chunpeng Wang (JILIN UNIVERSITY) |
Continuous Subsonic-Sonic Flows in a Convergent Nozzle |
This talk concerns continuous subsonic-sonic flows in a convergent nozzle with straight solid walls. It is shown that for the given inlet being a perturbation of an arc centered at the vertex of the nozzle and the given incoming mass flux belonging to an open interval depending only on the adiabatic exponent and the length of the arc, there is a unique continuous subsonic-sonic flow from the given inlet with the angle of the velocity orthogonal to the inlet line and the given incoming mass flux. Furthermore, the sonic curve of this continuous subsonic-sonic flow is a free boundary, where the flow is singular in the sense that while the speed is Holder continuous at the sonic state, yet the acceleration blows up at the sonic state" |
February 10, 2016, 4:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR |
Valentino Tosatti (NORTHWESTERN UNIVERSITY) |
Non-Kahler Calabi-Yau manifolds |
Calabi-Yau manifolds are often defined as compact Kahler manifolds with vanishing real first Chern class. Yau s theorem shows that these are precisely the compact complex manifolds which admit a Ricci-flat Kahler metric. What happens if we do not demand that the manifold be Kahler? It turns out that to obtain a meaningful theory one needs to require that the first Chern class vanishes in a stronger sense. I will present various results on the geometry of these manifolds, including a result (joint with Szekelyhidi and Weinkove) that shows that these are precisely the compact complex manifolds which admit a Gauduchon Hermitian metric with vanishing Chern-Ricci curvature" |
February 09, 2016, 9:50 - 10:50 am at CMSA Building, 20 Garden Street, Room G02 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Jonathan Weitsman (NORTHEASTERN UNIVERSITY) |
Quantization of b-symplectic manifolds |
b-symplectic (or log-symplectic) manifolds are Poisson manifolds with the property that the Poisson bivector field arises from a symplectic structure on the complement of a real hypersurface, and has a prescribed vanishing on that hypersurface. This is a least degenerate case of Poisson geometry which we can try to use as a laboratory to apply techniques developed in symplectic geometry to obtain intuition about quantization in the Poisson setting. Recent work with V. Guillemin and E. Miranda on desingularization of b-symplectic forms leads to a proposed scheme for quantization of these manifolds in the case where the b-symplectic form has certain integrality properties and where an abelian group acts in a Hamiltonian fashion and satisfies a technical nondegeneracy condition. We show that in this case we obtain a finite quantization, which we conjecture should arise from the index of a Fredholm operator acting on sections of an appropriate line bundle. This is joint work with V. Guillemin and E. Miranda" |
February 09, 2016, 4:15 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Hossein Movasati (IMPA) |
Calabi-Yau modular forms: Are they as useful as elliptic modular forms? |
In this talk we give an overview of the theory of Calabi-Yau modular forms based on the references [1,2,3,4]. The main ingredient of the theory is a family of non-rigid Calabi-Yau varieties. We give many analogies of this theory with the classical theory of elliptic modular forms. In the case of elliptically fibered Calabi-Yau four and three folds we explain how both theories are related to each other. 1. H. Movasati, Modular-type functions attached to mirror quintic Calabi-Yau varieties , Math. Zeit., Vol 281, Issue 3, 2015, pp. 907-929. 2 H. Movasati, Gauss-Manin connection in disguise: Calabi-Yau modular forms 3. M. Alim, H. Movasati, E. Scheidegger, S-T Yau, Gauss-Manin connection in disguise: Calabi-Yau threefolds 4. B. Haghighat, H. Movasati, S-T Yau, Calabi-Yau modular forms in limit: Elliptic Fibrations" |
February 08, 2016, 12:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| THURSDAY SEMINAR |
Ben Knudsen (HARVARD UNIVERSITY) |
The derivatives of the identity fnctor |
" |
February 08, 2016, 3:00 - 5:00 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Pranav Pandit (UNIVERSITĂ€T WIEN) |
Categorical KĂ€hler Geometry |
The Donaldson-Uhlenbeck-Yau theorem gives a differential-geometric description of the algebro-geometric notion of stability for vector bundles. I will outline a framework for studying analogous phenomena in a context where certain higher categories play the role of geometric spaces. This approach to formalizing features of the notion of stability for D-branes in N = (2,2) SCFTs is informed by the study of Bridgeland stability structures on Fukaya categories with coefficients. This talk is based on joint work in progress with Fabian Haiden, Ludmil Katzarkov and Maxim Kontsevich" |
February 04, 2016, 9:50 - 10:50 am at CMSA Building, 20 Garden Street, Room G02 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Camillo DeLellis (INSTITUT FĂŒR MATHEMATIK UNIVERSITĂ€T ZĂŒRICH) |
From Nash to Onsager, funny coincidences across differential geometry and the theory of turbulence |
The incompressible Euler equations were derived more than 250 years ago by Euler to describe the motion of an inviscid incompressible fluid. It is known since the pioneering works of Scheffer and Shnirelman that there are nontrivial distributional solutions to these equations which are compactly supported in space and time. If they were to model the motion of a real fluid, we would see it suddenly start moving after staying at rest for a while, without any action by an external force. A celebrated theorem by Nash and Kuiper shows the existence of C1 isometric embeddings of a fixed flat rectangle in arbitrarily small balls of the threedimensional space. You should therefore be able to put a fairly large piece of paper in a pocket of your jacket without folding it or crumpling it. In a first joint work with Laszlo Szekelyhidi we pointed that these two counterintuitive facts share many similarities. This has become even more apparent in some recent results due to us, Tristan Buckmaster and Philip Isett on a longstanding conjecture of Lars Onsager in the theory of fully developed turbulence" |
February 03, 2016, 4:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Antti Knowles (ETH ZURICH) |
An optimal rotational invariant estimator for general covariance matricesâ |
We consider sample covariance matrices in the high-dimensional regime where the number of variables is comparable to the number of samples. The underlying population covariance matrix is allowed to be very general and include outliers. We prove that there exists a consistent, unified, and optimal rotational invariant estimator of the population covariance matrix that depends only on observable quantities. All results hold at a local scale of individual eigenvalues, with optimal large deviation error bounds. As a result, we find that the outliers have to be shrunk even more towards unity than the prediction based on the typical locations of the outliers. Joint work with J. Bun and J. Yin" |
February 03, 2016, 2:30 PM at CMSA Building, 20 Garden Street, Room G02 |
| HARVARD LOGIC SEMINAR |
Ilijas Farah (YORK UNIVERSITY) |
Set theory and representations of C*-algebras |
In the 1960s Glimm proved a dichotomy result for representations of locally compact groups and C*-algebras. This result was later refined by Effros and in 1990 Harrington, Kechris and Louveau proved the Glimm âEffros Dichotomy, a landmark result in descriptive set theory and abstract classification theory. I shall discuss the complexity of the space of (irreducible) representations of a C*-algebra from the set-theoretic vantage point, both in separable and nonseparable case. Some compelling problems remain open in the latter case" |
February 03, 2016, 4:00 - 6:00 PM at 2 Arrow Street, Room #420 |
| NUMBER THEORY SEMINAR |
Alexander Lubotzky (THE HEBREW UNIVERSITY / YALE UNIVERSITY) |
From Ramanujan graphs to Ramanujan complexes |
Ramanujan graphs are optimal expanders (from spectral point of view). Explicit constructions of such graphs were given in the 80 s as quotients of the Bruhat-Tits tree associated with GL(2) over a local field F, by suitable congruence subgroups. The spectral bounds were proved using works of Hecke, Deligne and Drinfeld on the Ramanujan conjecture in the theory of automorphic forms. The work of Lafforgue, extending Drinfeld from GL(2) to GL(n), opened the door for the construction of Ramanujan complexes as quotients of the Bruhat-Tits buildings. This gives finite simplicial complexes which on one hand are random like and at the same time have strong symmetries. Recently various applications have been found in combinatorics, coding theory and in relation to Gromov s overlapping properties. We will describe these developments and some recent applications. In particular, we will present a joint work with Tali Kaufman and David Kazhdan and a work of S. Evra and T. Kaufman in which these complexes are uses to answer a question of Gromov." |
February 03, 2016, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR |
Yi Zhang (FUDAN UNIVERSITY) |
Hodge Bundles on Smooth Compactifications of Siegel Varieties |
This is a joint work with S.T.Yau. We construct a canonical Hodge bundle on a Siegel variety so that the holomorphic tangent bundle can be embedded into the Hodge bundle and the canonical Bergman metric on a Siegel variety is same as the induced Hodge metric. We then study extensions of the tangent bundle over any smooth toroidal compactification, and apply these results to get asymptotic formula of the dimension of Siegel cusp modular forms" |
February 02, 2016, 9:50 - 10:50 am at CMSA Building, 20 Garden Street, Room G02 |
| DIFFERENTIAL GEOMETRY SEMINAR |
William Meeks (UMASS AMHERST) |
Embedded spheres in homogeneous 3-manifolds |
If X is a homogenoues 3-manifold diffeomorphic to R^3, then X is isometric to a Lie group with a left invariant metric G. Given an oriented surface in X, then one can define,by left translation, what is called the left invariant Gauss map of the surface to the 2-sphere; this map generalizes the classical Gauss map when the metric Lie group is the Abelian group R^3. In the case that S is an immersed sphere of constant mean curvature in a metric Lie group X, the speaker together with Pablo Mira, Joaquin Perez and Antonio Ros have shown that the left invariant Gauss map of S is always a diffeomorphism. It has been conjectured that when a metric Lie group X is diffeomorphic to R^3 and the left invariant Gauss map of a sphere S in X is a diffeomorphism, then S must be embedded. In the case that the underlying Lie group structure on X admits an algebraic open book structure, then have proved this conjecture. This embeddedness proof will be the main topic of the talk" |
February 02, 2016, 4:15 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Yukinobu Toda (MIT) |
Wall-crossing formulas of higher rank Donaldson-Thomas invariants |
The Donaldson-Thomas invariants count stable coherent sheaves on Calabi-Yau 3-folds, and their rank one theory is related to Gromov-Witten invariants. Around 2008-2010, Bridgeland and myself studied wall-crossing formulas of rank one DT invariants and proved several properties, e.g. DT/PT correspondence, rationality. In this talk, I explain that the similar properties also hold for higher rank DT invariants." |
February 01, 2016, 12:00 PM at CMSA Building, 20 Garden Street, Room G02 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Xiaoli Han (TSINGHUA UNIVERSITY) |
The symplecitic and Lagranian mean curvature flow |
I will introduce the notition of the symplectic and Lagrangian mean curvature flows. Then I will talk the long time exsitence and convergence. I will also talk the nature of the singularity when the symplectic and Lagrangian mean curvature flows blow up" |
January 28, 2016, 9:50 - 10:50 am at CMSA Building, 20 Garden Street, Room G02 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Conan Leung (IMS/THE CHINESE UNIVERSITY OF HONG KONG) |
Some modern aspects of Morse theory |
Abstract: we will explore various aspects of (complex) Morse theory in mathematical physics, including gauge theory and mirror symmetry" |
January 27, 2016, 4:00 PM at CMSA Building, 20 Garden Street, Room G10 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Louigi Addario (MCGILL UNIVERSITY) |
Slowdown of the front for branching Brownian motion with decay mass |
Consider a standard branching Brownian motion whose particles have varying mass. At time t, if a total mass m of particles have distance less than one from a fixed particle x, then the mass of particle x decays at rate m. The total mass increases via branching events: on branching, a particle of mass m creates two identical mass-m particles. One may define the front of this system as the point beyond which there is a total mass less than one (or beyond which the expected mass is less than one). This model possesses much less independence than standard BBM. Nonetheless, it is possible to prove that (in a rather weak sense) the front is at distance ~ c t^{1/3} behind the typical BBM front. Joint work with Sarah Penington (Oxford)" |
January 27, 2016, 2:30 PM at CMSA Building, 20 Garden Street, Room G02 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Conan Leung (IMS/THE CHINESE UNIVERSITY OF HONG KONG) |
Donald-Thomas invariants for Calabi-Yau fourfolds |
In this talk, I will describe the geometry and topology of moduli space of Donaldson-Thomas connections on Calabi-Yau fourfolds. This is a joint work with Yalong Cao" |
January 26, 2016, 4:15 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Phil Sosoe (CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS) |
The Chemical Distance in Critical Percolation |
Take a square of side length n in Z^2, viewed as a square lattice, with edges between points that differ by one in one of the coordinates. Remove each of the edges at random, with probability 1/2. This process is called critical percolation. With probability uniformly bounded below in n, there remains a connected path of edges connected the left side to the right side of the square. How many edges does such a crossing typically contain? I will introduce percolation and discuss some results on the question of the distance" |
December 14, 2015, 3:00 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Matthew J. Holman (HARVARD SMITHSONIAN CENTER FOR ASTROPHYSICS) |
Dynamical Chaos in Kepler Planetary Systems |
Of the Kepler planets that have been reported to date, a significant fraction are in systems with multiple transiting planets. In some cases, the signature of the gravitational interactions between planets in these systems can be seen in the variations of their times of transit. By carefully modeling the transit times, as well as investigating long-term stability, we are able to measure or constrain the masses and orbits of the transiting bodies in some of these systems, verifying that they are indeed planets. Although this approach is particularly effective for closely packed and near-resonant systems, it has also been applied to a broad range of systems. These include circumbinary planets, as well as systems with additional non-transiting planets. Some of the Kepler planetary systems exhibit evidence of dynamical chaos on remarkably short time scales, yet these systems are likely to be long-lived. I will highlight the theoretical advances in our understanding of dynamical chaos and stability that have been prompted by the Kepler planetary systems" |
December 09, 2015, 4:00 - 5:00 PM at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Sörin Petrat (IST, AUSTRIA) |
Derivation of Mean-field Dynamics for Fermions |
" |
December 08, 2015, 1:15 pm at Jefferson 453 |
| MATHEMATICAL PHYSICS SEMINAR |
Roland Bauerschmidt (HARVARD UNIVERSITY) |
Renormalization Group Analysis of Self-Avoiding Walk and Spin Models in 4D |
" |
December 08, 2015, 4:15 PM at Jefferson 356 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Piotr Surowka (HARVARD UNIVERSITY PHYSICS) |
Anomalies, Information Geometry and (Turbulent) Hydrodynamics - inspiration for mathematicians |
I will show how hydrodynamics is modified in the presence of quantum field theory anomalies. Because of the non-dissipative nature of the modification I will construct a partition function which compactly describes the transport properties of the system and I will explain how the anomalous properties can be understood in terms of heat kernels and elucidate subtleties that show up. I will also explain why finite temperature anomalies are not captured by topological indices. In the next step I will show how to move away from equilibrium for systems with anomalies and introduce information geometry and the Fisher-Rao metric in the parameter space, which is a useful tool to study systems close to thermal equilibrium. Finally I will comment on the potential utility of anomalies and symmetry-based analysis to study far-from-equilibrium phenomena such as turbulence." |
December 07, 2015, 12:00 - 2:00 PM at Science Center 232 |
| BASIC NOTIONS SEMINAR |
Yum-Tong Siu (HARVARD UNIVERSITY) |
Recent Results and Problems in Several Complex Variables Involving Construction of Holomorphic Sections |
Many highly significant problems in several complex variables involve the construction of holomorphic sections of bundles with special properties. For example, deformational invariance of plurigenera, finite generation of the canonical ring, the abundance conjecture, effective results in algebraic geometry, hyperbolicity problems, and analogues of strong rigidity problems in the setting of Cauchy-Riemann geometry. Besides briefly surveying problems involving the construction of holomorphic sections, the talks will focus mainly on the following two recent results. (i) Hyperbolicity problem of nonexistence of nonconstant holomorphic maps from the affine complex line. (ii) The problem of Grauert-Schneider on the splitting of unstable plane bundle over high-dimensional complex projective space" |
December 07, 2015, 3:00 PM at Science Center 507 |
| THURSDAY SEMINAR |
Bhargav Bhatt (UNIVERSITY OF MICHIGAN) |
Crystalline cohomology |
" |
December 03, 2015, 3:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Scott Kominers (HARVARD SOCIETY OF FELLOWS) |
Generalized Matching Market Design: Theory and Practice |
In recent years, matching theory has been widely applied in the design of real-world labor markets and school choice programs. At the same time, new theoretical discoveries have shown how to extend matching algorithms to more complex markets. In this talk, I will survey my work on generalized matching, focusing on cumulative offer algorithms and weakened substitutability conditions. Then, I will detail how my generalized matching work led to the elimination of walk-zones in the Boston public school match in 2013. Finally, I will close with a broader discussion of my ongoing economic design projects, including (1) systems for screening out patent trolls and (2) data-driven city design" |
December 02, 2015, 4:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Benedict Gross (HARVARD UNIVERSITY) |
On some Artin L-series |
Let p be a prime with p == 3 (mod 4). Then the group PGL(2,p) has a unique irreducible representation V of dimension (p-1) which is the direct sum of an irreducible representation and its dual when restricted to the subgroup PSL(2,p). I will first describe some properties of this representation, and its generalization to PGSp(2g,p) when g is odd. I will then describe how to realize these finite groups as Galois groups over Q. Finally, I will consider Artin s conjecture on the holomorphic continuation of the Artin L-functions L(V,s) in the light of the global conjectures of Langlands" |
December 02, 2015, 3:00 - 4:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Philip Engel (HARVARD UNIVERSITY) |
TBA |
TB" |
December 01, 2015, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Bong Lian (BRANDEIS UNIVERSITY) |
Large complex structure limits of Calabi-Yau manifolds |
LCSL s are special types of degenerations CY manifolds that play an important role in mirror symmetry. They are known to exist for a large class of cases which I will briefly review. We then discuss some new constructions of these LCSLs. This is based on joint work with S. Bloch, A. Huang, D. Srinivas, S.-T. Yau, and X. Zhu" |
December 01, 2015, 4:15 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Roger Casals (MIT) |
Legendrian Presentation of Weinstein Domains |
In this talk we will discuss the Legendrian front description of Weinstein manifolds. This provides diagramatic computations of wrapped Fukaya categories and the symplectic coho- mology for certain Weinstein domains, which feature on the A{side of Homological Mirror Symmetry. The required de nitions and necessary results will be provided. In the rst part, we present the dictionary between Legendrian presentations and adapted open books decompositions. In the second part, we explore applications to Weinstein cobordisms, ex- act Lagrangians and biLefschetz brations with Am{Milnor bres. This is joint work with E. Murphy" |
November 30, 2015, 12:00 - 2:00 PM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR |
Hongwei Xu (CMS AT ZHEJIANG UNIVERSITY) |
Mean curvature flow meets Ricci flow: Convergence and sphere theorems of submanifolds arising from Yau rigidity theory |
In 1975, S.-T. Yau established the rigidity theory of CMC submanifolds, which plays an important role in the study of the mean curvature flow, and curvature and topology of submanifolds. During the past four decades, the Yau rigidity theory has been developed by several geometers and I. Using the Ricci flow and stable currents, Xu-Zhao initiated the study of differential pinching problem of submanifolds. Afterwards, Gu-Xu extented Brendle-Schoen s 1/4-pinching differentiable sphere theorm to the case of submanifolds in a Riemannian manifold with arbitrary codimension $p(\ge 0)$. As a consequence, we proved an optimal differentiable sphere theorm for submanifolds in Euclidean spaces. Itâs the first optimal differentiable sphere theorem for submanifolds of arbitrary dimension and codimension. Mean while, by using the mean curvature flow, Andrews-Baker obtained the same differentiable sphere theorm for submanifolds in Euclidean spaces independently. Later Baker and Liu-Xu-Ye-Zhao proved a sharp convergence theorem for the mean curvature flow of submanifolds in space forms. Recntly, my students and I proved several new sphere theorems for submanifolds via the Ricci flow. Most recently, motivated by the Yau rigidity theory and by developing new techniques, Lei and I verified a new sharp convergence theorem for the mean curvature flow of submanifolds in spheres and an optimal convergence theorem for the mean curvature flow of submanifolds in hyperbolic spaces, which improve the convergence theorems due to Baker, Huisken and Liu-Xu-Ye-Zhao. Notice that Andrews-Baker-Gu-Xuâs optimal pinching condition implies positivity of the sectional curvature. Lei-Xuâs pinching condition implies that the Ricci curvature of the initial submanifold is positive, but does not imply positivity of the sectional curvature. Consequently, we obtain an optimal differentiable sphere theorem for submanifolds in hyperbolic spaces and a new differentiable sphere theorem for submanifolds in spheres" |
November 24, 2015, 10:00 AM at Science Center 232 |
| MATHEMATICAL PHYSICS SEMINAR |
Daniel Harlow (HARVARD UNIVERSITY) |
Operator Algebras and Entropy in Lattice Gauge Theory |
" |
November 24, 2015, 1:15 pm at Jefferson 453 |
| MATHEMATICAL PHYSICS SEMINAR |
Victor Kac (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
Algebraic Theory of Integrable Systems |
" |
November 24, 2015, 4:15 PM at Jefferson 356 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Nima Lashkari (MIT) |
Holographic relative entropy is a Noether charge |
In this talk, we discuss the importance of quantum relative entropy function in the study of universal phenomena in field theory and gravity. In holography, we show that the relative entropy of spherical subsystems geometrizes. This can be thought of as an extension of the celebrated Ryu-Takayanagi proposal. The gravity dual of relative entropy is a conserved charge associated with the part of the geometry called entanglement wedge" |
November 23, 2015, 12:00 - 2:00 PM at Science Center 232 |
| BASIC NOTIONS SEMINAR |
Joe Harris (HARVARD UNIVERSITY) |
Variations of Hodge Structures |
" |
November 23, 2015, 3:00 PM at Science Center 507 |
| THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY ) |
Mahowald's theorem on E_2 algebras |
" |
November 19, 2015, 3:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Nicolai Krylov (UNIVERSITY OF MINNESOTA) |
To the theory of viscosity solutions for uniformly parabolic Isaacs equations |
We show how a theorem about the solvability in $W^{1,2}_{\infty}$ of special parabolic Isaacs equations can be used to obtain the existence and uniqueness of viscosity solutions of general uniformly nondegenerate parabolic Isaacs equations. We apply it also to establish the $C^{1+\chi}$ regularity of viscosity solutions and show that finite-difference approximations have an algebraic rate of convergence. The main coefficients of the Isaacs equations are supposed to be in $C^{\gamma}$ with respect to the spatial variables with $\gamma$ slightly less than $1/2$" |
November 19, 2015, 10:00 AM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Peng Jian (HARVARD SCHOOL OF PUBLIC HEALTH) |
Inference of transcriptional regulation in cancers |
Despite the rapid accumulation of tumor molecular profiling datasets and transcription factor (TF) ChIP-seq profiles, efforts integrating TF binding with the tumor profiling data and understanding on how TFs regulate tumor gene expression have been limited. To systematically search for cancer associated TFs, we comprehensively integrated 686 ENCODE ChIP-seq profiles with 7857 TCGA tumor profiling data on gene expression, copy number alteration (CNA), DNA methylation and somatic mutation over 21 cancer types. For efficient and accurate inference on gene regulatory rules across a large number and variety of profiling datasets, we developed an algorithm Rabit (Regression analysis with background integration). In each tumor sample, Rabit tests whether the TF target genes from ChIP-seq show strong differential regulation controlling for background effect from CNA and DNA methylation. Rabit also refines the TF selection by matching the TF expression and mutation with activities on its putative targets across tumors, and prioritizes the most relevant ChIP-seq in a tumor type when multiple ChIP-seq for a TF are available. Our predicted TF impact on tumor gene expression is highly consistent with the knowledge from cancer related gene databases, and reveals many novel aspects of transcriptional regulation in tumor progression. We also applied Rabit on RNA binding protein motifs and found some alternative splicing factors could affect tumor-specific gene expression by binding to target gene 3âUTR regions. Thus, Rabit (http://rabit.dfci.harvard.edu) is a general platform for predicting the oncogenic role of gene expression regulators" |
November 18, 2015, 4:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Louis-Pierre Arguin (CUNY) |
The maximum of the characteristic polynomial of random unitary matrices |
A recent conjecture of Fyodorov, Hiary & Keating (FHK) states that the maxima of the characteristic polynomial of random unitary matrices behave like the maxima of a specific class of Gaussian fields, the so-called log-correlated Gaussian fields. These include important examples such as branching Brownian motion and the 2D Gaussian free field. In this talk, we will highlight the connections between the two problems. We will outline the proof of the conjecture for the leading order of the maximum. We will also discuss the connections with the FHK conjecture for the maximum of the Riemann zeta function on the critical line. This is based on joint works with D. Belius (NYU), P. Bourgade (NYU), and A. Harper (Cambridge)" |
November 18, 2015, 2:00 PM at Science Center 232 |
| NUMBER THEORY SEMINAR |
Carl Wang Erickson (BRANDEIS UNIVERSITY) |
Ordinary pseudorepresentations, modular forms, and Iwasawa theory |
When we study Hida families of ordinary modular forms that are congruent to Eisenstein series, the associated module with Galois action is not always a representation, i.e. not locally free. However, it does carry a Galois pseudorepresentation, which is the data of characteristic polynomial coefficients. Joint work with Preston Wake has produced a universal deformation ring for ordinary pseudorepresentations, which can be compared with the Hida Hecke algebra. I will discuss how this comparison is related to cyclotomic Iwasawa theory, and produces a new proof of some of the residually reducible modularity results of Skinner and Wiles." |
November 18, 2015, 3:00 - 4:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Xin Zhou (MIT) |
Min-max theory in Gaussian space and Entropy Conjecture |
Minimal surfaces in the Gaussian space are called self-shriners, which model the singularities of Mean Curvature Flow. Self-shrinkers are unstable with respect to the second variation of area. Any variational construction of self-shrinkers must be of min-max type. In this talk, we will introduce a min-max theory for constructing self-shrinkers. As an application, we will address a conjecture concerning the entropy of closed surfaces. The entropy is a quantity which measures complexity of a surface. Colding-Ilmanen-Minicozzi-White conjectured that the entropy of a closed surface is bounded from below by that of a round sphere. We will give a min-max proof of this conjecture for two spheres. In fact, the entropy is in many ways similar to that of the Willmore functional, and our argument is analogous in many ways to that of Marques-Neves on the Willmore problem. This is based on a joint work with Dan Ketover" |
November 17, 2015, 4:15 PM at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Bas Janssens (UTRECHT) |
Reflection Positivity for Majoranas and Spins |
" |
November 17, 2015, 4:15 PM at Jefferson 356 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR |
Ovidiu Savin (COLUMBIA UNIVERSITY) |
Examples of singular minimizers in the calculus of variations |
We construct a singular global minimizer from R^3 to R^2 to a uniformly convex smooth integrand in the calculus of variations. This is a joint work with C. Mooney" |
November 17, 2015, 10:00 AM at Science Center 232 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Curt McMullen (HARVARD UNIVERSITY) |
Cubic curves and Teichmuller theory |
" |
November 17, 2015, 3:00 PM at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Thomas Spencer (INSTITUTE FOR ADVANCED STUDY) |
Randomness in Classical and Quantum Dynamics |
" |
November 17, 2015, 1:15 pm at Jefferson 453 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Mu-Tao Wang (COLUMBIA UNIVERSITY) |
Stability of Lagranian curvature flows |
I shall present some new stability theorems of Lagrangian curvature flows in both the cotangent bundle case and the Calabi-Yau case. The talk will be based on joint work with Knut Smoczyk and Mao-Pei Tsui, and joint work with Chung-Jun Tsai." |
November 16, 2015, 12:00 PM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Nicholas Zygouras (UNIVERSITY OF WARWICK) |
From disorder relevance to the 2d Stochastic Heat Equation |
We consider statistical mechanics models defined on a lattice, in which disorder acts as an external random field. Such models are called disorder relevant, if arbitrarily weak disorder changes the qualitative properties of the model. Via a Lindeberg principle for multilinear polynomials we show that disorder relevance manifests itself through the existence of a disordered high-temperature limit for the partition function, which is given in terms of Wiener chaos and is model specific. When disorder becomes marginally relevant a fundamentally new structure emerges, which leads to a universal scaling limit for all different (currently directed polymer) models that fall in this class. A notable such representative is the two dimensional SHE with multipicative space-time white noise (which in the SPDE language is characterised as \critical). In this case certain analogies with Gaussian Multiplicative Chaos and log-correlated Gaussian fields appear" |
November 16, 2015, 2:00 PM at Science Center 530 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Caitlin Leverson (DUKE UNIVERSITY) |
Legendrian link invariants |
Given a plane field $dz-xdy$ in $\mathbb{R}^3$. A Legendrian knot is a knot which at every point is tangent to the plane at that point. One can similarly define a Legendrian knot in any contact 3-manifold (manifold with a plane field satisfying some conditions). In this talk, we will talk about Legendrian knots in $\mathbb{R}^3$, $J^1(S^1)$, and $\#^k(S^1\times S^2)$. In particular, we will look at the relationship between two Legendrian knot invariants, normal rulings and augmentations of the Chekanov-Eliashberg differential graded algebra. No knowledge of the Chekanov-Eliashberg DGA will be assumed" |
November 13, 2015, 3:30 - 4:30 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Zhouping Xin (CHINESE UNIVERSITY OF HONG KONG) |
Nonlinear Asymptotic Stability of Lane-Emden Solutions for The Viscous Gaseous Star Problem |
In this talk, I will present some recent results on the dynamical stability of the Lane-Emden solutions for the evolution of viscous gaseous stars under radial-symmetric perturbations. The nonlinear asymptotic stability of the Lane-Emden solution is proved with detailed rates of point-wise convergence. Besides the geometric singularity at the center of the symmetry , the main difficulty lies in the lower regularity (Holder continuity with exponent half) of the sound speed across the free vacuum boundary. Some new weighted nonlinear functionals are introduced to obtain higher estimates which are uniform both in time and also up to the vacuum boundary. Some of main ideas of the analysis will be discussed" |
November 12, 2015, 1st talk: 9:30 - 10:30 am at Science Center 232 |
| THURSDAY SEMINAR |
Peter Scholze (UNIVERSITY OF BONN) |
TBA |
" |
November 12, 2015, 3:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Nicolai Krylov (UNIVERSITY OF MINNESOTA) |
On the existence of $\bf W^{2}_{p}$ solutions for fully nonlinear elliptic equations under relaxed convexity assumptions |
" |
November 12, 2015, 2nd talk: 10:30 - 11:30 am at Science Center 232 |
| NUMBER THEORY SEMINAR |
Cristian Popescu (UC SAN DIEGO) |
Abstract l-adic 1-motives and applications |
We will define a family of Iwasawa modules which emerged from our joint work with Greither on the equivariant main conjecture in Iwasawa theory. We will discuss their Iwasawa theoretic properties with an eye on applications to various open problems in the theory of special values of equivariant Artin L-functions. Note: Audience members who are less familiar with this subject might benefit from attending the Basic Notions Seminar lecture of November 9" |
November 11, 2015, 3:00 - 4:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Stan Osher (joint work with Jerome Darbon) (UCLA) |
Overcoming the curse of dimensionality for certain Hamilton-Jacobi (HJ)equations arising in control theory and elsewhere |
It is well known that certain HJ PDE s play an important role in analyzing continuous dynamic games and control theory problems. The cost of standard algorithms, and, in fact all PDE grid based approsimations is exponential in the space dimension and time, with huge memory requirements. Here we propose and test methods for solving a large class of HJ PDE relevant to optimal control without the use of grids or numerical approximations. Rather we use rhe classical Hopf formulas for solving initial value problems for HJ PDE. We have noticed that if the Hamiltonian is convex and positively homogeneous of degree one that very fast methods (related to those used in compressed sensing) exist to solve the resulting optimization problem. We seem to obtain methods which are polynomial in dimension. We can evaluate the solution in very high dimensions in between 10^(-4) and 10^(-8) seconds per evaluation on a laptop. The method requires very limited memory and is almost perfectly parallelizable. In addition, as a step often needed in this procedure, we have developed a new and equally fast and efficient method to find, in very high dimensions, the projection of a point exterior to a compact set A onto A. We can also compute the distance to such sets much faster than fast marching or fast sweeping algorithms. The term curse of dimensionality was coined by Richard Bellman in 1957 when he did his pioneering work on dynamic optimization" |
November 11, 2015, 4:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR |
Jerome Darbon (CNRS/CMLA ECOLE NORMALE SUPERIEURE DE CACHAN) |
On Convex Finite-Dimensional Variational Methods in Imaging Sciences and Hamilton-Jacobi Equations |
We consider standard finite-dimensional variational models used in signal/image processing that consist in minimizing an energy involving a data fidelity term and a regularization term. We propose new remarks from a theoretical perspective which give a precise description on how the solutions of the optimization problem depend on the amount of smoothing effects and the data itself. The dependence of the minimal values of the energy is shown to be ruled by Hamilton-Jacobi (HJ) equations, while the minimizers u(x,t) for the observed images x and smoothing parameters t are given by u(x,t)= x - \nabla H(\nabla_x E(x,t)) where E(x,t) is the minimal value of the energy and H is a Hamiltonian related to the data fidelity term. Various vanishing smoothing parameter results are derived illustrating the role played by the prior in such limits. We will briefly introduce how the approach can be adapted to cope with a class of optimal control problems involving HJ equations with positively 1-homogeneous Hamiltonians. The fast numerical algorithms for solving the latter on overcoming the curse of dimensionality will be given in the talk of Stanley Osher" |
November 10, 2015, 1st talk: 9:30 - 10:30 am at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR |
Adam Jacob (UC DAVIS) |
(1,1) forms with specified Lagrangian phase |
In this talk I will define a complex version of the special Lagrangian graph equation with potential introduced by Harvey-Lawson. I will discuss existence of solutions on a compact Kahler manifold under certain analytic assumptions. I will also talk about a conjecture relating existence in general to an algebro-geometric notion of stability (analogous to slope stability for holomorphic vector bundles), and provide motivation from mirror symmetry. This is joint work with Tristan C. Collins and S.-T. Yau" |
November 10, 2015, 2nd talk: 10:30 - 11:30 am at Science Center 232 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Boris Hanin (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
Nodal Sets of Random Eigenfunctions of the Harmonic Oscillator |
Random eigenfunctions at energy E of the isotropic harmonic oscillator in R^d have an U(d) symmetry and are in some ways analogous to random spherical harmonics of fixed degree on S^d, whose nodal sets have been the subject of many recent studies. However, there is a fundamentally new aspect to this ensemble, namely the existence of allowed and forbidden regions. In the allowed region, the Hermite functions behave like spherical harmonics, while in the forbidden region, Hermite functions are exponentially decaying and it is unclear to what extent they oscillate and have zeros. The purpose of this talk is to present several results about the expected volume of the zero set of a random Hermite function in both the allowed and forbidden regions. This is joint work with Steve Zelditch and Peng Zhou" |
November 10, 2015, 4:15 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Cristian Popescu (UC SAN DIEGO) |
The arithmetic of special values of L-functions |
The well-known analytic class number formula, linking the special value at s=0 of the Dedekind zeta function of a number field to its class number and regulator, has been the foundation and prototype for the highly conjectural theory of special values of L-functions. We will discuss generalizations of the class number formula to the context of equivariant Artin L-functions which capture refinements of the Brumer-Stark and Coates-Sinnott conjectures. These generalizations relate various algebraic-geometric invariants associated to a global field, e.g. its Quillen K-groups and etale cohomology groups, to various special values of its Galois-equivariant L-functions. They illustrate the subtle interactions of number theory with complex and p-adic analysis, algebraic geometry, topology and homological algebra" |
November 09, 2015, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Yan Guo (BROWN UNIVERSITY - DIVISION OF APPLIED MATHEMATICS) |
Regularity of Boltzmann Solutions in Convex Domains |
Boundary interactions play an important role in the study of PDE arising in the kinetic theory. The presence of the grazing set in the phase space makes the boundary characteristic but not uniformly characteristic, which leads to considerable difficulty to study regularity. In this talk, solutions to the Boltzmann equation are shown to be C^1 away from the grazing set in a bounded convex domain" |
November 09, 2015, 1:00 - 2:00 PM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Alireza Behtash (NORTH CAROLINA STATE UNIVERSITY) |
Lefschetz Thimbles and Supersymmetric Quantum Mechanics |
I will try to give an overview of supersymmetric quantum mechanics (SQM) from a different perspective. I will focus on $\mathcal{N}=2$ that is more interesting than $\mathcal{N}=1$ which will be covered briefly near the end of my talk. I will say a little about a possible semi-classical approach to $\mathcal{N}=4$ SQMs by giving a very basic example. The tools we will need are (1) the axiom of" |
November 09, 2015, 12:00 - 1:00 PM at Science Center 232 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Thomas Walpuski (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
A proposal for U(1)â"gauge theory on G_2â"manifolds |
Asking the question which geometric structures enable one to formally setup an analogue of the ChernâSimons functional, familiar from low-dimensional gauge theory, one is naturally led to G_2âmanifolds and the notion of G_2âinstantons. However, considerable issues (to do with failure of compactness) arise when trying to actually construct invariants from the G_2âanalogue of the ChernâSimons functional. Joint work with Andriy Haydys suggests that some of this issues may be overcome using generalised SeibergâWitten equations associated with the ADHM construction. This leads to a preliminary proposal of a conjectural gauge theoretic invariant for G2âmanifolds, which is very unwieldy. However, one can consider the edge case where the structure is U(1). Unlike the naive approach to U(1)âgauge theory on G_2âmanifolds, this does not yield a theory that is a priori trivial. I will describe three possible geometric degenerations and (my naive) expectations of how this proposal works out in these cases" |
November 06, 2015, 3:30 - 4:30 PM at Science Center 507 |
| HARVARD, BRANDEIS, MIT, NORTHEASTERN JOINT COLLOQUIUM AT HARVARD |
Tom Goodwillie (BROWN UNIVERSITY) |
Characteristic classes for bundles of manifolds |
Most smooth fiber bundles having closed disks as fibers are exotic in the sense that they do not arise from vector bundles. This has been known since the 1970s, using algebraic K-theory. Allen Hatcher suggested a concrete way of constructing exotic bundles using the space G/O. Kiyoshi Igusa provided an invariant called higher Reidemeister torsion that can detect exotic bundles and showed that it is nontrivial on Hatcher s construction. Goodwillie, Igusa, and Ohrt extended some of these ideas to settings involving manifolds with free cyclic group actions, and Goodwillie and Igusa are working on further generalizations involving arbitrary finite groups and non-free actions" |
November 05, 2015, Tea at 4:00 PM, the Austine & Chilton McDonnell Common Room, Science Center 4th Floor, Talk at 4:30 pm at Science Center Hall A |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Thomas Y. Hou (CALIFORNIA INSTITUTE OF TECHNOLOGY) |
Blowup or no blowup? The interplay between theory and computation in the study of 3D Euler equations |
Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This question is closely related to the Clay Millennium Problem on 3D Navier-Stokes Equations. We first review some recent theoretical and computational studies of the 3D Euler equations. Our study suggests that the convection term could have a nonlinear stabilizing effect for certain flow geometry. We then present strong numerical evidence that the 3D Euler equations develop finite time singularities. To resolve the nearly singular solution, we develop specially designed adaptive (moving) meshes with a maximum effective resolution of order $10^12$ in each direction. A careful local analysis also suggests that the blowing-up solution is highly anisotropic and is not of Leray type. A 1D model is proposed to study the mechanism of the finite time singularity. Very recently we prove rigorously that the 1D model develops finite time singularity. This is a joint work of Prof. Guo Luo" |
November 04, 2015, 4:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Vadim Gorin (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
Largest eigenvalues in random matrix beta-ensembles: structures of the limit |
Despite numerous articles devoted to its study, the universal scaling limit for the largest eigenvalues in general beta log--gases remains a mysterious object. I will present two new approaches to such edge scaling limits. The outcomes include a novel scaling limit for the differences between largest eigenvalues in submatrices and a Feynman-Kac type formula for the semigroup spanned by the Stochastic Airy Operator. (based on joint work with M.Shkolnikov)" |
November 04, 2015, 2:00 PM at Science Center 232 |
| NUMBER THEORY SEMINAR |
Michael Harris (COLUMBIA UNIVERSITY) |
Modularity theorems in the function field setting and local Langlands parametrization |
Let G be a reductive group over a global field of positive characteristic. In a major breakthrough, Vincent Lafforgue has recently shown how to assign a semisimple Langlands parameter to a cuspidal automorphic representation of G. The parameter is a homomorphism of the global Galois group into the Langlands L-group ^LG of G. I will report on my joint work in progress with Böckle, Khare, and Thorne, whose goal is to develop the Taylor-Wiles-Kisin method in the setting of Lafforgue s correspondence. New (representation-theoretic and Galois-theoretic) issues arise when we seek to extend the earlier work of Böckle and Khare on the case of GL(n) to general reductive groups. I will describe hypotheses on the Langlands parameter that allow us to apply modularity arguments unconditionally, and explain how we reduce the proof of the surjectivity of Lafforgue s correspondence to a pair of conjectures that should be accessible with the help of the stable twisted trace formula" |
November 04, 2015, 3:00 - 4:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Binglong Chen (SUN YAT-SEN UNIVERSITY) |
On the local regularity of Einstein spacetimes |
On the local regularity of Einstein spacetimes Abstract: Given a spacetime manifold satisfying vacuum Einstein field equation, and an observer on the manifold, we will construct a canonical coordinate system around this observer so that the coefficients of the metric tensor can gain the optimal (quantitative) regularity" |
November 03, 2015, 4:15 PM at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Xiao-Gang Wen (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
A Classification of Phases of Matter with No Symmetry in Two Spatial Dimensions |
" |
November 03, 2015, 1:15 pm at Jefferson 453 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR |
Thomas Y. Hou (CALIFORNIA INSTITUTE OF TECHNOLOGY) |
Existence and stability of self-similar singularities for a 1D model of the 3D axisymmetric Euler equations |
We investigate the self-similar singularity for a 1D model of the 3D axisymmetric Euler equations, which is motivated by a particular singularity formation scenario observed in a recent numerical computation by Hou and Luo. Using a very delicate method of analysis which involves computer aided proof, we prove the existence of a discrete family of self-similar profiles for this model. The self-similar profiles we obtain agree with those obtained by direct numerical simulations of the model. Moreover, the self-similar profile seems to enjoy some stability property. The self-similar profiles we construct are non-conventional in the sense that they do not decay to zero at infinity but grow with certain fractional power. Such behavior is also observed in the numerical computation of the 3D Euler equations and is very different from the Leray type of self-similar solutions of the 3D Euler equations. We are currently investigating the possibility of extending this method to study the singularity formation of the 2D Boussinesq system" |
November 03, 2015, 10:00 AM at Science Center 232 |
| MATHEMATICAL PHYSICS SEMINAR |
Adrian Ocneanu (PENNSYLVANIA STATE UNIVERSITY) |
Higher Symmetry Models and Quantum Field Theory |
" |
November 03, 2015, 4:15 PM at Jefferson 356 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Rohini Ramadas (UNIVERSITY OF MICHIGAN) |
Hurwitz correspondences on compactifications of M0,N |
Hurwitz correspondences are multivalued maps from M0,N1 to M0,N2 that descend from holomorphic maps on Teichmuller space. We consider the dynamics of Hurwitz self-correspondences and ask: On which compactifications of M0,N should they be studied? We compare a Hurwitz self-correspondence H on two different compactifications: the stable curves compactification Mbar0,N and an alternate weighted stable curves compactification. We use this comparison to show that, for k > ( dim M0,N - 1 )/2, the k-th dynamical degree of H is the absolute value of the largest eigenvalue of the pushforward map induced by H on a comparatively small quotient of H2k(M0,N)" |
November 03, 2015, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Ryan Mickler (NORTHEASTERN UNIVERSITY) |
A new look at Chern-Simons on circle bundles |
We consider Chern-Simons theory on 3-manifold M that is the total space of a circle bundle over a 2d base ÎŁ. We show that this theory is equivalent to a new 2d TQFT on the base, which we call Caloron BF theory, that can be obtained by an appropriate type of push-forward of higher abelian gerbes. This is a gauge theory on a bundle with structure group given by the affine level k central extension of the loop group LG. The space of fields of this 2d theory is naturally symplectic, and this provides a new formulation of a result of Beasley-Witten about the equivariant localization of the Chern-Simons path integral on such 3-manifolds. If time permits, we will discuss a class of D-branes in this theory" |
November 02, 2015, 12:00 - 2:00 PM at Science Center 232 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY |
Richard Hind (NOTRE DAME) |
Embeddings of Lagrangian tori |
I will survey some rigidity and flexibility results for symplectic embeddings, and ask whether rigidity results for polydisks can be seen from properties of their singular Lagrangian boundary. By producing some optimal embeddings of Lagrangian tori we will see that in general this is not the case. This is joint work with Emmanuel Opshtein" |
October 30, 2015, 3:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
The Filtration on THH (Characteristic p Case) |
" |
October 29, 2015, 3:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Pin Yu (TSINGHUA UNIVERSITY) |
Shock formations for 3 dimensional wave equations |
We study a family of 3 dimensional quasi-linear wave equations derived from variational principle. We exhibit a family of smooth initial data and show that the foliation of the incoming characteristic hypersurfaces collapses. No symmetry condition is imposed on the initial datum. The proof is inpired by the techniques used in studying the formation of shocks for compressible Euler equations and the formation of black holes in general relativity" |
October 29, 2015, 10:00 AM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Cris Moore (SANTA FE INSTITUTE) |
Statistical inference, statistical physics, and the community detection problem |
There is a deep analogy between statistical inference â where we try to fit a model to data, or more generally understand the posterior distribution of models given the data â and statistical physics, where we define a probability distribution in terms of some energy function. Many concepts like energy landscapes, partition functions, free energy, the cavity method, and phase transitions can be usefully carried over from physics to machine learning and computer science. At the very least, these techniques are a source of conjectures that have stimulated new rigorous work in machine learning, computer science, and probability theory; at their best, they offer strong intuitions about the structure of these problems and their possible solutions. One recent success of this flow of ideas is the discovery of a sharp phase transition in community detection in sparse graphs. This appeared in Decelle et al. in the physics literature, and was then made rigorous in beautiful work by Mossel, Neeman, and Sly, and Massoulie. Analogous transitions exist in many other inference problems, where our ability to find patterns in data jumps suddenly as a function of how noisy or how sparse they are. I will discuss why and how the detectability transition occurs, review what is now known rigorously, and present a number of open questions that cry out for proofs. This is based on joint work with many people, including Aurelien Decelle, Florent Krzakala, Lenka Zdeborova, and Pan Zhang" |
October 28, 2015, 4:00 - 5:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Lassina Dembele (UNIVERSITY OF WARWICK AND ICERM) |
Lifts of Hilbert modular forms and applications to modularity |
In this talk, we will discuss the existence of certain theta lifts for Hilbert modular forms, and their connection to the modularity of abelian varieties. These lifts are generalisations of a construction of Johnson-Leung and Roberts for real quadratic fields. (This is joint work with Clifton Cunningham." |
October 28, 2015, 3:00 - 4:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Monther R. Alfuraidan & Mohamed Amine Khamsi (KING FAHD UNIVERSITY & UNIVERSITY OF TEXAS AT EL PASO) |
Graphical approach to some fixed point problems |
In this joint talk, we will discuss a new area that overlaps between metric fixed point theory and graph theory. This new area yields interesting generalizations of the Banach contraction principle in metric and modular spaces endowed with a graph. The bridge between both theories is motivated by the fact that they often arise in industrial fields such as image processing engineering, physics, computer science, economics, ladder networks, dynamic programming, control theory, stochastic filtering, statistics, telecommunication and many other applications" |
October 28, 2015, 11:00 AM at Science Center 530 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX AND PROBABILITY SEMINAR |
Vu-Lan Nguyen (UNIVERSITĂ© PARIS DIDEROT ) |
Variants of geometric RSK, geometric PNG and the multipoint distribution of the log-gamma polymer |
The geometric Robinson-Schensted-Knuth (gRSK) correspondence has played an important role in the recent analysis of the directed polymer model with a log-Gamma potential. In particular, it has led to the confirmation of the Tracy-Widom GUE asymptotic distribution of its point-to-point partition function. In a joint work with Nikos Zygouras, we reformulate the gRSK correspondence in a way that leads to explicit integral formulae for the joint distribution of the point-to-point partition functions at different space-time points" |
October 28, 2015, 2:00pm at Science Center 232 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Thomas Walpuski (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
G2â"instantons over twisted connected sums |
In joint work with H. SĂĄ Earp, we introduced a method to construct G2âinstantons over compact G2âmanifolds arising as the twisted connected sum of a matching pair of building blocks. I will recall some of the background (including the twisted connected sum construction and a short discussion as to why one should care about G2âinstantons), discuss our main result and explain how to interpret it in terms of certain Lagrangian subspaces of a moduli space of stable bundles on a K3 surface. Finally, I will talk about how to use our construction to produce a rather concrete example of a G2âinstanton over twisted connected sum recently discovered by Crowley and Nordström" |
October 27, 2015, 4:15 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Ana Caraiani (PRINCETON UNIVERSITY) |
On vanishing of torsion in the cohomology of Shimura varieties |
I will discuss joint work with Peter Scholze showing that torsion in the cohomology of certain compact unitary Shimura varieties occurs in the middle degree, under a genericity assumption on the corresponding Galois representation. I will focus on the constructions underlying the proof, in particular on the geometry of the Hodge-Tate period morphism for Shimura varieties" |
October 27, 2015, 3:00 PM at MIT E17-128 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Liang Kong (UNIVERSITY OF NEW HAMPSHIRE & CMSA, HARVARD) |
Boundary-bulk relation for topological orders in any dimensions |
Recently, tremendous efforts have been made by theorists in condensed matter physics to understand a new type of phases of matter, called topological orders. The boundary-bulk relation (or bulk-edge correspondence) plays an important role in the study of topological orders. In this talk, I will start with a proposal of a precise mathematical formulation of the boundary-bulk relation for topological orders in any dimensions. This formulation automatically includes the relation between dualities and domain walls. Then I will construct a family of 2+1D lattice models to explicitly demonstrate this boundary-bulk relation. In a seminar scheduled on the same day (9:00-10:30AM), I will discuss the boundary-bulk relation (or holographic phenomena) in more general context in both mathematics and physics" |
October 26, 2015, 12:00 - 2:00 PM at Science Center 232 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Mohammed Abouzaid (COLUMBIA UNIVERSITY) |
Nearby Lagrangians are simply homotopic |
I will describe joint work with Thomas Kragh proving that closed exact Lagrangians in cotangent bundles are simply homotopy equivalent to the base. The main two ideas are (i) a Floer theoretic model for the Whitehead torsion of the projection from the Lagrangian to the base, and (ii) a large scale deformation of the Lagrangian which allows a computation of this torsion" |
October 23, 2015, 3:30 - 4:30 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Xiangdi Huang (CHINESE ACADEMY OF SCIENCES) |
On Nash's problem for compressible flows |
We establish a unified blow-up criterion for strong solutions of various compressible models, including baratropic, fully compressible and heat-conducting magneto hydrodynamic flows, which is analogous to the Serrin s criterion of Navier-Stokes equations. It gives an affirmative answer to a problem proposed by J. Nash in 1958. As an application, we prove global-in-time classical solutions of compressible flows allowing vacuum and large fluctunation of initial data provided the initial energy is small. In the end, we prove a strong version of Nashâs problem based on new observations" |
October 22, 2015, 10:00 AM at Science Center 232 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
The Topological Hochschild Homology of Z/p |
" |
October 22, 2015, 3:00 - 5:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
David Hansen (COLUMBIA UNIVERSITY) |
Critical p-adic L-functions |
I ll explain some new results on the critical p-adic L-functions associated with an elliptic curve over Q at a prime of good ordinary reduction. In particular, I ll explain why the two approaches to defining such a p-adic L-function (due to Kato and Pollack-Stevens) in fact yield the same function. This comparison explains a certain pattern (discovered numerically by Pollack-Stevens) in the zeros of the p-adic L-function; I ll describe this as well" |
October 21, 2015, 3:00 - 4:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Zhouping Xin (CHINESE UNIVERSITY OF HONG KONG) |
Entropy and Uniqueness of Weak Solutions to The Multi-Dimensional Compressible Euler Systems |
For the ideal compressible Euler systems, which are fundamental in fluid-dynamics and pro-type examples of nonlinear hyperbolic systems, one of the main features is that the characteristic speeds of a wave propagation depend on the wave itself which leads to the finite-time formation of shocks in general. Thus one has to work with weak solutions globally. Yet the uniqueness of the physical solutions becomes a challenging issue. In the one- dimensinal case, various admissible criterion have been introduced to rule out the non-physical solutions. In particular, the physical entropy can guarantee the uniqueness of weak solutions at least in the case of small variations. However, in higher space dimensions, for some given initial data, there are infinitely many highly oscillatory solutions (wild solutions) which are bounded, measurable and satisfying the physical entropy. In talk, I will review some progress on the constructions of such wild solutions by a method of convex integration; present some results on the structure of such wild solutions; and investigate the effects of lower order dissipations. Some open problems will be discussed." |
October 21, 2015, 4:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Nicholas Cook (UCLA) |
Random regular digraphs: singularity and spectrum |
We consider two random matrix ensembles associated to large random regular digraphs: (1) the 0/1 adjacency matrix, and (2) the adjacency matrix with i.i.d. bounded edge weights. Motivated by universality conjectures, we show that the spectral distribution for the latter ensemble is asymptotically described by the circular law, assuming the graph has degree linear in the number of vertices. Towards establishing the same result for the unweighted adjacency matrix, we prove that it is invertible with high probability, even for sparse digraphs with degree growing only poly-logarithmically" |
October 21, 2015, 2:00 - 3:00 PM at Science Center 232 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Michael Anderson (STONY BROOK) |
Boundary value problems for Einstein metrics and a conjecture of Bartnik |
We discuss elliptic boundary value problems for the Einstein equations. We ll then discuss corresponding existence results in dimension 3 and the simplest case in dimension 4, namely static vacuum Einstein metrics. This leads to a partial solution of a conjecture of Bartnik in general relativity (the static extension conjecture)." |
October 20, 2015, 4:15 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Anand Deopurkar (COLUMBIA UNIVERSITY) |
Syzygies, GIT, and the log MMP for Mg |
Let X be a projective variety with homogeneous coordinate ring R. We can encode the data of X in Pn as a point in a Grassmannian using linear-algebraic information from R. As X varies, the locus of such points forms a natural parameter space. For example, for sufficiently large m, the m th graded piece of R leads to the Hilbert scheme. I will describe an analogous construction using syzygies and its role in the log minimal model program for Mg" |
October 20, 2015, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Yifan Wang (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
Argyres-Douglas theories, Hitchin systems and Compound Du Val singularities |
Argyres-Douglas theories are ubiquitous 4d N=2 superconformal field theories first discovered as nontrivial IR fixed points of 4d N=2 supersymmetric gauge theories. They have mutually non-local massless BPS states and in general do not have a weak coupling expansion. A large class of these theories can be constructed from M5 branes of ADE type wrapping a sphere whose stable configuration is governed by the corresponding Hitchin system with a single irregular singularity, as well as from IIB string theory probing a general 3-fold singularity. In this talk, I will present a classification of the Argyres-Douglas theories that arise from irregular singularities of Hitchin systems, and identify the equivalent IIB geometric description in terms of isolated quasi-homogenous cDV (compound Du Val) singularities. I will also discuss extensions of the M5 brane construction that involve degeneration limits of the irregular singularity, an additional regular puncture, and outer-automorphism twists" |
October 19, 2015, 12:00 - 2:00 PM at Science Center 232 |
| BASIC NOTIONS SEMINAR |
Wilfried Schmid (HARVARD UNIVERSITY) |
Automorphic distributions |
Automorphic distributions determine, and are determined by, automorphic representations. I shall describe how they can be used to prove the analytic continuation and holomorphy of certain Langlands L-functions" |
October 19, 2015, 3:00 - 4:00 PM at Science Center 507 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Cheuk Yu Mak (MINNESOTA) |
Divisorial caps, uniruled caps and Calabi-Yau caps |
We illustrate how a nice symplectic cap captures properties of symplectic fillings of a contact 3-manfiold. Three kinds of symplectic caps are introduced. Divisorial caps are motivated from compactifying divisors in algebraic geometry. Uniruled caps give strong restriction to symplectic fillings for a class of contact 3-manifolds strictly larger than the planar ones. Calabi-Yau caps, in particular, can be used to derive uniform Betti numbers bounds on Stein fillings of the standard unit cotangent bundle of any hyperbolic surface. This is a joint work with Tian-Jun Li and Kouichi Yasui" |
October 16, 2015, 3:30 - 4:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY ) |
Cyclotomic spectra and the de Rham-Witt complex |
" |
October 15, 2015, 3:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Zhouping Xin (CHINESE UNIVERSITY OF HONG KONG) |
On Global Well-Posedness of The Compressible Navier-Stokes Systems with Large Oscillations |
I this lecture, I will discuss some issues involving the global (in time) well-posedness of strong solutions to the multi-dimensional compressible Navier-Stokes systems with data which may have large oscillations and vacuum. Blow-up phenomena will be discussed and global existence of regular solutions with small energy will be proved. Though such solutions have small energies, yet they may have large oscillations and contain vacuum in both interior and far fields. In particular, The uniqueness and regularity of weak solutions by P. L. Lions will be shown provided that the weak solutions have small Initial energy. Some of the main ideas for the analysis will be discussed" |
October 15, 2015, 10:00 AM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Boaz Barak (HARVARD UNIVERSITY SEAS) |
Convexity, Bayesianism, and the quest towards Optimal Algorithms |
In this high level and accessible talk I will describe a recent line of works aimed at trying to understand the intrinsic complexity of computational problems by finding *optimal* algorithms for large classes of such problems. In particular, I will talk about efforts centered on convex programming as a source for such candidate algorithms. As we will see, a byproduct of this effort is a computational analog of Bayesian probability that is of its own interest. I will demonstrate the approach using the example of the hidden (or planted) clique problem - a central problem in average case complexity with connections to machine learning, community detection, compressed sensing, finding Nash equilibrium and more. While the complexity of this problem is still wide open, this line of works has led to interesting insights on it" |
October 14, 2015, 4:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Wei Zhang (COLUMBIA UNIVERSITY) |
Cycles on the moduli of Shtukas and Taylor coefficients of L-functions (II) **Note: This is a continuation of Zhiwei Yun's talk, on Oct 13, 4:30-5:30pm in MIT room E17-122. |
In our joint work, we prove a generalization of Gross-Zagier formula in the function field setting. Our formula relates self-intersection of certain cycles on the moduli of Shtukas for GL(2) to higher derivatives of L-functions" |
October 14, 2015, 3:00 - 4:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Benjamin Schweinhart (CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS) |
Universality Conjectures for Curvature Flow on Graphs |
Curvature flow on graphs and cell complexes is an important model for grain growth in polycrystalline materials. I will introduce these concepts, and state several universality conjectures about their long term behavior. This talk is based on joint work with Robert MacPherson and Jeremy Mason" |
October 14, 2015, 2:00 - 3:00 PM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR |
Pengfei Guan (MCGILL UNIVERSITY) |
Isometric embeddings of $(S^2,g)$ to general warped product space $(N^3,\bar g)$. |
We discuss recent work on the Weyl problem of isometric embeddings of $(S^2, g)$ to general ambient space $(N^3, \bar g)$ with warped product structure. When $N^3$ is $R^3$, it is the classical Weyl s problem, which was solved by Nirenberg in 1950s (when $g$ is analytic, it was solved by H. Levy prior to Nirenberg s work). Pogorelov also considered problem when $N$ is the hyperbolic space $H^3$. Solutions to Weyl s problem in $R^3$ and $H^3$ have important applications in general relativity, e.g., the Brown-York and Liu-Yau quasi local masses. The recent work of Wang-Yau further indicates the importance of understanding isometric embedding problem. We establish curvature estimates for immersed surfaces in warped product space in general, discuss the existence of solutions of the problem.  In contrast to the space form cases, there is non-rigidity when $N^3$ is not a space form. Part of the work is jointly with Siyuan Lu. The openness and non-rigidity results are due to C. Li and Z. Wang" |
October 13, 2015, 10:00 AM at Science Center 232 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Alex Perry (HARVARD UNIVERSITY) |
Categorical joins |
Homological projective duality is a powerful theory developed by Kuznetsov for studying the derived categories of varieties. It can be thought of as a categorification of classical projective duality. I will describe a categorical version of the classical join of two projective varieties, and its relation to homological projective duality. I will discuss some applications to the structure of the derived categories of Fano varieties and to derived equivalences of Calabi-Yau varieties. This is work in progress with Alexander Kuznetso" |
October 13, 2015, 3:00 PM at MIT E17-122 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Adrian Zahariuc (HARVARD UNIVERSITY) |
Specialization of Quintic Threefolds to the Chordal Variety |
We consider a family of quintic threefolds specializing to a certain reducible threefold with two irreducible components. What are the flat limits of the rational curves in this degeneration? I will provide a âfirst approximationâ to the answer by describing the space of genus zero stable morphisms to the central fiber (as defined by J. Li)." |
October 13, 2015, 4:15 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Chunjing Xie (SHANGHAI JIAO TONG UNIVERSITY) |
Steady Euler flows past a wall or through a nozzle |
In this talk, we discuss the well-posedness theory for the steady Euler flows past a wall or through a nozzle. The steady Euler system is reduced to a single second order equation when the streamline of the flows have simple topological structure. Our focus is on the subsonic flows with large vorticity" |
October 08, 2015, 10:00 AM at Science Center 232 |
| HARVARD, BRANDEIS, MIT, NORTHEASTERN JOINT COLLOQUIUM AT HARVARD |
Kenji Fukaya (SIMONS CENTER FOR GEOMETRY & PHYSICS, STONY BROOK UNIVERSITY) |
SO(3) Floer homology with 3 manifold with boundary |
Donaldson invariant and its relative version which takes value in instanton Floer homology was the topic much studied. In 1990 s various people studied the problem to extend this 4 + 3 picture to include 2 dimension. In this talk I explain this problem and certain progress we made recently" |
October 08, 2015, 4:30 pm ; Tea at 4:00 PM, the Austine & Chilton McDonnell Common Room, Science Center 4th Floor at Science Center Hall A |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
THH without equivariant homotopy theory |
" |
October 08, 2015, 3:00 - 5:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Kiran S. Kedlaya (UNIVERSITY OF CALIFORNIA AT SAN DIEGO) |
Convergence polygons for p-adic differential equations |
Consider an ordinary differential equation whose coefficients are rational functions over Q. Just like over C, we can solve this differential equation formally in power series around any nonsingular p-adic point; any such formal solution does converge in a disc, but maybe a smaller disc than expected (e.g., the exponential series). However, one can quantify such failures in a uniform way, by defining a certain Newton polygon and viewing it as a function on the Berkovich analytic projective line. In this one way, one encapsulates much of the knowledge developed about p-adic differential equations from the 1960s (work of Dwork) to the present" |
October 07, 2015, 3:00 - 4:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Chris Rogan (HARVARD UNIVERSITY PHYSICS) |
Exploring the Frontier of Size and Energy with the Large Hadron Collider: sub-atomic particles, the Higgs Boson and beyond. |
The Large Hadron Collider (LHC) is the worldâs most powerful probe of the experimental physics frontier and the largest scientific instrument ever built. On the outskirts of Geneva, Switzerland at the CERN physics laboratory it has been used to collide protons at an unprecedented energy, allowing researchers to peer into the world of the smallest lengths scales currently accessible to mankind and unlock some of Natureâs previously hidden secrets. We view this world using particle detectors, the worldâs largest and most complex cameras which take snapshots of high-energy proton collisions millions of times a per second, revealing a violent and beautiful place that resembles the universe moments after the big bang, very unlike the everyday world we are accustomed to yet integral to its existence. This colloquium will provide an introduction to this subatomic world, the particles that reside there and the forces that govern them. It will describe the LHC machine and the particle detectors located there, how they work and what scientists use them for. We will review the accomplishments of the LHC experiments so far: the confirmation of the Standard Model of particle physics at a new energy and length scale and the discovery of the Higgs Boson. Finally we will look forward into the unknown and discuss what other answers the LHC may be able to provide in the coming years, such as the identity of the Dark Matter that pervades the universe" |
October 07, 2015, 4:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Martin Zirnbauer (COLOGNE/SIMONS CENTER) |
Bott periodicity and the "Periodic Table" of topological insulators and superconductors |
Bott periodicity is said to be one the most surprising phenomena in topology. Perhaps even more surprising is its recent appearance in condensed matter physics. Building on work of Schnyder et al, Kitaev argued that symmetry-protected ground states of gapped free-fermion systems, also known as topological insulators and superconductors, organize into a kind of periodic table governed by a variant of the Bott periodicity theorem. In this colloquium, I will sketch the mathematical background, the physical context, and some new results of this ongoing story of mathematical physics" |
October 07, 2015, 2:00 - 3:30 PM at Science Center 232 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
Algebraic and motive vector bundles |
I will discuss ongoing work with Aravind Asok and Jean Fasel on the problem of finding algebraic structures on (topological) complex vector bundles over algebraic varieties" |
October 06, 2015, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Song Sun (STONY BROOK) |
Singularities of Kahler-Einstein metrics and algebraic stability |
A natural question in Kahler geometry is to understand degenerations and singularity formations of Kahler manifolds (in particular, of Kahler-Einstein manifolds). Given a sequence of Kahler-Einstein manifolds satisfying certain non-collapsing hypothesis, we proved earlier that a Gromov-Hausdorff limit, which is a priori only a metric space, has a natural structure of a normal projective variety. These limit spaces admit metric tangent cones, which serve as local models for the metric singularities, and it is then interesting to ask for the meaning in terms of algebraic geometry. We will report recent progress towards this question. Our work suggests a notion of ``stabilityâ for germs of algebraic singularities. This talk is based on joint work with Simon Donaldson." |
October 06, 2015, 4:15 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR |
Binglong Chen (SUN YAT-SEN UNIVERSITY) |
Ricci flow and the moduli spaces of positive isotropic curvature metrics on four-manifolds |
It is well-known that in lower dimensions, the Ricci flow can often be used to give âcanonical geometric structuresâ on the manifolds. We observe that in the same time, the Ricci flow provides a deformation of the moduli spaces of Riemannian metrics, and it is possible that Ricci flow can be used to reveal the topological structures of the moduli spaces of Riemannian metrics with certain curvature restrictions. Our main result of the talk is to prove that the moduli spaces of positive isotropic curvature metrics on many 4-manifolds, including 4-sphere etc., are path-connected. This talk is based on a joint work with XianTao Huang.Â" |
October 06, 2015, 10:00 AM at Science Center 232 |
| BASIC NOTIONS SEMINAR |
Clifford Taubes (HARVARD UNIVERSITY) |
4-manifold topology (or maybe geometry) and hyperbolic knots in the 3-sphere |
A 4-manifold can be constructed that has some curious metric properties, or maybe it is many 4-manifolds masquerading as one, which would explain why it looks curious. I am not sure. Anyway, knots in the 3-sphere with complete finite volume metrics on their complements play a role in this story" |
October 05, 2015, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Erik Carlsson (CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS) |
agt and the segal sugawara construction |
the agt conjectures predict a relationship between certain Nekrasov partition functions in supersymmetric 4d gauge theory and correlation functions from Liouville conformal field theory. A mathematical study should involve constructing operators on the comology of the instanton moduli space that intertwine certain already existing algebraic structures due to many authors. The first case follows from the construction of the Ext operator on the Hilbert scheme of points on a general surface by Okounkov and myself, and in hindsight is sometimes called agt in rank 1. I ll explain what the original conjectures say mathematically, and present a recent construction that implies an important special case of the higher rank conjectures, which has some compelling geometric implications" |
October 05, 2015, 12:00 - 2:00 PM at Science Center 232 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Chris Wendl (UNIVERSITY COLLEGE LONDON) |
Tight contact structures on connected sums need not be contact connected sums |
In dimension three, convex surface theory implies that every tight contact structure on a connected sum M # N can be constructed as a connected sum of tight contact structures on M and N. I will explain some examples showing that this is not true in any dimension greater than three. The proof is based on a recent higher-dimensional version of a classic result of Eliashberg about the symplectic fillings of contact manifolds obtained by subcritical surgery. This is joint work with Paolo Ghiggini and Klaus NiederkrĂŒger" |
October 02, 2015, 3:30 - 4:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
An Introduction to the de Rham-Witt Complex |
" |
October 01, 2015, 3:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Pin Yu (TSINGHUA UNIVERSITY) |
Construction of Cauchy data of vacuum Einstein field equations evolving to black holes |
We show the existence of complete, asymptotically flat Cauchy initial data for the vacuum Einstein field equations, free of trapped surfaces, whose future development must admit a trapped surface. Moreover, the datum is exactly a constant time slice in Minkowski space-time inside and exactly a constant time slice in Kerr space-time outside. This is joint with Junbin Li" |
October 01, 2015, 10:00 AM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Leslie Valiant (HARVARD UNIVERSITY SEAS) |
Holographic Algorithms |
When are two mathematical functions the same? One might think that this can be generally answered immediately from their definitions. However, functions may have numerous unrecognizably dissimilar definitions. Fortunately, sameness can be often demonstrated systematically by certain linear mappings internal to the function definitions. These mappings, called holographic transformations, offer a powerful tool for showing that a function class is equivalent to one known to be efficiently computable, or, alternatively, that it is equivalent to one known to be in a completeness class suspected to be computationally intractable. We shall survey these ideas and their applications in computational complexity" |
September 30, 2015, 4:00 - 5:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Shouwu Zhang (PRINCETON UNIVERSITY) |
Faltings heights and Zariski density of CM abelian varieties |
In this talk, I will first present my joint work with Xinyi Yuan on the averaged version of Colmez conjecture on Faltings heights of CM abelian varieties in terms of Artin L-functions, and then describe how it is used by Tsimerman in his proof of the André-Oort s conjecture on Zariski density of CM points on Siegel moduli spaces" |
September 30, 2015, 4:30 - 5:30 PM *2nd seminar* at Science Center 530 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Kyle Luh (YALE UNIVERSITY) |
Random Matrices: l1 Concentration and Dictionary Learning with Few Samples |
Let X be a sparse random matrix of size n Ă p (p » n). We prove that if p â„ C n log4 n, then with probability 1 â o(1), X T v 1 is close to its expectation for all vectors v â Rn (simultaneously). The bound on p is sharp up to the polylogarithmic factor. The study of this problem is directly motivated by an algorithmic application. Let A be an n Ă n matrix, X be an n Ă p matrix and Y = AX . A challenging and important problem in data analysis, motivated by dictionary learning and other practical problems, is to recover both A and X , given Y . Under normal circumstances, it is clear that this problem is underdetermined. However, in the case when X is sparse and random, Spielman, Wang and Wright showed that one can recover both A and X efficiently from Y with high probability, given that p (the number of samples) is sufficiently large. Their method works for p â„ C n2 log2 n and they conjectured that p â„ C n log n suffices. The bound n log n is sharp for an obvious information theoretical reason. The matrix concentration result verifies the Spielman et. al. conjecture up to a log3 n factor. Our proof of the concentration result is based on two useful observations. The first is an eco- nomical way to apply the union bound. The second is a refined version of Bernsteinâs concentration inequality for sum of independent variables. Both have nothing to do with random matrices and are applicable in general settings. This is joint work with Van Vu" |
September 30, 2015, 2:00 PM at Science Center 232 |
| NUMBER THEORY SEMINAR |
Ben Howard (BOSTON COLLEGE) |
Faltings heights and orthogonal Shimura varieties |
In this talk, I will first give an overview of known results toward Colmezâs conjecture relating Faltings heights of CM abelian varieties to Artin L-functions, and then present my joint work with Fabrizio Andreatta, Eyal Goren, and Keerthi Madapusi Pera on the averaged version of Colmezâs conjecture" |
September 30, 2015, 3:00 - 4:00 PM *1st seminar* at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Yongbin Ruan (UNIVERSITY OF MICHIGAN) |
A mathematical theory of gauged linear sigma model (GLSM) |
GLSM was a physical model proposed by Witten in early 90 s to give a physical derivation of Landau-Ginzburg (LG) /Calabi-Yau (CY) correspondence. Since then, it found application in many area of geometry and physics such as mirror symmetry. In the talk, I will describe a mathematical theory of gauged linear sigma model by constructing a variety of new moduli spaces and their virtual cycles. The construction is purely algebraic and applies to so called the sector of compact type. Then, Witten s physical derivation of LG/CY correspondence can be interpreted as a series of wall-crossing formula of GLSM to connect FJRW-theory to GW-theory. If the time is permitted, other applications will be touched. This is a joint work with Huijun Fan and Tyler Jarvis" |
September 29, 2015, 3:00 PM at MIT E17-122 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Gabor Lippner (NORTHEASTERN UNIVERSITY) |
Sharp convexity estimates for harmonic functions on the lattice, via absolute monotonicity |
Propagation of smallness, and convexity-type, estimates play an important role in understanding both local and global behavior of eigenfunctions. Classical methods to prove such results break down in the discrete setting. In this talk I will describe a surprising connection between harmonic functions and absolute monotonicity, and show how this can be used to prove convexity results on the lattice. (Joint work with Dan Mangoubi." |
September 29, 2015, **2 - 3 pm** Special Time at Science Center 232 |
| GEOMETRIC ANALYSIS SEMINAR |
Xuqian Fan (JINAN UNIVERSITY) |
The Steklov eigenvalues on annuli |
We will discuss some known results about upper bounds of the Steklov eigenvalues on annuli, and th egeometric description for metrics attaining the supremum, including the joint wok with Tam and Yu." |
September 29, 2015, 10:00 AM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Shamil Shakirov (HARVARD UNIVERSITY) |
Refining Chern-Simons theory in genus two |
Chern-Simons knot invariants can be completely described in terms of Hilbert spaces of states associated with two-dimensional surfaces and linear operators associated with knots. In the case of genus 1 surface, this description admits a one-parameter deformation that is called refined Chern-Simons theory. It is natural to wonder if such deformations exist for higher genus surfaces. In this talk we will describe without proof an explicit construction of refined knot operators in genus 2. These operators pass many non-trivial checks such as modularity and topological invariance. Time permitting, we will discuss the relation to Cherednik s DAHA algebras, and possible generalizations" |
September 28, 2015, 12:00 - 2:00 PM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Li-Cheng Tsai (STANFORD UNIVERSITY) |
KPZ equation limit of interacting particle systems |
In this talk we survey the weak universality (i.e. convergence to the Kardar-Parisi-Zhang (KPZ) equation) of interacting particle systems in the KPZ universality class. Such universality is considerable more accessible when a Hopf-Cole (HC) transformation linearizing the particle system exists. Here we derive such a HC transformation for the Higher Spin Exclusion Process (HSEP), introduced by Corwin and Petrov (2015), and hence for all known integrable models of the KPZ class in 1+1 dimensions. We further leverage this result into the weak universality of the HSEP. Next, we consider non-nearest neighbor exclusion processes, where an exact HC transformation is unavailable. We show that, for a subclass of models permitting certain gradient type conditions, an approximated form of the HC transformation exists, and prove the weak universality of the processes." |
September 28, 2015, 2:00 PM at Science Center 232 |
| GAUGE THEORY, TOPOLOGY, AND SYMPLECTIC GEOMETRY SEMINAR |
Peter Kronheimer (HARVARD UNIVERSITY) |
The four-color theorem and spatial graphs |
Given a trivalent graph embedded in 3-space, we associate to it an instanton homology group, which is a finite-dimensional Z/2 vector space. The main result about the instanton homology is a non-vanishing theorem, proved using techniques from 3-dimensional topology: if the graph is bridgeless, its instanton homology is non-zero. It is not unreasonable to conjecture that, if the graph lies in the plane, the dimension of its instanton homology is equal to the number of Tait colorings of the graph (essentially the same as four-colorings of the planar regions that the graph defines). If the conjecture were to hold, then the non-vanishing theorem for instanton homology would imply the four-color theorem and would provide a human-readable proof. This program is joint work with Tom Mrowka" |
September 25, 2015, 3:30 - 4:30 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Felix Finster (UNIVERSITĂ€T REGENSBURG) |
Causal fermion systems and the causal action principle |
The theory of causal fermion systems is an approach to describe fundamental physics. It gives quantum mechanics, general relativity and quantum field theory as limiting cases and is therefore a candidate for a unified physical theory. From the mathematical perspective, causal fermion systems provide a general framework for desribing and analyzing non-smooth geometries. The dynamics of causal fermion systems is described by a variational principle called the causal action principle" |
September 24, 2015, 10:00 AM at Science Center 232 |
| THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
Witt vectors, THH, and equivariant stable homotopy theory |
" |
September 24, 2015, 3:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Felix Finster (UNIVERSITĂ€T REGENSBURG) |
Linear hyperbolic equations in a rotating black hole geometry |
Linear hyperbolic equations describe the dynamics of quantum mechanical particles (Dirac equation) and of classical waves (equations for scalar, electromagnetic or gravitational waves). After a brief review of relativity and black holes, we consider the Cauchy problem for a linear hyperbolic equation in the Kerr geometry, the mathematical model of a rotating black hole. For the Dirac equation, an integral representation of the propagator is obtained, which yields pointwise decay and allows to develop the complete scattering theory. We also outline the analysis for the scalar wave equation, where the situation is more interesting due to the phenomenon of superradiance. We finally give an outlook on electromagnetic and gravitational waves and explain how to analyze linear stability of the Kerr black hole using spectral methods" |
September 23, 2015, 4:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Xin Sun (MIT) |
Almost sure multifractal spectrum of SLE |
15 years ago B. Duplantier predicted the multifractal spectrum of Schramm Loewner Evolution (SLE), which encodes the fine structure of the harmonic measure of SLE curves. In this talk, I will report our recent rigorous derivation of this prediction. As a byproduct, we also confirm a conjecture of Beliaev and Smirnov for the a.s. bulk integral means spectrum of SLE. The proof uses various couplings of SLE and Gaussian free field, which are developed in the theory of imaginary geometry and Liouville quantum gravity. Â (Joint work with E. Gwynne and J. Miller." |
September 23, 2015, 2:00 - 3:30 PM at Science Center 232 |
| NUMBER THEORY SEMINAR |
Jessica Fintzen (HARVARD UNIVERSITY) |
Stable vectors in the Moy-Prasad filtration |
Reeder and Yu gave recently a new construction of certain supercuspidal representations of p-adic reductive groups (called epipelagic representations). Their construction relies on the existence of stable vectors in the first Moy-Prasad filtration quotient under the action of a reductive quotient. We will explain these ingredients and present a theorem about the existence of such stable vectors for all primes p. This builds on a result of Reeder and Yu about the existence of stable vectors for large primes. The above work forms part of a joint research project with Beth Romano" |
September 23, 2015, 3:00 - 4:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR |
Teng Fei (MIT) |
Some new solutions to the Strominger system |
We present new solutions to the Strominger system on a class of non-compact Calabi-Yau 3-folds obtained by twistor construction. These manifolds include the resolved conifold O(-1,-1) over P^1 as a special case" |
September 22, 2015, 10:00 AM at Science Center 232 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Daniel Halpern-Leistner (COLUMBIA UNIVERSITY) |
Equivariant Hodge theory |
Recent results have revealed a mysterious foundational phenomenon: some quotient stacks X/G behave as if they are proper schemes, even when G is a positive dimensional algebraic group and X itself is not proper. I will discuss this phenomenon from the perspective of Hodge theory. One can consider the noncommutative Hodge-de Rham sequence for the dg-category D^bCoh(X/G), whose first page is Hochschild homology and which converges to periodic cyclic homology. This spectral sequence agrees with the usual Hodge-de Rham sequence for smooth and proper schemes and thus degenerates on the first page. It turns out that this degeneration also occurs for many" |
September 22, 2015, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Atsushi Kanazawa (CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS) |
Tiling, SYZ and modular forms |
I will discuss mirror symmetry of a class of Calabi-Yau manifolds associated to the polytope tilings, generalizing the Hori-Vafa toric mirror symmetry. I will also explain a conjectural connection to the Yau-Zaslow formula and its 3-dimensional analogue (on Schoen s Calabi-Yau 3-folds). My talk is based on a joint work with Siu-Cheong Lau" |
September 21, 2015, 12:00 - 2:00 PM at Science Center 232 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Jianfeng Lin (UCLA) |
The unfolded Seiberg-Witten-Floer spectrum and its applications |
In 2003, Manolescu defined the Seiberg-Witten-Floer stable homotopy type for rational homology three-spheres. In this talk, I will explain how to construct similar invariants for a general three-manifold and discuss some applications of these new invariants. This is a joint work with Tirasan Khandhawit and Hirofumi Sasahira" |
September 18, 2015, 3:00 - 4:00 PM **Special time** at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Xiangdi Huang (CHINESE ACADEMY OF SCIENCES) |
On Nash's problem for compressible flows |
We establish a unified blow-up criterion for strong solutions of various compressible models, including baratropic, fully compressible and heat-conducting magneto hydrodynamic flows, which is analogous to the Serrin s criterion of Navier-Stokes equations. It gives an affirmative answer to a problem proposed by J. Nash in 1958. As an application, we prove global-in-time classical solutions of compressible flows allowing vacuum and large fluctunation of initial data provided the initial energy is small. In the end, we prove a strong version of Nashâs problem based on new observations" |
September 17, 2015, 10:00 AM at Science Center 232 |
| THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
Introduction to Topological Hochschild and cyclic homology |
" |
September 17, 2015, 3:00 - 4:05 PM **Special time** at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Subir Sachdev (HARVARD UNIVERSITY PHYSICS) |
Bekenstein-Hawking entropy and strange metals |
I will present the exact solution of a model of fermions with infinite-range interactions describing a metal without quasiparticle excitations. The entropy density has a non-vanishing zero temperature limit, and varies continuously with the density of the fermions. The physical properties of this strange metal match quantitively with those of the near-horizon properties of charged black holes, including the Bekenstein-Hawking (or Wald) entropy. I will also discuss recent experiments on the (slightly less) strange metal in graphene" |
September 16, 2015, 4:00 - 5:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Alina Bucur (UCSD AND ICERM) |
Statistics for points on curves over finite fields |
A curve is a one dimensional space cut out by polynomial equations. In particular, one can consider curves over finite fields, which means the polynomial equations should have coefficients in some finite field and that points on the curve are given by values of the variables in the finite field that satisfy the given polynomials. A basic question is how many points such a curve has, and for a family of curves one can study the distribution of this statistic. We will give concrete examples of families in which this distribution is known or predicted, and give a sense of the different kinds of mathematics that are used to study different families. Our main focus will be the family of cyclic prime degree covers, which can be approached both via the original combinatorial/analytic approach and via maps from the idele class group. This is joint work with Chantal David, Brooke Feigon, Nathan Kaplan, Matilde Lalin, Ekin Ozman and Melanie Matchett Wood" |
September 16, 2015, 3:00 - 4:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Scott Aaronson (MIT) |
BosonSampling and the Permanents of Gaussian Matrices |
I ll discuss BosonSampling: a proposal by myself and Alex Arkhipov to demonstrate" |
September 16, 2015, 2:00 - 3:30 PM at Science Center 232 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Claude LeBrun (STONY BROOK) |
Mass in KĂ€hler Geometry |
I will describe a simple formula, discovered in joint work with H.-J. Hein, for the mass of any asymptotically locally Euclidean (ALE) KĂ€hler manifold. For ALE scalar-flat KĂ€hler manifolds, the mass turns out to be a topological invariant, depending only on the underlying smooth manifold, the first Chern class of the complex structure, and the KĂ€hler class of the metric. When the metric is actually AE (asymptotically Euclidean), this formula not only implies a positive mass theorem for KĂ€hler metrics, but also yields a Penrose-type inequality for the mass." |
September 15, 2015, 4:15 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR |
Hongwei Xu (ZHEJIANG UNIVERSITY) |
Mean Curvature Flow and Sphere Theorem |
During the past three decades, a number of important sphere theorems via curvature flow have been proved by several geometers. In this talk, I will focus on submanifolds and discuss convergence theorems for mean curvature flow of submanifolds of arbitrary codimension. Consequently, we obtain the optimal differentiable sphere theorem" |
September 15, 2015, 10:00 AM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS MATHEMATICAL PHYSICS SEMINAR |
Wenbin Yan (CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS) |
(0,4) dualities |
I will discuss a class of two-dimensional N=(0,4) quiver gauge theories that flow to superconformal field theories. Dualities for the superconformal field theories are similar to the 4d N=2 theories of class S, labelled by a Riemann surface C. The dual descriptions arise from various pair-of-pants decompositions, that involves an analog of the TN theory. Especially, the superconformal index of such theories can be written in terms of a topological field theory on C. We interpret this class of SCFTs as the ones coming from compactifying 6d N=(2,0) theory on CP1Ă" |
September 14, 2015, 12:00 - 2:00 PM at Science Center 232 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Richard Schwartz (BROWN UNIVERSITY) |
The plaid model and outer billiards |
Outer billiards is a dynamical system that is similar in spirit to ordinary billiards, except that the ball moves around the outside of the table. Even for simple tables, such as kites (quadrilaterals with bilateral symmetry) the orbits produced have a rich combinatorial structure. I ll describe a combinatorial model, which I call the plaid model, which predicts the shapes of these orbits for kites. The model involves mathematics which is similar in spirit to what one sees for quasi-periodic tiling" |
September 11, 2015, 3:30 - 4:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
p-adic Hodge Theory and Topological Hochschild Homology |
" |
September 10, 2015, 3:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS EVOLUTION EQUATIONS SEMINAR |
Chunjing Xie (SHANGHAI JIAO TONG UNIVERSITY) |
Well/ill-posedness for the rotating shallow water system |
When the initial relative vorticity is zero, we show that rotating shallow water system has a global small smooth solution via exploring the dispersive mechanism of the system. For the smooth solutions with general initial data, in general, they will form a singularity in finite time at least in one dimensional setting. For the general solutions for 2D rotating shallow water system, we prove that there are infinitely many bounded admissible weak solutions. In particular, we can construct infinitely many bounded admissible weak solutions with only finite states" |
September 10, 2015, 10:00 AM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Mithat Unsal (NORTH CAROLINA STATE UNIVERSITY) |
What is QFT? Resurgent trans-series, Lefschetz thimbles, and new exact saddles |
Resurgent trans-series provide a novel mathematical formalism to unify perturbative and non-perturbative physics, leading to new insights into the general structure of quantum mechanics, field and and string theories. I will review the main ideas with some illustrative examples. In many quantum mechanical systems, all orders non-perturbative data is encoded into perturbation theory, and it can be decoded. In QFTs, there are cases in which resurgence provides a new interpretation of t Hooft s time-honored IR-renormalon puzzle, reveals the existence of many new saddles (such as magnetic and neutral bions), and potentially provide a non-perturbative continuum definition of QFT in a semi-classical domain! I will also describe a new perspective on path integration, which is intimately tied with resurgence theory and employs some tools of Picard-Lefschetz theory (complex gradient flow or complex Morse theory). This perspective leads to many dramatic and surprising results, e.g. the existence of complex, multi-valued, and even singular saddles which can be proven to contribute to path integration, and implies that the proper framework to study semi-classics in path integral formulation is yet to be develope" |
September 09, 2015, 4:30 - 5:30 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Erick Knight (HARVARD UNIVERSITY) |
A p-adic Jacquet-Langlands Correspondence |
I will construct a p-adic Jacquet-Langlands correspondence, which is a correspondence between Banach space representations of GL_2(Q_p) and Banach space representations of the unit group of the quaternion algebra D over Q_p. The correspondence satisfies local-global compatibility with the completed cohomology of Shimura curves, as well as a compatibility with the classical Langlands correspondence, in the sense that the D* representations can often be shown to have the expected locally algebraic vectors" |
September 09, 2015, 3:00 - 4:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Hossein Movasati (IMPA) |
Why should one compute the periods of algebraic cycles? |
Let $X$ be a smooth projective variety of dimension $2k$ over complex numbers and let $Z$ be a subvariety of $X$ of dimension $k$. One says that the infinitesimal Hodge conjecture (IHC) holds if the deformation space of the pair $(X,Z)$ inside the moduli space of $X$ is the same as the deformation space of the Hodge cycle $[Z]$ induced by $Z$. Hodge conjecture does not imply IHC, however, verifications of IHC in many explicit situations imply the Hodge conjecture for deformed Hodge cycles. In this talk I am going to explain how explicit computations of periods of differential forms over cycles $[Z]$ lead to the verifications of IHC. I will also prove that IHC holds for linear projective spaces inside hypersurfaces. This in two dimensional case ($k=1$), where the Hodge conjecture is well-known as Lefschetz $(1,1)$ theorem, is a result of Green and Voisin in 1990. Some partial results concerning complete intersections inside sextic hypersurfaces fourfolds (which are Calabi-Yau) will be given. One of the basic ingredients of the proof is the so called infinitesimal variation of Hodge structures. The talk is partially based on arXiv:1411.1766v1" |
September 08, 2015, 4:15 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GEOMETRIC ANALYSIS SEMINAR |
Binglong Chen (SUN YAT-SEN UNIVERSITY) |
On the geometry of complete positively curved Kahler manifolds |
We will give a survey on progress on Yauâs uniformization conjecture which states that a complete noncompact Kahler manifold with positive bisectional curvature is biholomorphic to a complex Euclidean space. The resolution of the conjecture depends on the understanding of the geometric structures on the manifolds, like the volume growth, the curvature decay, holomorphic functions (or sections) on the manifolds." |
September 08, 2015, 10:00 AM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Madhu Sudan (MICROSOFT RESEARCH) |
Robust Low-degree Testing |
Given a function f:F^m to F for a finite field F and integer d, a low-degree tester is a procedure that randomly samples the value of f on a few (potentially correlated) points and makes decision to accept/reject f based on this local view of f. Ideally the tester should accept polynomials of degree at most d with probability 1, and reject functions that are far (in normalized Hamming distance) from every degree d polynomial with probability growing with the distance, and it should do while keeping the local view small. A robust tester is even more ambitious: It would like the local views to be far from acceptable views (again in normalized Hamming distance) if the function being tested is far from acceptable strings. Theoretical computer science has long been interested in the study of low-degree testing --- good tests and analyses have found applications in the fields of probabilistically checkable proofs, locally testable codes, algebraic pseudorandomness, and most recently in the construction of some extremal small set expanders. In the talk I will briefly introduce the problem, mention some of the connections, and explain some basic lower bounds on the size of the local views that a tester can hope to work with. I will summarize some results that show that how testers come close to the lower limits while being robust. Time permitting I will describe a recent approach to robust analysis of low-degree testing via a very general abstract view that only uses the fact that low-degree polynomials are invariant under affine transformations of the domain (F^m), and that they form linear error-correcting codes of good-distance. Based on a long sequence of works, including some recent work with Alan Guo (MIT) and Elad Haramaty (Northeastern)" |
September 02, 2015, 4:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Zhengcheng Gu (PERIMETER INSTITUTE) |
Topological Quantum Field Theory approach for Bosonic Symmetry-Protected-Topological Phases with Abelian Symmetry in Three Dimensions |
Symmetry protected topological(SPT) phase is a generalization of topological insulator(TI). Different from the intrinsic topological phase, e.g., the fractional quantum hall(FQH) phase, SPT phase is only distinguishable from a trivial disordered phase when certain symmetry is preserved. Indeed, SPT phase has a long history in 1D, and it has been shown that the well known Haldane phase of S=1 Heisenberg chain belongs to this class. However, in higher dimensions, most of the previous studies focus on free electron systems. Until very recently, it was realized that SPT phase also exists in interacting boson/spin systems in higher dimensions. In this talk, I will discuss the general mechanism for bosonic SPT phases and propose a corresponding topological quantum field theory(TQFT)descriptions. I will focus on examples in three (spacial) dimensions, including bosonic topological insulators(BTI) " |
September 01, 2015, 4:15 PM at Science Center 507 |
| EVOLUTION EQUATIONS SEMINAR |
Long Jin (CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS) |
Scattering Resonances for Convex Obstacles |
In this talk, we discuss the distribution of scattering resonances for strictly convex obstacles in Euclidean spaces and various other background spaces. In particular, we show that under very general boundary conditions, including Dirichlet, Neumann and Robin boundary conditions, there is a cubic resonance free region near the real axis. Moreover, under certain pinched curvature conditions, the resonances appears in cubic bands and the counting functions of the resonances in each band satisfy a Weyl law similar to the one for eigenvalues on compact manifolds." |
September 01, 2015, 10:00 AM at Science Center 232 |
| MATHEMATICAL PHYSICS SEMINAR |
Babak Haghighat (HARVARD UNIVERSITY) |
Modularity of Yukawa-couplings for elliptic Calabi-Yau manifolds |
I will review mirror symmetry and the computation of genus zero Gromov-Witten potentials for Calabi-Yau manifolds. Then I will proceed to define Yukawa-couplings as 3-point functions for 3-folds and 4-point functions for 4-folds. In the Calabi-Yau 4-fold case I will show how these are related to the Gromov-Witten potentials. Finally, I will proceed to take the fiber limit and show how Picard-Fuchs equations simplify and relate to underlying modularity properties" |
August 31, 2015, 12:00 - 2:00 PM at Science Center 232 |
| SPECIAL LECTURE SERIES, 3RD LECTURE |
Alessandro Tomasiello (MILANO - BICOCCA) |
Higher-dimensional superconformal theories from string theory |
In dimensions higher than four, the structure of interacting quantum field theories becomes more mysterious. In string theory several higher-dimensional theories arise naturally. The most famous example is the elusive (2,0) theory living on the M-theory fivebranes, but many other constructions are possible, using singularities or D-brane intersections. Learning about these theories can teach us about both quantum field theory and about string theory. In these lectures, I will present a selection of old and new results in this field. After some observations in field theory, I will review the situation for six dimensions. Here we know the maximally supersymmetric (2,0) theory mentioned above, but more recently we are also learning quite a bit about (1,0) theories, and perhaps we are getting close to a classification, using both AdS/CFT and F-theory as our tools.In five dimensions, many theories can be realized in several dual ways (in IIA, IIB, M-theory), and I will show some conjectural connections to the six-dimensional ones, sometimes after compactifying to four dimensions. Organized by Shing-Tung Yau and Jonathan Mboyo Esole" |
May 29, 2015, 2:00 PM at Science Center 507 |
| SPECIAL LECTURE SERIES, 2ND LECTURE |
Alessandro Tomasiello (MILANO - BICOCCA) |
Higher-dimensional superconformal theories from string theory |
In dimensions higher than four, the structure of interacting quantum field theories becomes more mysterious. In string theory several higher-dimensional theories arise naturally. The most famous example is the elusive (2,0) theory living on the M-theory fivebranes, but many other constructions are possible, using singularities or D-brane intersections. Learning about these theories can teach us about both quantum field theory and about string theory. In these lectures, I will present a selection of old and new results in this field. After some observations in field theory, I will review the situation for six dimensions. Here we know the maximally supersymmetric (2,0) theory mentioned above, but more recently we are also learning quite a bit about (1,0) theories, and perhaps we are getting close to a classification, using both AdS/CFT and F-theory as our tools.In five dimensions, many theories can be realized in several dual ways (in IIA, IIB, M-theory), and I will show some conjectural connections to the six-dimensional ones, sometimes after compactifying to four dimensions. Organized by Shing-Tung Yau and Jonathan Mboyo Esole" |
May 26, 2015, 2:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Claudio Landim (IMPA) |
Condensing zero-range processes |
Zero-range processes with decreasing jump rates exhibit a condensation transition, where a positive fraction of all particles condenses on a single lattice site when the total density exceeds a critical value. Consider a condensing zero-range process with $N$ particles evolving on a fixed and finite set $S$. In the diffusive time scale $N^2$ the fraction of particles at each site evolves as a diffusion whose drift is unbounded. The process remains absorbed at the boundary once it attains it, and it performs, after this hitting time, a diffusion on a lower dimensional simplex, similar to the original one, until all particles concentrate on a single site. In a longer time scale $N^{1+\alpha}$, $\alpha>1$, the site which concentrates all particles evolves as a random walk on $S$ whose transition rates are proportional to the capacities of the underlying random walk" |
May 22, 2015, 11:30 am - 1:00 pm at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Xiao-Gang Wen (MIT) |
Symmetry-protected-topological order and algebraic topology |
Symmetry-protected-topological states are the simplest kind of highly entangled quantum state of matter. They have only trivial bulk excitations, but have non-trivial boundary excitations, characterized by gauge/gravitational anomalies. Since symmetry-protected-topological order is almost trivial, we are able to develop a systematic theory for them, based on group cohomology and algebraic topology. In this talk, I will give a brief review of the related developments" |
May 13, 2015, 4:00 - 5:00 PM at Science Center Hall E |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
Laura DeMarco (NORTHWESTERN UNIVERSITY) |
Complex Dynamics and Elliptic Curves |
In this talk, I will explain some connections between recent research in complex dynamics and the classical theory of elliptic curves and rational points. I will begin with a theorem of Mordell and Weil from the 1920s, presented from a dynamical point of view. I hope to explain how we have exploited this connection to prove new results about elliptic curves." |
May 13, 2015, 4:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Qingtao Chen (INTERNATIONAL CENTER FOR THEORETICAL PHYSICS) |
Quantum invariants, Skein relations and Volume Conjecture |
In knot theory, Jones, HOMFLY and Kauffman polynomials share a common feature that they can be defined via a purely combinatorial method called skein relation. In this way, a knot polynomial can be computed recursively by reducing its crossing numbers. But it s rather hard to search skein relations for quantum invariants such as colored HOMFLY and colored Jones invaraints. Recently, we proposed several conjectures of (congruent) skein relations at roots of unity for colored HOMFLY invariants and colored Jones polynomials etc. We have proved series of examples for these new conjectures, especially the knot case for colored Jones polynomials. The motivation behind this phenomenon involves several areas of mathematics as well as string theory, which may also shed some new light on the Volume conjecture. This is a joint work with Kefeng Liu, Pan Peng and Shengmao Zhu. Finally I will introduce a very recent discovery of new Volume Conjectures for hyperbolic 3-manifolds through Turaev-Viro type invariants and Reshetikhin-Turaev invariants. This is a joint work with Tian Yang" |
May 12, 2015, 4:30 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Noureddine El Karoui (UC BERKELEY) |
Some remarks on the bootstrap in high-dimension |
The bootstrap (Efron, 79) is a ubiquitous tool in applied statistics. The bootstrap seeks to address the following central question: is it possible to understand the fluctuation behavior of certain functions of the data by appropriately sampling from the observed dataset? (This question is of course important if one wants to create confidence intervals/error bars for functions of the data of interest to the data analyst without relying on asymptotic analysis.) After reviewing some classical results in the situation where one works with data whom dimension, p, is much smaller than the number of observations, n, I will discuss some results concerning the high-dimensional situation where p and n are of the same order of magnitude. As we will see, numerous issues arise in this setting, casting some doubts about the reliability of the bootstrap in high-dimension. No familiarity with resampling methods will be assumed. Based on joint work with Elizabeth Purdom." |
May 07, 2015, 12:00 - 1:30 pm at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Jeff Lichtman (HARVARD UNIVERSITY MCB) |
Graphing the Connectome |
" |
May 06, 2015, 3:00 PM at Science Center Hall A |
| MATHEMATICAL PHYSICS SEMINAR |
Zhengwei Liu (VANDERBILT AND HARVARD) |
The Classification and Construction of Subfactors |
We classify subfactors with a Yang-Baxter presentation and construct a new one-parameter family of semisimple tensor categories appeared in the classification. We obtain infinitely many new subfactors and fusion categories which are related to conformal inclusions." |
May 05, 2015, 2:00 PM at Science Center 530 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Valentino Tosatti (NORTHWESTERN UNIVERSITY) |
Degenerations and collapsing of Ricci-flat Calabi-Yau manifolds |
I will discuss the problem of understanding how Ricci-flat Calabi-Yau manifolds degenerate and collapse to lower-dimensional spaces, and how this is relevant to the Strominger-Yau-Zaslow picture of mirror symmetry. I will present some results in this direction, which are joint work with M. Gross, Y. Zhang, with H.J. Hein and with B. Weinkove, X.Yang" |
May 05, 2015, 1:30 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Gåbor Székelyhidi (UNIVERSITY OF NOTRE DAME) |
Kahler-Einstein metrics along the smooth continuity method |
I will discuss an equivariant version of the Yau-Tian-Donaldson conjecture, strengthening the result of Chen-Donaldson-Sun. This potentially gives new examples of Kahler-Einstein manifolds, and it can also be applied to the existence problem for Kahler-Ricci solitons. It is joint work with Ved Data" |
May 05, 2015, 4:15 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
June Huh (PRINCETON UNIVERSITY) |
Positive currents and algebraic cycles in permutohedral varieties |
A conjecture of Read predicts that the coefficients of the chromatic polynomial of a graph form a log-concave sequence. A related conjecture of Welsh predicts that the number of independent subsets of varying sizes form a log-concave sequence for any configuration of vectors in a vector space. The known proofs use that certain positive currents associated to the above combinatorial structures are limits of effective algebraic cycles, and the more general conjecture for possibly ânonrealizableâ combinatorial configurations is still open. I will give a survey of known results, and outline an approach to the general conjecture" |
May 05, 2015, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Philippe Sosoe (CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS) |
The chemical distance in critical percolation |
" |
May 04, 2015, 12:00 - 2:00 PM at Science Center 232 |
| GAUGE THEORY, TOPOLOGY, AND SYMPLECTIC GEOMETRY SEMINAR |
Yanir Rubinstein (UNIVERSITY OF MARYLAND) |
The degenerate special Lagrangian equation |
In joint work with J. Solomon, we introduce the {\it degenerate special Lagrangian equation} and develop the basic analytic tools to construct and study its solutions. This equation governs geodesics in the space of positive Lagrangians. It has intriguing relations to uniqueness, existence and stability notions related to special Lagrangians, Lagrangian mean curvature flow, and the topology of Hamiltonian isotopy classes" |
May 01, 2015, 3:30 - 4:30 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Alexander Merkurjev (UCLA) |
Suslin's Conjecture on the reduced Whitehead group of a simple algebra |
I will report on the proof of Suslin s Conjecture on the generic non-triviality of the reduced Whitehead group of a simple algebra" |
April 29, 2015, 3:00 PM at Science Center 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
Matthieu Astorg (UNIVERSITĂ© PAUL SABATIER) |
A polynomial endomorphism of C^2 with a wandering Fatou component |
For a holomorphic map f : M -> M, where M is a complex manifold, the Fatou set is the largest open set on which the iterates of f form a normal family, and a Fatou component is a connected component of the Fatou set. A celebrated theorem of Sullivan (1985) asserts that all Fatou components are eventually periodic when f is a rational map and M is the Riemann sphere. Various classes of counter-examples have been found and studied when M is the complex plane and f is an entire transcendental function. Building on ideas from M. Lyubich, we give a construction for counter-examples in dimension 2, where M is P^2, and f is a polynomial skew-product, using techniques from parabolic implosion. This is joint work with X. Buff, R. Dujardin, H. Peters and J. Raissy" |
April 29, 2015, 4:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Xiao-Gang Wen (MIT) |
Symmetry-protected-topological order and algebraic topology |
Symmetry-protected-topological states are the simplest kind of highly entangled quantum state of matter. They have only trivial bulk excitations, but have non-trivial boundary excitations, characterized by gauge/gravitational anomalies. Since symmetry-protected-topological order is almost trivial, we are able to develop a systematic theory for them, based on group cohomology and algebraic topology. In this talk, I will give a brief review of the related developments" |
April 29, 2015, 4:00 PM at Science Center Hall A |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Joseph Landsberg (TEXAS A & M UNIVERSITY) |
What is geometric complexity theory? |
Mulmuley and Sohoni (with help from Nori), building on work of Valiant, proposed a variant of the P v. NP problem in complexity theory that is formulated as a problem in algebraic geometry and representation theory. I will give an overview of this program and how it has lead to classical and modern questions in geometry regarding dual varieties, secant varieties, minimal free resolutions, and plethysm v. Kronecker coefficients" |
April 28, 2015, 3:00 PM at MIT 36-156 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Hsian-Hua Tseng (OHIO STATE UNIVERSITY) |
Virasoro beyond semi-simple cases |
The plan of this talk is to discuss Givental s approach to proving Virasoro constraints for Gromov-Witten theory in the semi-simple cases, and explains how to push this further to certain non-semisimple situations (joint work with J. Brown, T. Coates, and A. Givental). -- Organized by Prof. Shing-Tung Ya" |
April 28, 2015, 4:15 PM at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Senya B. Shlosman (AIX-MARSEILLE UNIVERSITY AND BROWN UNIVERSITY) |
Airy Diffusion and N1/3 Fluctuations in the 2D Ising Model |
Consider the two-dimensional Ising model at a temperature below the critical. Let a droplet of the (+) phase of linear size N floats in the sea of (-) phase and is pressed against a horizontal wall. I will explain that the fluctuations of the boundary of the droplet near the contact with the wall are of the order of N1/3. Its N1/3-scaling behavior is given by the Airy diffusion (work in progress with D. Ioffe and Y. Velenik)" |
April 28, 2015, 2:00 PM at Science Center 530 |
| SPECIAL NUMBER THEORY SEMINAR |
Jean-Pierre Serre (COLLĂšGE DE FRANCE ) |
Galois cohomological invariants |
These invariants are the analogs in Galois cohomology of Chern and Stiefel-Whitney classes in Topology. I shall discuss them mainly for finite groups, e.g. symmetric and alternating grou" |
April 27, 2015, 3:00 PM at Science Center Hall A |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Noppadol Mekareeya (CERN) |
Coulomb Branch and the Moduli Space of Instantons |
" |
April 27, 2015, 12:00 - 2:00 PM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Tyler Helmuth (ICERM AND BROWN UNIVERSITY) |
Loop-weighted Walk |
Loop-weighted walk is a one-parameter family of random walks that arise naturally in statistical mechanics and theoretical polymer chemistry. A loop-weighted walk receives weight $\lambda^{k}$ if it contains $k$ loops; whether this rewards or punishes the presence of loops depends on the value of the parameter $\lambda$. Two important aspects of this problem are that (i) it is highly non-Markovian and (ii) it lacks basic monotonicity properties. I will explain how the lace expansion, a technique for proving mean-field universality, can be used to establish the diffusive behaviour of loop-weighted walk in high dimensions" |
April 23, 2015, 2:00 - 3:00 PM at Science Center 232 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
Holly Krieger (MIT) |
A case of the dynamical André-Oort conjecture |
I will discuss the dynamical André-Oort conjecture proposed by Baker-DeMarco, focusing on a case suggested by Ingram and recently proved by Ghioca, Nguyen, Ye, and myself: if C is an irreducible plane curve containing infinitely many points (a,b) for which z^d+a and z^d+b are both post-critically finite, then C is a fiber of a projection, or the zero locus of h(x) = Ax for some (d-1)st root of unity A. The proof includes an analysis of the existence of linear maps on angles of external rays of the Mandelbrot set" |
April 22, 2015, 4:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Suvrat Raju (INTERNATIONAL CENTRE FOR THEORETICAL SCIENCES) |
The Information Paradox and the black hole interior in AdS/CFT |
We describe recent refinements of the information paradox, within the context of the AdS/CFT correspondence. We review a recent proposal that quantum gravity effects may be large enough to modify the structure of the horizon of a large black hole and create a firewall there. We test this idea by constructing local probes of the black hole geometry. This leads us to the conclusion that the horizon is smooth --- precisely in line with semi-classical expectations. However, an examination of how the arguments for the firewall are sidestepped points to some interesting aspects of locality in quantum gravity. We also discuss how this construction of operators in the black hole interior relates to the Tomita Takesaki theory of modular isomorphisms of von Neumann algebras. This talk will be addressed to a general mathematical physics audience. So, for a large part, we will not assume any prior familiarity with string theory or the information paradox" |
April 22, 2015, 4:00 PM at Science Center Hall A |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Wei-Kuo Cheng (UNIVERSITY OF CHICAGO) |
Self-averaging and universality in spin glasses |
Spin glasses are disordered spin systems originated from the desire of understanding the strange magnetic behaviors of certain alloys in physics. As mathematical objects, they are often cited as examples of complex systems and have provided several fascinating structures and conjectures. In this talk, we will consider several spin glass models and study quenched self-avergaging properties of some physical observables including the magnetization, the Hamiltonian and the cross overlap in the disorder chaos problem. Second, we will discuss some universal properties of the Gibbs measures and conclude in particular that the Parisi ultrametric structure of the Gibbs measure in the mixed p-spin model is universal under relevant moment matching assumptions. Based on the joint works with A. Auffinger and D. Panchenko" |
April 22, 2015, 11:30 am - 1:00 pm at Science Center 232 |
| NUMBER THEORY SEMINAR |
James Borger (AUSTRALIAN NATIONAL UNIVERSITY) |
Positivity and periodicity in global Witt vectors |
The p-typical Witt vectors of p-adic rings have played an important role in local number theory, and one might hope that multiple-prime Witt vectors of arithmetically global rings will be similarly useful in global number theory. As a step in that direction, I ll give two variations of the Witt vector functor which have a global nature. One deals with periodicity with respect to a modulus of a number field and is related to global class field theory; the other deals with positivity and is closely related to Schoenberg s classical theory of total positivity" |
April 22, 2015, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Steve Rosenberg (BOSTON UNIVERSITY) |
Diffeomorphism groups of Sasakian manifolds |
Using Chern-Simons classes on loop spaces, we show that the diffeomorphism group of a large class of compact Sasakian manifolds has infinite fundamental group. The main technique involves replacing the matrix trace used to define characteristic classes on a finite rank bundle with the Wodzicki residue to get characteristic classes on the tangent bundle to a loop space" |
April 21, 2015, 4:15 PM at Science Center 507 |
| A SPECIAL TALK IN BASIC NOTIONS |
Jean-Pierre Serre (COLLĂšGE DE FRANCE ) |
Linear representations of finite groups |
I shall review the basic results in char. 0, char. p > 0 (Brauer style and homotopy style) and char. 1" |
April 21, 2015, 3:00 PM at Science Center Hall D |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Giulia Sacca (STONY BROOK) |
Symplectic singularities and quiver varieties |
The aim of this talk is to study a class of singularities of moduli spaces of sheaves on K3 surfaces by means of Nakajima quiver varieties. The singularities in question arise from the choice of a non generic polarization, with respect to which we consider stability, and admit natural symplectic resolutions corresponding to choices of general polarizations. By considering appropriate Fourier-Mukai transforms, we show that these moduli spaces are, locally around a singular point, isomorphic to a quiver variety in the sense of Nakajima and that, via this isomorphism, the natural symplectic resolutions correspond to variations of GIT quotients of the quiver varieties. This is joint work with E. Arbarello" |
April 21, 2015, 4:00 - 5:00 PM *special time at Science Center 309A *special location |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Maria Rodriguez (HARVARD UNIVERSITY PHYSICS) |
Exact Solutions for Extreme Black Hole Magnetospheres |
" |
April 20, 2015, 12:00 - 2:00 PM at Science Center 232 |
| BASIC NOTIONS SEMINAR |
Dennis Gaitsgory (HARVARD UNIVERSITY) |
Langlands correspondence via shtukas, after V. Drinfeld, L. Lafforgue and V. Lafforgue |
I will explain idea of the Drinfeld shtuka, and how it is used for the proof of Langlands correspondence for function fields, outlining the main ideas of V. Lafforgue s groundbreaking paper" |
April 20, 2015, 3:00 PM at Science Center 507 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Danny Ruberman (BRANDEIS UNIVERSITY) |
Absolutely exotic 4-manifolds |
We show the existence of exotic smooth structures on contractible 4-manifolds. These structures are absolute, in the sense that they do not depend on a specific marking of the boundary. This is in contrast to the phenomenon of corks, which are exotic relative to an automorphism of their boundaries. The technique is to modify a relatively exotic manifold to give an exotic one for which we have a good understanding of the automorphism group of the boundary. This is joint work with Selman Akbulut." |
April 17, 2015, 3:30 - 4:30 PM at Science Center 507 |
| SPECIAL SEMINAR |
Po-Ning Chen (COLUMBIA UNIVERSITY) |
Quasi-local mass in general relativity |
While the total energy of an isolated system in general relativity is well-studied, the concept of energy in general relativity remains a challenging problem because of the lack of a quasi-local description. In this talk, we survey several definition of quasi-local mass including the Hawking mass, the Brown-York mass, and their applications. We then describe a new proposal of quasi-local mass/energy and discuss its application and properties. --Organized by Professor Shing-Tung Ya" |
April 15, 2015, 1:00 - 2:00 PM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Lionel Levine (CORNELL UNIVERSITY) |
Circles in the Sand |
I will describe the role played by an Apollonian circle packing in the scaling limit of the abelian sandpile on the square grid Z^2. The sandpile solves a certain integer optimization problem. Associated to each circle in the packing is a locally optimal solution to that problem. Each locally optimal solution can be described by an infinite periodic pattern of sand, and the patterns associated to any four mutually tangent circles obey an analogue of the Descartes Circle Theorem. Joint work with Wesley Pegden and Charles Smart" |
April 15, 2015, 11:30 am - 1:00 pm at Science Center 530 |
| NUMBER THEORY SEMINAR |
Stefan Patrikis (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
Deformations of Galois representations and exceptional monodromy |
I will explain how to realize the exceptional algebraic groups as algebraic monodromy groups of geometric (in the sense of Fontaine-Mazur) Galois representations, in particular obtaining the first such examples in types F4 and E6. The argument relies on lifting well-chosen mod p representations to characteristic zero, using a generalization (to essentially any reductive group) of a technique developed by Ravi Ramakrishna for type A1" |
April 15, 2015, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Xihong Lin (DEPT OF BIOSTATISTICS, HARVARD H. T. CHAN SCHOOL OF PUBLIC HEALTH) |
Statistical Analysis of Massive Genetic and Genomic Data |
The human genome project in conjunction with the rapid advance of high throughput technology has transformed the landscape of health science research. The genetic and genomic era provides an unprecedented promise of understanding genetic underpinnings of complex diseases or traits, studying gene-environment interactions, predicting disease risk, and improving prevention and intervention, and advancing precision medicine. A large number of genome-wide association studies conducted in the last ten years have identified over 1,000 common genetic variants that are associated with many complex diseases and traits. Massive targeted, whole exome and whole genome sequencing data as well as different types of âomics data have become rapidly available in the last few years. These massive genetic and genomic data present many exciting opportunities as well as challenges in data analysis and result interpretation. They also call for more interdisciplinary knowledge and research, e.g., in statistics, machine learning, data curation, molecular biology, genetic epidemiology and clinical science. In this talk, I will discuss analysis strategies for some of these challenges, including rare variant analysis of whole-genome sequencing association studies; analysis of multiple phenotypes (pleiotropy), and integrative analysis of different types of genetic and genomic data" |
April 15, 2015, 4:00 PM at Science Center Hall A |
| SPECIAL SEMINAR |
Geoffrey CompĂšre (UNIVERSITĂ© LIBRE DE BRUXELLES) |
Extension of Virasoro symmetries near extremal black hole horizons |
Infinite dimensional algebras often appear in theoretical physics. Here we show how to realize an infinite dimensional algebra which contains several Virasoro and U(1) Kac-Moody algebras in the vicinity of an extremal black hole horizon. We construct a set of smooth metrics which forms a representation of the algebra thanks to the existence of a symplectic structure. Several physical properties of extremal black holes will be discussed. --Organized by Prof. S.T. Ya" |
April 15, 2015, 2:00 - 3:00 PM at Science Center 232 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
Simion Filip (UNIVERSITY OF CHICAGO) |
Families of K3 surfaces and their asymptotic properties |
I will discuss two questions about families of K3 surfaces that have their origin in the theory of translation surfaces. The first is concerned with a family of K3s over a hyperbolic Riemann surface. Their cohomology groups form a local system and I will describe a formula for its top Lyapunov exponent. This will be analogous to the Eskin-Kontsevich-Zorich formula in the case of translation surfaces. The second question will concern an analogue for K3s of counting cylinders on a translation surface. I will provide the necessary background from dynamics and from the theory of K3 surfaces" |
April 15, 2015, 4:00 - 5:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Bong Lian (BRANDEIS UNIVERSITY) |
Some applications of period integrals |
This talk is based on work in progress, joint with J. Chen, A. Huang, S.-T. Yau, and X. Zhu. I will discuss two emerging applications. One is to construct a new type of vanishing conditions for certain special functions, including generalized hypergeometric functions. In some sense, these vanishing condition generalizes zeros of hypergeometric functions -- a classical problem that goes back a century. The new basic idea is that these functions can be realized as period integrals of families of algebraic varieties that are governed by certain explicit differential systems. By using a new algebraic realization of these systems as D-modules, we can construct explicit (differential) zeros of those special functions. The second application I will discuss is to describe certain new (regular holonomic) differential systems for period mappings" |
April 14, 2015, 4:15 PM at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Bas Janssens (INSTITUTE OF MATHEMATICS, UNIVERSITY OF UTRECHT) |
Projective Unitary Representations of Infinite- Dimensional Lie Groups |
Projective unitary representations of a Lie group G encode the way that symmetries occur in Quantum Mechanics. This talk will be about how to go back and forth between projective unitary reps of G, unitary reps of a central extension G , and unitary reps of the corresponding Lie algebra g for infinite dimensional Lie groups G, and on how to use this in representation theory. This covers gauge groups, diffeomorphism groups, and (differential geometric versions of) the affine Kac-Moody groups" |
April 14, 2015, 2:00 PM at Science Center 530 |
| GAUGE THEORY, TOPOLOGY, AND SYMPLECTIC GEOMETRY SEMINAR |
Dan Pomerleano (IMPERIAL COLLEGE) |
Symplectic cohomology in the topological limit |
In Sheridan s proof of homological mirror symmetry for Calabi-Yau hypersurfaces in projective space, he highlighted an interesting class of affine varieties known as Kahler pairs. In this talk, we will explain how to compute their symplectic cohomology. This is joint work with Sheel Ganatra" |
April 10, 2015, 3:30 - 4:30 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Cumrun Vafa (HARVARD UNIVERSITY PHYSICS) |
On Mathematical Aspects of String Theory |
This talk reviews some of the mathematical underpinnings of string theory. The emphasis will be on the role of duality symmetries and their mathematical implications, which will be discussed using concrete examples" |
April 08, 2015, 4:00 PM at Science Center Hall A |
| NUMBER THEORY SEMINAR |
Paul Hamacher (HARVARD UNIVERSITY) |
The geometry of the Newton stratification of a PEL-Shimura variety |
In this talk we consider the Newton stratification on the reduction of Shimura varieties of PEL type with hyperspecial level structure, i.e. the stratification by isogeny class of the Barsotti-Tate of the universal Abelian variety . The main result is a formula for the dimension of Newton strata and the description their closure. As a consequence of this we prove a generalization of Grothendieck s conjecture on the deformation of Barsotti-Tate groups." |
April 08, 2015, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Yuchen Pei (UNIVERSITY OF WARWICK) |
A q-weighted version of the Robinson-Schensted algorithm |
The Robinson-Schensted algorithm is a combinatorial algorithm which plays a fundamental role in the theory of Young tableaux and symmetric functions. It also provides a combinatorial framework for the study of certain particle systems including the totally asymmetric simple exclusion process (TASEP). In this talk I will describe a q-weighted version, which can be viewed as a randomised version of this algorithm, and which provides a similar framework for the study of the q-Whittaker functions and the q-TASEP particle system. I will also describe how a well known symmetry property of the classical algorithm carries over to the q-setting, via a branching version of the growth diagram technique introduced by Sergey Fomin. Part of this talk is based on joint work with Neil O Connell" |
April 08, 2015, 11:30 am - 1:00 pm at Science Center 232 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Barbara Bolognese (NORTHEASTERN UNIVERSITY) |
TBA |
" |
April 07, 2015, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Thomas Walpuski (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
G2-instantons, associative submanifolds and generalized Seiberg-Witten equations |
" |
April 07, 2015, 4:15 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Shing-Tung Yau (HARVARD UNIVERSITY) |
Period integrals of algebraic manifolds and their differential equations (Joint works with Bong Lian and An Huang) |
" |
April 06, 2015, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Anda Degeratu (UNIVERSITY OF FREIBERG) |
Analysis on QAC Spaces |
In this talk I will introduce the class of quasi-asymptotically conical (QAC) manifolds, a less rigid Riemannian formulation of the QALE geometries introduced by Joyce in his study of crepant resolutions of Calabi-Yau orbifolds. Our set-up is in the category of real stratified spaces and Riemannian geometry. Given a QAC manifold, we identify the appropriate weighted Sobolev spaces, for which we prove the finite dimensionality of the null space for generalized Laplacian as well as their Fredholmness. The methods we use are based on techniques developed in geometric analysis by Grigor yan and Saloff-Coste,  as well as Colding and Minicozzi, and Peter Li. We show that our geometries satisfy the volume doubling property and the Poincaré inequality, and we use these properties to analyze the heat kernel behaviour of a generalized Laplacian and to establish Li-Yau type estimates for it. With these estimates we construct a parametrix for our operator and establish our Fredholm results.  This work is joint with Rafe Mazzeo" |
April 06, 2015, 12:00 - 2:00 PM at Science Center 232 |
| GAUGE THEORY, TOPOLOGY, AND SYMPLECTIC GEOMETRY SEMINAR |
Tara Holm (CORNELL UNIVERSITY) |
The Topology of Toric Origami Manifolds |
A folded symplectic form on a manifold is a closed 2-form with the mildest possible degeneracy along a hypersurface. A special class of folded symplectic manifolds are the origami manifolds. In the classical case, toric symplectic manifolds can classified by their moment polytope, and much about their topological invariants can be read directly from the polytope. In this talk we examine the toric origami case: we will describe how toric origami manifolds can also be classified by their combinatorial moment data, and present some results about the topology of toric origami manifolds. This is joint work with Ana Rita Pires" |
April 03, 2015, 3:30 - 4:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
Motivic vector bundles |
" |
April 02, 2015, 3:30 - 5:30 pm at Science Center Hall E |
| NUMBER THEORY SEMINAR |
Yunqing Tang (HARVARD UNIVERSITY) |
Algebraic solutions of differential equations over the projective line minus three points |
The GrothendieckâKatz p-curvature conjecture predicts that an arithmetic differential equation whose reduction modulo p has vanishing p-curvatures for almost all p, has finite monodromy. It is known that it suffices to prove the conjecture for differential equations on the projective line minus three points. In this talk, I will focus on this case and introduce a p-adic convergence condition, which would hold if the p-curvature is defined and vanishes. Using the algebraicity criteria established by Andr\ e, Bost, and Chambert-Loir, I will prove a variant of this conjecture for the projective line minus three points, which asserts that if the equation satisfies the above convergence condition for all p, then its monodromy is trivial." |
April 01, 2015, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Sunil Chhita (UNIVERSITY OF BONN, ICERM) |
The two-periodic Aztec diamond |
Random domino tilings of the Aztec diamond shape exhibit interesting features and statistical properties related to random matrix theory. As a statistical mechanical model it can be thought of as a dimer model or as a certain random surface. We consider the Aztec diamond with a two-periodic weighting which exhibits all three possible phases that occur in these types of models, often referred to as solid, liquid and gas.  This model is considerably harder to analyze than the uniform model which only has two phases, liquid and solid. I will give an overview of some of the asymptotic results for the two-periodic Aztec diamond that have been obtained in joint work with Kurt Johansso" |
April 01, 2015, 11:30 am - 1:00 pm at Science Center 232 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
Kevin Pilgrim (INDIANA UNIVERSITY) |
On the classification of critically fixed rational maps |
I will discuss the classification of rational maps each of whose critical points is also a fixed-point" |
April 01, 2015, 4:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Hong-Jian He (TSINGHUA UNIVERSITY) |
Higgs Boson as the Origin of Mass and Inflation |
The discovery of a spin-0 Higgs boson (125GeV) at CERN Large Hadron Collider (LHC) is a milestone in fundamental science, and marks a historical turning point of particle physics. Why is it expected not to be the same Higgs boson as predicted by the Standard Model of particle physics? Does it provide the origin of masses for all elementary particles? Can it serve as the inflaton to drive cosmological inflation for hot big bang? How would the new physics associated with this Higgs boson be probed at high energy colliders and cosmic observations? In this colloquium, I will discuss some clues and implications of the above questions" |
April 01, 2015, 4:00 PM at Science Center Hall A |
| DIFFERENTIAL GEOMETRY SEMINAR |
Washington Taylor (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
Classifying elliptic Calabi-Yau threefolds and fourfolds, and Mordell-Weil groups from the physics of F-theory |
Recent developments motivated by the physics of F-theory have led to new tools and insights for classifying elliptic Calabi-Yau threefolds and fourfolds. The physical notion of Higgsing can be used to understand both the structure of the base of such elliptic fibrations, and aspects of the Mordell-Weil group. This talk will describe some aspects of these developments and results on classifying elliptic Calabi-Yau threefolds, fourfolds, and low rank Mordell-Weil groups" |
March 31, 2015, 4:15 PM at Science Center 507 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Cagatay Kutluhan (SUNY AT BUFFALO) |
A Heegaard Floer analogue of algebraic torsion |
We explain how to construct a refinement of the contact invariant in Heegaard Floer homology that is better at distinguishing overtwisted contact structures from tight ones" |
March 27, 2015, 3:30 - 4:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Marc Hoyois (MIT) |
Morel's A^1-homotopical classification of vector bundles, part II |
" |
March 26, 2015, 3:30 - 5:30 pm at Science Center Hall E |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Alan Hammond (UC BERKELEY) |
KPZ Line Ensemble: a marriage of integrability and probability |
The KPZ equation, introduced by Kardar, Parisi and Zhang, is a stochastic PDE that models randomly evolving interfaces that are subject to constraining forces such as surface tension. It is anticipated to be a universal object, in the sense that many microscopic models will share the KPZ equation as an accurate asymptotic description of their late time behavior. This view is supported by extensive numerical evidence, recent experimental evidence involving liquid crystal instabilities, and a limited but growing body of mathematically rigorous work. In recent work arXiv:1312.2600 with Ivan Corwin, we present a new technique for the analysis of the KPZ equation. The solution to the equation is represented as the lowest indexed curve in an N-indexedensemble of curves, which we call a KPZ line ensemble. Curves within the ensemble enjoy a natural invariance under resampling, the H-Brownian Gibbs property, which property has the effect of energetically penalizing, but not absolutely forbidding, the crossing of adjacently indexed curves. This property is inherited from the O Connell Yor semi-discrete continuum random polymer ensemble after a limiting procedure is applied. The H-Brownian Gibbs property is an integrable one, in the sense that the precursor O Connell-Yor ensemble is known to enjoy it by virtue of this ensemble s algebraic structure. However, it also offers a powerful probabilistic tool for the analysis of the KPZ equation. Since the solution of this equation is embedded in a KPZ line ensemble, we may analyse it using the H-Brownian Gibbs property, and in this way derive significant new estimates regarding the regularity and local structure of the KPZ solution. As I will aim to explain, these new estimates are valid uniformly in the time parameter for the KPZ equation, even after a natural rescaling of the equation is undertaken which accesses the fluctuation behavior of the KPZ evolutio" |
March 25, 2015, 11:30 am - 1:00 pm at Science Center 232 |
| NUMBER THEORY SEMINAR |
Brian Conrad (STANFORD UNIVERSITY) |
A Lefschetz Principle in non-archimedean geometry |
In analytic geometry over a non-archimedean field it is often convenient to work over a ground field that is algebraically closed, but that can create some difficulties because such fields have non-noetherian valuation ring. We explain a technique based on deformation theory and formal algebraic spaces to reduce certain problems in relative non-archimedean geometry to the case of a discretely-valued ground field, and give an application to de Rham cohomology, answering a question of P. Scholze. This is joint work with O. Gabber" |
March 25, 2015, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Peter Qian (UNIVERSITY OF WISCONSIN, MADISON) |
Some Statistical Aspects of Uncertainty Quantification |
Computer simulations, such as computational fluid dynamics, finite element analysis, agent-based models and multi-physics codes, are widely used in science, engineering and business for studying complex phenomena. As simulation models are never perfect and possess various uncertainties, including random initial condition and boundary conditions, input uncertainty and model discrepancy, uncertainty quantification (UQ) plays a big role in simulation-based decision-making. Without a rigorous mathematical framework for UQ in a simulation model, the simulation results and the consequent decision-making can be misleading. As statisticians, we all know the heart of statistics is the quantification of uncertainty. The motivation behind this talk is to discuss three statistical aspects of the emerging field of UQ. First, scalable design of experiments methods are developed to efficiently run complex simulations in parallel. These designs can be divided into slices and have a natural interface with high performance computing platforms. Second, a theoretical framework is introduced to investigate the statistical and numerical tradeoff of an approximation model for a black-box simulation code with Big Data. Guided by this framework, a sequential method called iKriging is introduced to build an accurate approximation model with a large number of observations. Third, a new statistical method is introduced to efficiently solve optimization under uncertainty problems. The key idea of the method is to embed negative dependence among batches to significantly reduce the variability of sample average approximations of a stochastic program. A number of examples will be used for illustrating the developed methods" |
March 25, 2015, 4:00 PM at Science Center Hall A |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
Adam Epstein (UNIVERSITY OF WARWICK) |
Generalizing Douady's Magic Formula |
Adrien Douady observed that the dyadic affine transformation $\theta \mapsto \frac{1}{4}\theta +\frac{1}{2}$ sends angles of external rays landing on the main cardioid of the Mandelbrot set to angles of rays landing on the real axis. We show that every hyperbolic component gives rise to such a formula" |
March 25, 2015, 4:00 - 5:00 PM at Science Center 507 |
| SPECIAL DIFFERENTIAL GEOMETRY SEMINAR |
Joergen Andersen (AARHUS UNIVERSITY) |
Basics of Geometric Quantization and moduli spaces of flat connections |
In this talk we will start with a brief introduction to geometric quantization for general symplectic manifolds. Following this we will move to the application of geometric quantization on the moduli spaces of flat connections on surfaces. Towards the end of the talk we will discuss analogies with the quantization of the cohomology of Calabi-Yau manifolds relevant to the study of the holomorphic anomaly equations coming from string theory" |
March 25, 2015, 2:00 PM at Science Center 530 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Jesus Martinez-Garcia (JOHNS HOPKINS ) |
On the moduli space of cubic surfaces and their anticanonical divisors |
We study variations of GIT quotients of log pairs (X,D) where X is a hypersurface of some fixed degree and D is a hyperplane section. GIT is known to provide a finite number of possible compactifications of such pairs, depending on one parameter. Any two such compactifications are related by birational transformations. We describe an algorithm to study the stability of the Hilbert scheme of these pairs, and apply our algorithm to the case of cubic surfaces. Finally, we relate this compactifications with the (conjectural) moduli space of log K-semistable pairs. This is work in progress with Patricio Gallardo (University of Georgia)" |
March 24, 2015, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Laura Schaposnik (UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN) |
Higgs bundles, spectral data, and applications |
Higgs bundles (introduced by N. Hitchin in 1987) are pairs of holomorphic vector bundles and holomorphic 1-forms taking values in the endomorphisms of the bundle. The moduli space of Higgs bundles carries a natural Hyperkahler structure, through which we can study Lagrangian subspaces (A-branes) or holomorphic subspaces (B-branes) with respect to each structure. Notably, these A and B-branes have gained significant attention in string theory. We shall begin the talk by first introducing Higgs bundles for complex Lie groups and the associated Hitchin fibration, and recalling how to realize Langlands duality through spectral data. We shall then look at a natural construction of families of subspaces which give different types of branes. Finally, by means of spectral data, we shall relate these subspaces to the study of 3-manifolds and surface group representations. We shall conclude with some conjectures related to Langlands duality" |
March 24, 2015, 4:15 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
An Huang (HARVARD UNIVERSITY) |
Chain integral solutions to GKZ system. |
" |
March 23, 2015, 12:00 - 2:00 PM at Science Center 232 |
| BASIC NOTIONS SEMINAR |
Brian Conrad (STANFORD UNIVERSITY) |
The arithmetic Lefschetz Principle |
In complex algebraic geometry there is a general technique called the Lefschetz Principle which roughly says that for certain appropriately-formulated algebro-geometric problems over a general field of characteristic 0, it is sufficient to solve the problem over the complex numbers (where one has access to analytic and topological methods). But this idea has relevance far beyond its traditional setting, and in fact underlies a wide array of powerful methods (sometimes called spreading out) for relating problems in characteristic 0 (even over the complex field) or over the integers to problems over (many) finite fields, where new tools become available (point-counting, Frobenius, etc.). This has been widely used by experts since the 1960 s but is not generally explained in the literature outside of EGA. We will illustrate the basic idea with a few interesting examples, not assuming prior familiarity with the usual Lefschetz Principle (or EGA)" |
March 23, 2015, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Yuri Bakhtin (COURANT INSTITUTE) |
Burgers equation with random forcing |
The Burgers equation is one of the basic nonlinear evolutionary PDEs. The study of ergodic properties of the Burgers equation with random forcing began in 1990 s. The natural approach is based on the analysis of optimal paths in the random landscape generated by the random force potential. For a long time only compact cases of the Burgers dynamics on a circle or bounded interval were understood well. In this talk, I will discuss the Burgers dynamics on the entire real line with no compactness or periodicity assumption on the random forcing. The main result is the description of the ergodic components and existence of a global attracting random solution in each component. The proof is based on ideas from the theory of rst or last passage percolation. My new work on kicked forcing is an extension of joint work with Eric Cator and Kostya Khanin on Poissonian forcing" |
March 18, 2015, 11:30 am - 1:00 pm at Science Center 530 |
| INFORMAL COMBINATORICS SEMINAR |
Anand Louis (PRINCETON UNIVERSITY) |
Hypergraph Heat Operators and Applications |
Graph and hypergraph partitioning problems are a central topic of research in the study of algorithms and complexity theory, with connections to sampling algorithms, mixing time of Markov chains, metric embeddings, among others. There has been a lot of work studying the eigenvalues of a graph and relating it to combinatorial properties of the graph. It has remained open to define a suitable spectral model for hypergraphs whose spectra can be used to estimate various combinatorial properties of the hypergraph. I will define a heat operator for hypergraphs which generalizes the heat kernel for graphs. I will demonstrate the utility of this operator by showing generalizations of some known results from spectral graph theory to hypergraphs; for e.g. bounding various hypergraph expansion parameters via eigenvalues, bounding the diameter of the hypergraph, mixing time of this operator, etc." |
March 13, 2015, 1:00 - 2:00 PM at Science Center 530 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Jingyu Zhao (COLUMBIA UNIVERSITY) |
Periodic Symplectic Cohomologies |
Periodic cyclic homology group associated to a mixed complex was introduced by Goodwillie. In this talk, I will explain how to apply this construction to the symplecticcochain complex of a Liouville domain and obtain two periodic symplectic cohomology theories, which are called periodic symplectic cohomology and finitely supported periodic symplectic cohomology, respectively. The main result is that there is a localization theorem for the finitely supported periodic symplectic cohomology" |
March 13, 2015, 3:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Jeremy Hahn (HARVARD UNIVERSITY) |
Wilson spaces as atomic even spaces |
" |
March 12, 2015, 3:30 - 5:30 pm at Science Center Hall E |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
Sam Taylor ( YALE UNIVERSITY) |
Hyperbolic extensions of free groups |
Every subgroup $G$ of the outer automorphism group of a finite-rank free group $F$ naturally determines a free group extension $1\to F \to E_G \to G\to 1$. In this talk, I will discuss geometric conditions on the subgroup $G$ that imply its corresponding extension $E_G$ is hyperbolic. These conditions are in terms of the action of G on the free factor complex of $F$ and allow one to easily build new examples of hyperbolic free group extensions. This is joint work with Spencer Dowdall" |
March 11, 2015, 04:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Shrenik Shah (COLUMBIA UNIVERSITY) |
Some strong twisted base changes for unitary similitude groups |
Labesse, Morel, Skinner, and Shin have attached twisted base changes (on general linear groups) to regular cohomological cuspidal automorphic representations on certain unitary similitude groups. The expected local-global compatibility relations hold at places where the group is split or where the similitude group and representation are unramified. We improve this to include certain limited cases where the group is ramified. This allows us to construct some strong twisted base changes unconditionally for unitary similitude groups, which are needed in recent work of Skinner-Urban on the Bloch-Kato conjecture. We obtain new cases of the generalized Ramanujan conjecture in this setting. Our approach combines automorphic and p-adic methods" |
March 11, 2015, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Yan Guo (BROWN UNIVERSITY - DIVISION OF APPLIED MATHEMATICS) |
Absence of shocks in Euler-Maxwell system for two-fluid models in plasma |
As the cornerstone of two-fluid models in plasma theory, Euler-Maxwell (Euler-Poisson) system describes the dynamics of compressible ion and electron fluids interacting with their own self-consistent electromagnetic field. It is also the origin of many famous dispersive PDE such as KdV, NLS, Zakharov, ...etc. The electromagnetic interaction produces plasma frequencies which enhance the dispersive effect, so that smooth initial data with small amplitude will persist forever for the Euler-Maxwell system, suppressing possible shock formation. This is in stark contrast to the classical Euler system for a compressible neutral fluid, for which shock waves will develop even for small smooth initial data. A survey along this direction for various two-fluid models will be given during this talk" |
March 11, 2015, 4:00 PM at Science Center Hall A |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Ankur Moitra (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
Tensor Prediction, Rademacher Complexity and Random 3-XOR |
Here we study the tensor prediction problem, where the goal is to accurately predict the entries of a low rank, third-order tensor (with noise) given as few observations as possible. We give algorithms based on the sixth level of the sum-of-squares hierarchy that work with roughly m = n^3/2 observations, and we complement our result by showing that any attempt to solve tensor prediction with fewer observations through the sum-of-squares hierarchy would run in moderately exponential time. In contrast, information theoretically roughly m = n observations suffice. This work is part of a broader agenda of studying computational vs. statistical tradeoffs through the sum-of-squares hierarchy. In particular, for linear inverse problems (such as tensor prediction) the natural sum-of-squares relaxation gives rise to a sequence of norms. Our approach is to characterize their Rademacher complexity. Moreover, both our upper and lower bounds are based on connections between this, and the task of strongly refuting random 3-XOR formulas, random matrix theory and the resolution proof system. This talk is based on joint work with Boaz Bara" |
March 11, 2015, 11:30 am - 1:00 pm at Science Center 232 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Klaus Hulek (LEIBNIZ UNIVERSITY HANNOVER) |
Stable cohomology of compactifications of Ag |
A well known result of Borel says that the cohomology of Ag stabilizes. This was generalized to the Satake compactification by Charney and Lee. In this talk we will discuss whether the result can also be extended to toroidal compactifictaions. As we shall see this cannot be expected for the second Vornoi compactification, but we shall show that the cohomology of the perfect cone compactification does stabilize. We shall also discuss partial compactifications, in particular the matroidal locus. This is joint work with Sam Grushevsky and Orsola Tommasi" |
March 10, 2015, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Daniel Cristofaro-Gardiner (HARVARD UNIVERSITY) |
Symplectic embeddings and lattice point enumeration |
Embedding problems in symplectic geometry are in general poorly understood. In dimension four, however, powerful techniques exist for making these kind of problems more tractable. I will survey some recent progress concerning symplectic embeddings of four-dimensional âtoric domainsâ. It turns out that in many cases, Hutchingsâ âembedded contact homology capacitie" |
March 10, 2015, 4:15 PM at Science Center 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Liang Kong (UNIVERSITY OF NEW HAMPSHIRE AND TSINGHUA UNIVERSITY) |
Lattice models for 2+1D topological orders with gapped boundaries |
This is an introductory talk on lattice models for 2+1D topological orders with gapped boundaries. I will start with Kitaev s toric code model, then move on to general Levin-Wen models enriched by gapped boundaries and domain walls. I will explain the boundary-bulk relation in the framework of Levin-Wen models. At the end, I will provide a dictionary between mathematical notions and physics notions. It is a joint work with Alexei Kitaev." |
March 10, 2015, 2:00 - 3:30 PM at Science Center 530 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Peng Gao (HARVARD UNIVERSITY MATHEMATICS DEPT) |
An example of a non-reductive GIT quotient |
" |
March 09, 2015, 12:00 - 2:00 PM at Science Center 232 |
| BASIC NOTIONS SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Representation Theory Between Characteristic Zero and Characteristic p |
Let G be a finite group. One can study representations of G over any field k: that is, vector spaces over k equipped with an action of G. In general, such representations behave very differently in characteristic zero (where all representations are completely reducible) and in characteristic p (where, if G is a p-group, there are no irreducible representations other than the trivial representation). In this talk, I will discuss representation theory over more exotic fields known as Morava K-theories, which in some sense interpolate between fields of characteristic zero and fields of characteristic p and share many pleasant features of both. No prior familiarity with Morava K-theory will be assumed" |
March 09, 2015, 3:00 PM at Science Center 507 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Laura Starkston (UNIVERSITY OF TEXAS - AUSTIN) |
Symplectic fillings of Seifert fibered spaces |
Although the existence of a symplectic filling is well-understood for many contact 3-manifolds, complete classifications of all symplectic fillings of a particular contact manifold are more rare. Relying on a recognition theorem of McDuff for closed symplectic manifolds, we can understand this classification for certain Seifert fibered spaces with their canonical contact structures. Even in cases without complete classification statements, the techniques used can suggest constructions of symplectic fillings with interesting topology. These fillings can be used in cut-and-paste operations to construct examples of exotic 4-manifolds" |
March 06, 2015, 3:30 - 4:30 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Nikita Nekrasov (CENTER FOR GEOMETRY & PHYSICS, STONY BROOK) |
Crossed instantons and qq-characters |
I will describe a compactification of the moduli space of instantons in gauge theory on the union of two copies of Euclidean space R^4 intersecting transversely in R^8, and its orbifolds. The theory of qq-characters, deformations of the characters of Kac-Moody groups and q-characters of quantum affine algebras, is an application, leading to the solution of quantum many-body systems such as elliptic Calogero-Moser." |
March 06, 2015, 4:00 PM at Science Center Hall A |
| THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
Constructing algebraic vector bundles on projective spaces |
" |
March 05, 2015, 3:30 - 5:30 pm at Science Center Hall E |
| NUMBER THEORY SEMINAR |
Alexander Stasinski (DURHAM UNIVERSITY) |
Representation zeta functions of simple Lie groups and reductive groups over local rings |
A representation zeta function is a Dirichlet series whose nth coefficient is the number of n-dimensional representations of a given group. They were first introduced for compact semisimple Lie groups by E. Witten who also proved that their special values at positive even integers are rational multiples of powers of \pi. In a seminal paper, M. Larsen and A. Lubotzky studied representation zeta functions of several classes of linear groups, including certain simple Lie groups and linear groups over local rings. Zeta functions of these groups appear naturally as the local factors in the Euler product of representation zeta functions of arithmetic groups. One of the main objects of study is the abscissa of convergence of a representation zeta function, which governs the polynomial degree of the representation growth. Larsen and Lubotzky proved that the abscissa of Witten zeta functions of simple Lie groups is r/k, where r is the rank of the group and k is the number of positive roots. We will give a new proof o" |
March 04, 2015, 3:00 PM at Science Center 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
Alden Walker (UNIVERSITY OF CHICAGO) |
Circle actions on the boundary of Schottky space |
To a complex parameter c, we associate the two-generator iterated function system {z -> cz-1, z -> cz+1}. I ll describe how the IFS for certain parameters (those on the boundary of the connectedness locus) can give rise to circle actions. A finite amount of data encoded in these circle actions describes the set of cut points in the limit set of the IFS. In addition, these circle actions can be thought of as double covers of Lorenz maps and generalizations. This talk should be broadly accessible, and pictures will be provided. This is joint work with Danny Calegari" |
March 04, 2015, 4:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Ivan Corwin (CLAY INSTITUTE, COLUMBIA, INSTITUTE HENRI POINCARE, PACKARD FOUNDATION) |
Stochastic quantum integrable systems |
We describe recent work involving interacting particle systems related to quantum integrable systems. This theory serves as an umbrella for exactly solvable models in the Kardar-Parisi-Zhang universality class, as well as provides new examples of such systems, and new tools in their analysis" |
March 04, 2015, 11:30 am - 1:00 pm at Science Center 232 |
| MATHEMATICAL PHYSICS SEMINAR |
Liming Ge (UNIVERSITY OF NEW HAMPSHIRE) |
Entropy Occurs in Number Theory |
Entropy, a notion initiated in physics by Boltzmann, has blossomed in mathematics. Amongst all Kolmogorov s and Shannon s entropies are two important but distinct ones. We shall introduce a new notion of entropy for arithmetic functions (or subsets of natural numbers) that shares properties of entropies in both dynamics and information theory. Its connections with classical number theory and topological dynamics are explained" |
March 03, 2015, 2:00 PM at Laboratory for Integrated Science (LISE), 15 Oxford St, Room 303 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Baris Coskunuzer (MIT & KOC UNIVERSITY) |
Minimal Surfaces with Arbitrary Topology in H^2xR |
In this talk, we show that any open orientable surface can be embedded in H^2xR as a complete area minimizing surface. Furthermore, we will discuss the asymptotic Plateau problem in H^2xR, and give a fairly complete solution." |
March 03, 2015, 4:15 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Michael Rapoport (UNIVERSITY OF BONN) |
On accessible p-adic period domains |
This will be an update on my talk on p-adic period domains in 2010. I will concentrate on the question when period domains are non-trivial, a question that came up in relation to the results of Scholze on the Gross-Hopkins map to Lubin-Tate space" |
March 02, 2015, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Guglielmo Lockhart (HARVARD UNIVERSITY PHYSICS) |
Self-dual strings of 6d SCFTs and local elliptic CYs |
" |
March 02, 2015, 12:00 - 2:00 PM at Science Center 232 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Daniel Halpern-Leistner (COLUMBIA UNIVERSITY) |
Morse-like stratifications of moduli problems in algebraic geometry |
For a Hermitian vector bundle on a Riemann surface, the gradient descent flow of the Yang-Mills functional on the space of Hermitian connections defines a stratification of the moduli of complex structures (up to gauge equivalence) on that vector bundle. In algebraic geometry, this corresponds to the Harder-Narasimhan stratification of the moduli of algebraic vector bundles on the Riemann surface -- the gradient descent flow line for an unstable bundle is analogous to its Harder-Narasimhan filtration. I will show how to reformulate the question of existence and uniqueness of the Harder-Narasimhan filtration as a convex optimization problem on a large topological space associated to the vector bundle. I will discuss how this leads to a framework for constructing stratifications of this kind for moduli problems which are not specifically described as infinite dimensional symplectic reductions" |
February 27, 2015, 3:30 - 4:30 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Noureddine El Karoui (UC BERKELEY) |
On high-dimensional robust regression and inefficiency of maximum likelihood methods |
I will discuss the behavior of widely used statistical methods in the high-dimensional setting where the number of observations, n, and the number of predictors, p, are both large. I will present limit theorems about the behavior of the corresponding estimators, their asymptotic risks etc... The results apply not only to robust regression estimators, but also Lasso-type estimators and many much more complicated problems. Some of the results answer a question raised by Huber in his seminal 73 paper on robust regression. Many surprising statistical phenomena occur: for instance, maximum likelihood methods are shown to be (grossly) inefficient, and loss functions that should be used in regression are shown to depend on the ratio p/n. This means that dimensionality should be explicitly taken into account when performing simple tasks such as regression. More generally, we ll see that intuition based on results obtained in the small p, large n setting leads to misconceptions and the use of suboptimal procedures. It also turns out that inference is possible in this setting. We ll also see that the geometry of the design matrix plays a key role in these problems and use this fact to disprove claims of universality of some of the results. Mathematically, the tools needed mainly come from random matrix theory, measure concentration and convex analysis. Based on several papers, including some which are joint work with Derek Bean, Peter Bickel, Chingwhay Lim and Bin Yu" |
February 26, 2015, 12:50 - 1:50 pm at Science Center 232 |
| THURSDAY SEMINAR |
Marc Hoyois (MIT) |
Morelâs A^1-homotopical classification of vector bundles, part I |
" |
February 26, 2015, 3:30 - 5:30 pm at Science Center Hall E |
| HARVARD, BRANDEIS, MIT, NORTHEASTERN JOINT COLLOQUIUM AT HARVARD |
Melanie Matchett Wood (UNIVERSITY OF WISCONSIN, MADISON) |
Random groups in number theory and random integral matrices |
There are certain finite abelian groups that arise from objects in number theory that are quite mysterious and of great interest, for example the class group arising from a finite extension of the rational numbers, or the Tate-Shafarevich group of an elliptic curve y^2=x^3+ax+b (for some rational numbers a,b). We discuss the question of what a class group of a random extension, or the Tate-Shafarevich group of a random elliptic curve, looks like, and explain heuristics of several authors including Cohen and Lenstra, and Delaunay, for how these random groups behave. Finally we will relate the predictions of these heuristics to phenomena that can be seen and proven about random integral matrices" |
February 26, 2015, 4:30 PM at Science Center Hall A |
| NUMBER THEORY SEMINAR |
Noam Elkies (HARVARD UNIVERSITY) |
How many points can a genus-3 curve have? |
Caporaso, Harris, and Mazur showed that under the Bogomolov-Lang conjectures there is, for every integer g>1 and every number field K, an upper bound B(g,K) on #C(K) as C ranges over all genus-g curves over K. In the case g=3, we use K3 surfaces X with large NS_Q(X) to search for curves C/Q with many rational points, as we did some years ago for g=2. For hyperelliptic curves we tie the record of 176 points, set in 1995 by Keller and Kulesz, with a new curve that (unlike the Keller-Kulesz curve) has no extra symmetries" |
February 25, 2015, 3:00 PM at Science Center 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
Alex Kontorovich (RUTGERS UNIVERSITY) |
Equidistribution of Shears and Applications |
A shear is a unipotent translate of a cuspidal geodesic ray in the quotient of the hyperbolic plane by a non-uniform discrete group (possibly of infinite co-volume). In joint work with Dubi Kelmer, we prove the regularized equidistribution of shears under large translates. We give applications including to moments of GL(2) automorphic L-functions, and to effective counting of integer points on affine homogeneous varieties (in particular resolving a missing case of the Eskin-McMullen/Duke-Rudnick-Sarnak machinery). No prior knowledge of these topics will be assumed." |
February 25, 2015, 4:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Nike Sun (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
The exact k-SAT threshold for large k. |
We establish the random k-SAT threshold conjecture for all k exceeding an absolute constant k(0). That is, there is a single critical value c*(k) such that a random k-SAT formula at clause-to-variable ratio c is with high probability satisfiable for c < c*(k), and unsatisfiable for c > c*(k). The threshold c*(k) matches the explicit prediction derived by statistical physicists on the basis of the one-step replica symmetry breaking (1RSB) heuristic. In the talk I will describe the main obstacles in computing the threshold, and explain how they are overcome in our proof. Joint work with Jian Ding and Allan Sly" |
February 25, 2015, 11:30 am - 1:00 pm at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Chi-Wang Shu (BROWN UNIVERSITY - DIVISION OF APPLIED MATHEMATICS) |
Discontinuous Galerkin method for hyperbolic equations with delta-singularities |
Discontinuous Galerkin (DG) methods are finite element methods with features from high resolution finite difference and finite volume methodologies and are suitable for solving hyperbolic equations with nonsmooth solutions. In this talk we will describe our recent work on the study of DG methods for solving hyperbolic equations with $\delta$-singularities in the initial condition, in the source term, or in the solutions. For such singular solutions, many numerical techniques rely on modifications with smooth kernels and hence may severely smear such singularities, leading to large errors in the approximation. On the other hand, the DG methods are based on weak formulations and can be designed directly to solve such problems without modifications, leading to very accurate results. We will discuss both error estimates for model linear equations, in negative norm and in strong norm after post-processing, and applications to nonlinear systems including the rendez-vous systems and pressureless Euler equations involving $\delta$-singularities in their solutions. For the nonlinear case a high order accuracy bound-preserving limiter is crucial to maintain nonlinear stability and to avoid blowups of the numerical solution. This is joint work with Yang Yang, Dongming Wei and Xiangxiong Zhang" |
February 25, 2015, 4:00 PM at Science Center Hall A |
| DIFFERENTIAL GEOMETRY SEMINAR |
Juergen Jost (MAX PLANCK INSTITUTE) |
Super Riemann surfaces, metrics, and the gravitino |
" |
February 24, 2015, 4:15 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Matthew Grimes (CU - BOULDER) |
Universal moduli spaces of vector bundles and the log-minimal model program on the moduli of curves |
It is well-known that for a fixed degree and rank every smooth curve admits a moduli space of slope semi-stable vector bundles. A natural question to ask is if these moduli spaces can be stitched together to form a universal moduli space of vector bundles over the moduli space of curves. Simpson showed that this is possible over the moduli space of automorphism-free curves, and work of Caporaso (rank 1) and Pandharipande provides a universal moduli space of vector bundles over the moduli space of Deligne--Mumford-stable curves. My talk will discuss recent work in this area extending these results to the construction of a universal moduli space of vector bundles over Schubert s moduli space of pseudo-stable curves" |
February 24, 2015, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Baosen Wu (HARVARD UNIVERSITY) |
New vector bundles in heterotic string compactification |
" |
February 23, 2015, 12:00 - 2:00 PM at Science Center 232 |
| BASIC NOTIONS SEMINAR |
Daniel Cristofaro-Gardiner (HARVARD UNIVERSITY) |
Length and volume on contact three-manifolds |
The Weinstein conjecture states that on any closed manifold, a âReebâ vector field must have at least one closed orbit. The three dimensional version of this conjecture was proved several years ago by Taubes. It is natural to then ask whether there is always a closed orbit with an a priori upper bound on its period. For scaling reasons, this is not possible; however, it is conjectured that such a bound exists once one fixes the contact volume of the manifold. I will discuss this conjecture, and explain recent joint work with Michael Hutchings and Vinicius Ramos proving an asymptotic version. I will also explain an application to the problem of bounding the number of Reeb orbits from below" |
February 23, 2015, 3:00 PM at Science Center 507 |
| HARVARD LOGIC SEMINAR |
Will Boney (UNIVERSITY OF ILLINOIS AT CHICAGO) |
Tameness in Abstract Elementary Classes |
Tameness is a locality property of Galois types in AECs. Since its isolation by Grossberg and VanDieren 10 years ago, it has been used to prove new results (upward categoricity transfer, stability transfer) and replace set-theoretic hypotheses (existence of independence notions). In this talk, we will outline the basic definitions, summarize some key results, and discuss some open questions related to tameness" |
February 23, 2015, 4:30 - 5:30 PM at Logic Center, 2 Arrow St, Rm 420 |
| GAUGE THEORY, TOPOLOGY AND SYMPLECTIC GEOMETRY SEMINAR |
Alexandra Kjuchukova (UNIVERSITY OF PENNSYLVANIA) |
On the classification of branched covers of four-manifolds |
Given two simply-connected closed oriented topological four-manifolds X and Y, I ask: can Y be realized as a branched cover of X? For B a surface embedded in X with an isolated singularity, I will prove a necessary condition for the existence of an irregular dihedral branched covering map $f: Y \to X$ with branching set B. Conversely, given a simply-connected oriented closed four-manifold X, I will outline a construction realizing as irregular dihedral covers of X infinitely many of the manifolds Y afforded by the necessary condition" |
February 20, 2015, 3:30 - 4:30 pm at Science Center 507 |
| HARVARD, BRANDEIS, MIT, NORTHEASTERN JOINT COLLOQUIUM AT HARVARD |
Matthew Kahle (OHIO STATE UNIVERSITY) |
Recent Progress in stochastic topology |
The study of random topological spaces: manifolds, simplicial complexes, knots, and groups, has received a lot of attention in recent years. This talk will mostly focus on random simplicial complexes, and especially on a certain kind of topological phase transition, where the probability that that a given homology group is trivial passes from 0 to 1 within a very narrow window. The archetypal result in this area is the ErdĆ`sâRĂ©nyi theorem, which characterizes the threshold edge probability where the random graph becomes connected. One recent breakthrough has been in the application of Garland s method, which allows one to prove homology-vanishing theorems by showing that certain Laplacians have large spectral gaps. This reduces problems in random topology to understanding eigenvalues of certain random matrices, and the method has been surprisingly successful. Part of this is joint work with Christopher Hoffman and Elliot Paquette" |
February 19, 2015, 4:30 PM at Science Center Hall A |
| THURSDAY SEMINAR |
Clark Barwick (MIT) |
The Bass-Quillen Conjecture |
We present Lindelâs proof of the geometric case of the Bass-Quillen Conjecture" |
February 19, 2015, 3:30 - 5:30 PM at Science Center Hall E |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Dylan Thurston (INDIANA UNIVERSITY) |
Rubber Bands and Rational Maps |
Given a topological branched covering $f: (S^2,P) \to (S^2, P)$ of the sphere by itself, with branch values contained in $P$, can $f$ be realised as a rational map? William Thurston gave a criterion in 1982: If $f$ has a hyperbolic orbifold, it can be realised as a rational map iff there is not an invariant multicurve satisfying certain conditions. This condition is hard to apply in practice, since it involves checking infinitely many multicurves. We give a positive combinatorial condition, using the notion of \em{domination} of graphs, a stricter condition than being 1-Lipshitz. In more physical terms, $f$ is realised as a rational map iff, for some (or equivalently any) rubber-band spine $G$ for $S^2 \setminus P$, a sufficiently large inverse image $f^{-n}(G)$ of $G$ is looser than $G$" |
February 18, 2015, 4:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Maksym Radziwill (RUTGERS UNIVERSITY) |
A new proof of Selberg's central limit theorem |
In the 1940 s Selberg proved that after suitable normalization the distribution of the modulus of the Riemann zeta function on the critical line is log-normal. Despite several further refinements (going until the late 1970 s) this remained a difficult theorem. In this talk I am going to present a very recent simple proof of Selberg s theorem (joint work with K. Soundararajan). The talk will be reasonably self-contained and should give an idea of some recent innovations in the field. Those are closely tied to a probabilistic way of thinking about number-theoretic problems" |
February 18, 2015, 11:30 am - 1:00 pm at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Avi Loeb (HARVARD ASTRONOMY DEPARTMENT / INSTITUTE FOR THEORY & COMPUTATION) |
A Closer Look at Black Holes |
Several new techniques are currently being employed to probe the strong gravitational field in the vicinity of black holes. Long baseline interferometry at sub-millimeter wavelengths sets constraints on the silhouette of the black holes in the Galactic center (SgrA*) and M87. Stars which get tidally disrupted as they orbit too close to a single black hole are being discovered at cosmological distances. Electromagnetic counterparts of black hole binaries in galaxy mergers are being identified, and can be used to calibrate the rate of gravitational wave sources. Most interestingly, the recoil induced by the anisotropic emission of gravitational waves in the final plunge of binaries leaves unusual imprints on their host galaxies. Finally, the lecture will describe new constraints on the contribution of primordial black holes to the dark matter" |
February 18, 2015, 4:15 PM at Science Center Hall A |
| NUMBER THEORY SEMINAR |
Preston Wake (UNIVERSITY OF CHICAGO) |
Eisenstein Hecke algebras and pseudorepresentations |
The Iwasawa main conjecture (IMC) states that p-adic Dirichlet L-functions encode very important invariants of the class groups of cyclotomic fields. Motivated by a conjecture of Sharifi, we show that ring-theoretic properties of Eisenstein Hecke algebras encode even finer information about class groups than is provided by the IMC. In an ongoing joint work with Carl Wang Erickson, we show that these Eisenstein Hecke algebras are related to pseudodeformation ring" |
February 18, 2015, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Siu-Cheong Lau (HARVARD UNIVERSITY) |
A constructive approach to homological mirror symmetry |
Homological mirror symmetry conjecture asserts an equivalence between the category of Lagrangian submanifolds and the category of coherent sheaves of the mirror. The conjecture has been verified in several interesting cases by computing generators and relations of the categories. However such a computational approach hardly explains why homological mirror symmetry exists in general. In this talk I will introduce a mirror construction which always comes with a functor between the two categories. It produces mirrors which are not reachable by the original SYZ construction, and is naturally connected with non-commutative geometry" |
February 17, 2015, 4:15 - 5:30 pm at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Representation Theory Between Characteristic Zero and Characteristic p |
Let G be a finite group. One can study representations of G over any field k: that is, vector spaces over k equipped with an action of G. In general, such representations behave very differently in characteristic zero (where all representations are completely reducible) and in characteristic p (where, if G is a p-group, there are no irreducible representations other than the trivial representation). In this talk, I will discuss representation theory over more exotic fields known as Morava K-theories, which in some sense interpolate between fields of characteristic zero and fields of characteristic p and share many pleasant features of both. No prior familiarity with Morava K-theory will be assumed" |
February 16, 2015, 3:00 PM at Science Center 507 |
| THURSDAY SEMINAR |
Krishanu Sankar (HARVARD UNIVERSITY) |
Serre's problem on projective modules over a polynomial ring |
" |
February 12, 2015, 3:30 - 5:30 pm at Science Center Hall E |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
John H. Hubbard (CORNELL UNIVERSITY) |
On complex HĂ©non Maps |
Our best description of Julia sets for polynomials in one variable comes from laminations invariant under $z\mapsto z^d$, leading to the pinched disk model. I will describe this, and an attempt at generalizing this description to HĂ©non maps, leading to a ``pinched ball model . Unlike the case of polynomials, where invariant laminations are well understood, we have only the faintest idea of what ``invariant laminations might exist for HĂ©non mappings." |
February 11, 2015, 4:00 - 5:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Richard Freeman (HARVARD ECONOMICS) |
Understanding the world of knowledge through Big Data networks and graph theory |
" |
February 11, 2015, 4:15 PM at Science Center Hall A |
| NUMBER THEORY SEMINAR |
Abhinav Kumar (MIT/STONY BROOK) |
Moduli spaces of reducible Jacobians of genus 2 curves via Hilbert modular surfaces of square discriminant |
A reducible principally polarized abelian surface, with an (n,n)- isogeny to a product of elliptic curves, corresponds to a point on the Humbert surface of discriminant n^2 in the moduli space A_2 of ppas. Points on the double cover, which is a Hilbert modular surface, correspond to maps C -> E of degree n from a genus 2 curve to an elliptic curve. Explicit families of such reducible Jacobians for n = 2,3,4 were studied classically by Jacobi, Hermite, Bolza etc. in the guise of reduction of abelian integrals. I will give an alternate method to compute these moduli spaces explicitly by interpreting the Hilbert modular surface as a moduli space of K3 surfaces, and describe the results for n <= 11" |
February 11, 2015, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Jacob Fox (MIT) |
Combinatorics of Permutations |
A fundamental question in enumerative combinatorics asks: how many permutations on n letters avoid a given permutation? The famous Stanley-Wilf conjecture states that the answer grows exponentially in n. Marcus and Tardos proved this conjecture a decade ago with a remarkably simple argument. It was widely believed that the exponential constant, known as the Stanley-Wilf limit, grows quadratically in the size of the given permutation. We disprove this conjecture, showing that it grows exponentially in a power of the permutation size for almost all permutations. The proof utilizes tools from extremal and probabilistic combinatorics and new concepts including dyadic random matrices and interval minors" |
February 11, 2015, 11:30 am - 1:00 pm at Science Center 530 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Jesus Martinez-Garcia (JOHNS HOPKINS ) |
On the moduli space of cubic surfaces and their anticanonical divisors |
We study variations of GIT quotients of log pairs (X,D) where X is a hypersurface of some fixed degree and D is a hyperplane section. GIT is known to provide a finite number of possible compactifications of such pairs, depending on one parameter. Any two such compactifications are related by birational transformations. We describe an algorithm to study the stability of the Hilbert scheme of these pairs, and apply our algorithm to the case of cubic surfaces. Finally, we relate this compactifications with the (conjectural) moduli space of log K-semistable pairs. This is work in progress with Patricio Gallardo (University of Georgia)" |
February 10, 2015, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Valentino Tosatti (NORTHWESTERN UNIVERSITY) |
Degenerations and collapsing of Ricci-flat Calabi-Yau manifolds |
I will discuss the problem of understanding how Ricci-flat Calabi-Yau manifolds degenerate and collapse to lower-dimensional spaces, and how this is relevant to the Strominger-Yau-Zaslow picture of mirror symmetry. I will present some results in this direction, which are joint work with M. Gross, Y. Zhang, with H.J. Hein and with B. Weinkove, X.Yang" |
February 10, 2015, 4:15 - 5:30 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Maria Rodriguez (HARVARD UNIVERSITY PHYSICS) |
Exact Solutions for Extreme Black Hole Magnetospheres |
" |
February 09, 2015, 12:00 - 2:00 PM at Science Center 232 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Elisenda Grigsby (BOSTON COLLEGE) |
(Sutured) Khovanov homology and representation theory |
Khovanov homology associates to a link L in the three-sphere a bigraded vector space arising as the homology groups of an abstract chain complex defined combinatorially from a link diagram. It detects the unknot (Kronheimer-Mrowka) and gives a sharp lower bound (Rasmussen, using a deformation of E.S. Lee) on the 4-ball genus of torus knots. When L is realized as the closure of a braid--or more generally, of a balanced tangle--one can use a variant of Khovanov s construction due to Asaeda-Przytycki-Sikora and L. Roberts to define its sutured Khovanov homology, an invariant of the tangle closure in the solid torus. In this talk, I will describe some of the representation theory of the sutured Khovanov homology of a tangle closure. It (perhaps unsurprisingly) carries an action of the Lie algebra sl(2). More surprisingly, this action extends to the action of a slightly larger Lie superalgebra whose structure hints at a unification with the Lee deformation. This is joint work with Tony Licata and Stephan Wehr" |
February 06, 2015, 3:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
Algebraic vector bundles, introduction and overview |
" |
February 05, 2015, 4:00 - 6:00 PM at Science Center 507 |
| HARVARD, BRANDEIS, MIT, NORTHEASTERN JOINT COLLOQUIUM AT HARVARD |
Laure Saint-Raymond (ENS PARIS / HARVARD) |
From Newton's dynamics to the heat equation |
The goal of this lecture is to show how the brownian motion can be derived rigorously from a deterministic system of hard spheres in the limit where the number of particles $N$ tends to infinity, and their diameter simultaneously converges to 0. As suggested by Hilbert in his sixth problem, we will use the linear Boltzmann equation as an intermediate level of description for the dynamics of one tagged particle. We will discuss especially the origin of irreversibility, which is a fundamental feature of both the brownian motion and the Boltzmann equation having no counterpart at the microscopic level" |
February 05, 2015, 4:30 PM at Science Center Hall A |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Horng-Tzer Yau (HARVARD UNIVERSITY) |
Random matrices, Dyson Brownian Motion and Quantum Unique Ergodicity |
" |
February 04, 2015, 4:00 PM at Science Center Hall A |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Janosch Ortmann (UNIVERSITY OF TORONTO) |
Polymer models, particle systems and the KPZ universitality class |
KPZ universality describes a scaling behaviour that differs from the central limit theorem by the size of the fluctuations ($n^{1/3}$ instead of $n^{1/2}$) and the limiting distribution. Instead of the Gaussian, the Tracy-Widom distributions from random matrix theory appear in the limit. One approach to showing that a particular model belongs to the KPZ universality class is to obtain exact formulas for the distribution a particular observable; the height function for particle systems and the partition function in the case of polymer models. Until recently this had succeeded for only one discrete polymer model, namely the log-gamma polymer introduced by Seppalainen. Based on joint work with Neil O Connell I will discuss a polymer model with gamma weights." |
February 04, 2015, 11:30 am - 1:00 pm at Science Center 232 |
| NUMBER THEORY SEMINAR |
Bjorn Poonen (MIT) |
An adelic approach to counting Selmer group elements |
I will sketch an adelic approach towards understanding the Bhargava-Shankar theorems on the average size of Selmer groups of elliptic curves over Q" |
February 04, 2015, 3:00 - 4:00 pm at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Ronen Mukamel (UNIVERSITY OF CHICAGO) |
Kronecker's congruence and TeichmĂŒller curves in positive characteristic |
" |
February 04, 2015, 4:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
George Daskalopoulos (BROWN UNIVERSITY) |
Rigidities of Teichmueller space |
I will discuss applications of harmonic maps to solve rigidity questions of Teichmu Ìlcer space. This is joint work with C. Mese and builds further on the fundamental work of Gromov-Schoen and Jost-Yau.Â" |
February 03, 2015, 4:15 - 5:30 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Peng Zhao (SIMONS CENTER FOR GEOMETRY & PHYSICS, STONY BROOK) |
Cluster algebras from dualities of 2d N=(2,2) quiver gauge theories |
" |
February 02, 2015, 12:00 - 2:00 PM at Science Center 232 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
R. Inanc Baykur (UNIVERSITY OF MASSACHUSETTS AMHERST) |
Multisections of Lefschetz fibrations and topology of symplectic 4-manifolds |
We initiate an extensive study of multisections of Lefschetz fibrations via positive factorizations in framed mapping class groups. Using our techniques, we can reformulate and tackle various interesting conjectures and problems related to the topology of symplectic 4-manifolds. In this talk we will focus on the conjectural smooth classification of symplectic Calabi-Yaus and their fundamental groups in real dimension 4. If time permits, we will discuss some other applications as well; such as Stipsicz s conjectures on minimality and fiber sum decompositions, constructions of inequivalent Lefschetz fibrations and exotic pencils. Several parts of this work is joint with K. Hayano and N. Monden" |
January 30, 2015, 3:30 PM at Science Center 507 |
| **CANCELLED** NUMBER THEORY SEMINAR |
Alexander Lubotzky (HEBREW UNIVERSITY) |
From Ramanujan graphs to Ramanujan complexes |
**CANCELLED** Ramanujan graphs are optimal expanders (from spectral point of view). Explicit constructions of such graphs were given in the 80 s as quotients of the Bruhat-Tits tree associated with GL(2) over alocal field F, by suitable congruence subgroups. The spectral bounds were proved using works of Hecke, Deligne and Drinfeld on the" |
January 28, 2015, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Maksym Radziwill (RUTGERS UNIVERSITY) |
A new proof of Selberg's central limit theorem |
In the 1940 s Selberg proved that after suitable normalization the distribution of the modulus of the Riemann zeta function on the critical line is log-normal. Despite several further refinements (going until the late 1970 s) this remained a difficult theorem. In this talk I am going to present a very recent simple proof of Selberg s theorem (joint work with K. Soundararajan). The talk will be reasonably self-contained and should give an idea of some recent innovations in the field. Those are closely tied to a probabilistic way of thinking about number-theoretic problems" |
January 28, 2015, 12:00 - 1:00 PM at Science Center 232 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR **CANCELLED** |
Vasudevan Srinivas (TATA INSTITUTE OF FUNDAMENTAL RESEARCH) |
Stratified vector bundles on simply connected varieties in positive characteristic |
**CANCELLED** -This talk is a report on some joint work with Helene Esnault. We showed that on a smooth quasi-projective variety over the algebraic closure of a finite field, with trivial etale fundamental group, all stratfifed vector bundles are trivial, provided the variety admits a normal compactification with codimension 2 boundary. I will give some background, and discuss the steps going into the proof, one of which is a variant of the Grothendieck LEFF condition due to J.-B. Bost" |
January 27, 2015, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Chris Beasley (NORTHEASTERN UNIVERSITY) |
Self-Linking for Legendrian Knots |
" |
January 26, 2015, 12:00 - 2:00 PM at Science Center 232 |
| SPECIAL LECTURE SERIES |
Gaetan Chenevier (CNRS) |
Modular forms of classical groups and even unimodular lattices |
Details. The set X_n of isometry classes of even, unimodular lattices in euclidean space R^n has been determined for n <= 24, thanks to works of Mordell, Witt and Niemeier. The vector space of complex-valued functions on X_n is in a natural way a space of automorphic forms for the orthogonal group of the quadratic form (x_1)^2 + (x_2)^2 + ... + (x_n)^2 on Q^n, and as such, it is equipped with a collection of Hecke operators. In this series of lectures, I will explain how to determine the collection of automorphic representations, or if one prefers the n-dimensional l-adic Galois representations, associated with the Hecke eigenforms occurring in those spaces for n <= 24. This provides a rather curious list of automorphic representations, which turn out to be all non-tempered and build from certain Siegel modular forms of genus 1 and 2. As an application, it allows one to determine the p-neighborhood graph of the Niemeier lattices for each prime p. (The Wikipedia page on Niemeier lattices gives a nice representation of this graph for p = 2, which is due to Borcherds.) In dimension n = 16 which is the first interesting case, I will give an elementary proof based on Siegel theta series and triality. In dimension n = 24, the proof that I will present relies in particular on Arthur s recent results on the automorphic spectrum of classical groups. I will try to introduce Arthur s theory during the lectures. This is joint work with Jean Lannes" |
January 22, 2015, 3 - 4:30 PM at Science Center 507 |
| SPECIAL LECTURE SERIES |
Gaetan Chenevier (CNRS) |
Modular forms of classical groups and even unimodular lattices |
Details**See Jan 22, 2015 postin" |
January 20, 2015, 3 - 4:30 PM at Science Center 507 |
| SPECIAL LECTURE SERIES |
Gaetan Chenevier (CNRS) |
Modular forms of classical groups and even unimodular lattices |
Notes [PDF]**See Jan 22, 2015 postin" |
January 14, 2015, 3 - 4:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Michael Brown (UNIVERSITY OF NEBRASKA) |
A Generalization of the Atiyah-Bott-Shapiro Construction Applied to Matrix Factorizations |
" |
December 11, 2014, 4:00 - 5:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Joël Bellaiche (BRANDEIS UNIVERSITY) |
The eigencurve at classical points of weight one |
I will explain the proof of joint result with Mladen Dimitrov, that at regular classical points of weight one, the p-adic eigencurve is smooth, and is even etale over the weight space except at points which correspond to forms that have real multiplication by a quadratic field in which p is split. We use a Galois deformation calculation of a type already considered in earlier works, such as Calegari-Mazur, but introduce a new method to avoid using the Leopoldt conjecture, allowing for an unconditional result. I ll also discuss some applications of that result" |
December 10, 2014, 3:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Atanas Atansov, 3-4 pm / Eric Larson, 4-5 pm (HARVARD UNIVERSITY) |
Interpolation and vector bundles on curves |
We aim to address the following: When is there a (smooth) curve of degree d and genus g passing through n general points in Pr? In the first hour, we will start by relating these statements to a property of the normal bundle of curves in projective space, and look at several important examples and related questions. In the second hour, we give a resolution to this problem for rational curves (a result originally due to Sacchiero and Ran). Unlike the original methods, our techniques are geometric and coordinate-free; they moreover naturally generalize to curves of higher genus. We will end by giving a sketch of this generalization to arbitrary nonspecial curves (i.e., the range d â„ g + r). This is joint work with D. Yang" |
December 09, 2014, 3 - 5 pm at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Nike Sun (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
The exact k-SAT threshold for large k |
We establish the satisfiability threshold for random k-SAT for all k >= k_0. That is, there exists a limiting density alpha_s(k) such that a random k-SAT formula of clause density alpha is with high probability satisfiable for alpha < alpha_s(k), and unsatisfiable for alpha > alpha_s(k). The satisfiability threshold alpha_s(k) is given explicitly by the one-step replica symmetry breaking prediction from statistical physics. Joint work with Jian Ding and Allan Sly" |
December 05, 2014, 1:30 - 3:30 pm at Science Center 530 |
| SPECIAL LECTURE |
Hugh Woodin (HARVARD UNIVERSITY) |
Must the Continuum Hypothesis have an answer? |
This public lecture is an extra session of the seminar-course" |
December 04, 2014, 2:00 - 4:00 PM at Hall C **New Location** |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
S.T. Chui (UNIVERSITY OF DELAWARE) |
What's wrong with the finite elements method for Maxwell's equations. Kirchoff's law beyond lumped circuit element |
Ordinary magnets lose their effectiveness at frequencies above gigahertzes. A recent trend in metamaterials to create artificial magnets at optical frequencies is to exploit magnetic resonances in metallic strcutures. We discuss our recent work to understand and predict properties of such structures [2]. This consists of a rigorous extension of the Kirchoff law to beyond that with lumped circuit elements. Our approach provides for a physical way to understand metallic wire networks. For example, there is a folklore that, for a metallic wire of arbitrary shape of length L, the resonance wavelengths is close to twice its length divided by an integer, =2L/n. But no proof has ever been given. In our approach, this problem becomes analytically tractable. We have tested our method for a simple example of the transmission through a planar array of split rings and found that it requires much less memory and is two orders of magnitude faster than current commercial codes. This method can be extended to arbitrary surfaces with conformal harmonic maps. A simple example is the metallic disk." |
December 04, 2014, 1:15 pm at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Michael Brenner (HARVARD UNIVERSITY SEAS) |
Droplet splashing and other hydrodynamic singularities |
" |
December 03, 2014, 4:15 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS SPECIAL SEMINAR |
Frederic E. Daum (RAYTHEON COMPANY) |
Bayesian particle flow for estimation, decisions, and transport |
We derive a new algorithm to compute Bayesâ rule, using particle flow rather than a point wise multiplication. The particle flow is induced by a log-homotopy of the conditional density from the prior to the posteriori. This algorithm is similar to Monge-Kantorovich transport, but it is much simpler and faster, because we do not use any optimality criteria. In particular, there is no relevant notion of physical effort to transport our particles.  Consequently, we do not pick the flow to minimize a convex functional, and hence we avoid solving a variational problem. Moreover, we do not use resampling of particles or proposal densities or importance sampling or any Markov chain Monte Carlo method. But rather, we design the particle flow with the solution of a linear first order highly underdetermined PDE. We solve our PDE analytically as a formula, rather than using numerical methods, in order to reduce computational complexity. We have many methods to solve this PDE, but the best methods all avoid explicitly computing the normalizing constant of the conditional density. Our theory applies to smooth nowhere vanishing probability densities, and it is similar to JĂŒrgen Moserâs coupling. We compare the new flow with state-of-the-art methods, including: Hamiltonian Monte Carlo, Metropolis-adjusted Langevin (MALA), regularized particle filters, auxiliary particle filters, etc. Our particle flow is many orders of magnitude faster than standard particle filters for the same accuracy. Furthermore, our filter beats the extended Kalman filter accuracy by several orders of magnitude for difficult nonlinear problems. The computational complexity for nonlinear filtering generally depends on: dimension of the state vector, stability of the plant, initial uncertainty of the state vector, measurement accuracy, shape of the conditional density (e.g., log-concave), Lipschitz constants of the log-densities, smoothness of the densities, and ill-conditioning of the Fisher information matrix" |
December 03, 2014, 3:00 PM - 4:00 PM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Hau-tieng Wu (UNIVERSITY OF TORONTO) |
Graph connection Laplacian, principal bundle structure and ptychographic image processing |
Spectral methods like Diffusion Maps and Laplacian Eigenmaps in data analysis are based on eigenvectors and eigenvalues of graph Laplacians. Recently, we introduced a generalized framework called the graph connection Laplacian (GCL) as a new framework to data science. In this talk, in addition to showing that under the principle bundle framework, the eigenvectors and eigenvalues of the GCL converge to the connection Laplacian of the associated vector bundle in the limit of infinitely many i.i.d. random samples, we show how the noise, which is inevitable in data analysis, impacts the GCL framework. An application of this framework to the ptychography imaging problem (an imaging technique aiming to obtain an atomic resolution image of a macro object, which is a special phase retrieval problem) based on GCL will be discussed to show the strength of the proposed framework. If time permits, its application to other problems like cryo-EM and physiological dynamics will also be mentioned. This is a joint work with Noureddine El Karoui, Stefano Marchesini, Yu-Chao Tu and Amit Singer" |
December 03, 2014, 12:00 - 2:00 PM at Science Center 232 |
| NUMBER THEORY SEMINAR |
Moshe Adrian (UNIVERSITY OF TORONTO) |
On the local converse problem for GL(n,F) |
Let F be a non-archimedean local field of characteristic zero. The local converse problem for GL(n,F) asks to what extent the twisted gamma factors determine a representation of GL(n,F). Jacquet has formulated a conjecture on precisely which family of twisted gamma factors should uniquely determine a representation of GL(n,F). Because of recent work of Dihua Jiang, Chufeng Nien, and Shaun Stevens, this conjecture is now settled in many cases. I will report on recent work to extend their results, joint work with Baiying Liu, Shaun Stevens, and Peng Xu. I will then discuss some new sharpness results on Jacquet s conjecture, which is joint with Baiying Liu and Shaun Stevens" |
December 03, 2014, 3:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Chenyang Xu (INSTITUTE FOR ADVANCED STUDY) |
Maximal order pole of motivic Zeta function |
(Joint with Johannes Nicaise) By applying minimal model program and investigating how it changes the dual complex, we prove a conjecture of Veys, which says that the opposite of the log canonical threshold is the only possible pole of maximal order of the motivic zeta function associated with an effective divisor D on a smooth variety X" |
December 02, 2014, 4:00 PM at MIT E-17-122 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Xin Zhou (MIT) |
Shape of the min-max minimal hypersurface in manifold of positive Ricci curvature in all dimensions |
We will discuss the shape of the min-max minimal hypersurface produced by Almgren and Pitts corresponding to the fundamental class of a Riemannian manifold of positive Ricci curvature. We will give a characterization of the Morse index, area and multiplicity. The min-max minimal hypersurface will have a singular set of codimension 7, and the talk will give new ideas to deal with the singularity issu" |
December 02, 2014, 4:15 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Atsushi Kanazawa (HARVARD - CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS) |
Geometric transitions and SYZ mirror symmetry |
" |
December 01, 2014, 12:00 - 2:00 PM at Science Center 232 |
| NUMBER THEORY SEMINAR |
N/A () |
N/A |
**No seminar due to the Thanksgiving holiday*" |
November 26, 2014, at |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Roland Bauerschmidt (HARVARD UNIVERSITY) |
Supersymmetry in statistical mechanics |
" |
November 24, 2014, 12:00 - 2:00 PM at Science Center 232 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Jim Bryan (UNIVERSITY OF BRITISH COLUMBIA) |
The Donaldson-Thomas theory of K3xE and the Igusa cusp form |
Donaldson-Thomas invariants are fundamental deformation invariants of Calabi-Yau threefolds. We describe a recent conjecture of Oberdieck and Pandharipande which predicts that the (three variable) generating function for the Donaldson-Thomas invariants of K3xE is given by the reciprocal of the Igusa cusp form of weight 10. For each fixed K3 surface of genus g, the conjecture predicts that the corresponding (two variable) generating function is given by a particular meromorphic Jacobi form. We prove the conjecture for K3 surfaces of genus 0 and genus 1. Our computation uses a new technique which mixes motivic and toric methods" |
November 24, 2014, 4:00 PM *New time* at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS TOPOLOGICAL INSULATORS SERIES |
Alexei Kitaev (CALIFORNIA INSTITUTE OF TECHNOLOGY, FUNDAMENTAL PHYSICS PRIZE WINNER) |
The classification of short-range entangled topological phases |
" |
November 20, 2014, 1:30 PM at Science Center 530 |
| GAUGE THEORY, TOPOLOGY, AND SYMPLECTIC GEOMETRY SEMINAR |
Michael Hutchings (UC BERKELEY) |
Beyond ECH capacities |
ECH (embedded contact homology) capacities give obstructions to symplectically embedding one four-dimensional symplectic manifold with boundary into another. Cristofaro-Gardiner showed that these obstructions are sharp when the domain is a âconcave toric domainâ and the target is a âconvex toric domainâ. However ECH capacities often do not give sharp obstructions, for example in many cases when the domain is a polydisk. We use refined information from ECH to give stronger symplectic embedding obstructions when the domain is a convex toric domain. In particular we obtain new and sometimes sharp symplectic embedding obstructions when the domain is a polydisk and the target is a polydisk or an ellipsoid" |
November 20, 2014, 3:30 - 4:30 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Harrison Zhou (YALE UNIVERSITY) |
Asymptotic Normality and Optimalities in Estimation of Large Gaussian Graphical ModelÂČ |
The Gaussian graphical model, a popular paradigm for studying relationship among variables in a wide range of applications, has attracted great attention in recent years. This paper considers a fundamental question: When is it possible to estimate low-dimensional parameters at parametric square-root rate in a large Gaussian graphical model? A novel regression approach is proposed to obtain asymptotically efficient estimation of each entry of a precision matrix under a sparseness condition relative to the sample size. When the precision matrix is not sufficiently sparse, or equivalently the sample size is not sufficiently large, a lower bound is established to show that it is no longer possible to achieve the parametric rate in the estimation of each entry. This lower bound result, which provides an answer to the delicate sample size question, is established with a novel construction of a subset of sparse precision matrices in an application of Le CamÂčs Lemma. Moreover, the proposed estimator is proven to have optimal convergence rate when the parametric rate cannot be achieved, under a minimal sample requirement. The proposed estimator is applied to test the presence of an edge in the Gaussian graphical model or to recover the support of the entire model, to obtain adaptive rate-optimal estimation of the entire precision matrix as measured by the matrix lq operator norm, and to make inference in latent variables in the graphical model. All these are achieved under a sparsity condition on the precision matrix and a side condition on the range of its spectrum. This significantly relaxes the commonly imposed uniform signal strength condition on the precision matrix, irrepresentability condition on the Hessian tensor operator of the covariance matrix or the l1 constraint on the precision matrix. Numerical results confirm our theoretical findings. The ROC curve of the proposed algorithm, Asymptotic Normal Thresholding (ANT), support recovery significantly outperforms that of the popular GLasso algorithm" |
November 19, 2014, 12:00 - 2:00 PM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
H.T. Kung (HARVARD UNIVERSITY SEAS) |
Parallel Sparse Coding with Applications in Compressive Sensing and Machine Learning |
" |
November 19, 2014, 4:15 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Ila Varma (PRINCETON UNIVERSITY) |
The mean number of 3-torsion elements in ray class groups of quadratic fields |
In 1971, Davenport and Heilbronn determined the mean number of 3-torsion elements in the class groups of quadratic fields, when ordered by discriminant. I will describe some aspects of the proof of Davenport and Heilbronn s theorem; in particular, they prove a relationship via class field theory between the number of 3-torsion ideal classes of quadratic fields and the number of nowhere totally ramified cubic fields over Q. This argument generalizes to give a relationship between 3-torsion elements of the ray class groups of quadratic fields and certain pairs of cubic fields satisfying explicit rami cation conditions. I will illustrate how the combination of this fact with Davenport-Heilbronn s asymptotics on the number of cubic fields of bounded discriminant allows one to compute the mean number of 3-torsion elements in ray class groups of quadratic fields. If time permits, I will discuss the analogous theorems computing the mean size of 2-torsion elements in ray class groups of cubic fields ordered by discriminant generalizing Bhargava" |
November 19, 2014, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Alina Marian (NORTHEASTERN UNIVERSITY) |
Verlinde sheaves and tautological classes on the moduli space of K3 surfaces |
" |
November 18, 2014, 4:15 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Adam Jacob (HARVARD UNIVERSITY) |
Partial differential equations arising from mirror symmetry |
" |
November 17, 2014, 12:00 - 2:00 PM at Science Center 232 |
| BASIC NOTIONS SEMINAR / FACULTY COLLOQUIUM |
Wilfried Schmid (HARVARD UNIVERSITY) |
A new look at mixed Hodge modules |
" |
November 17, 2014, 3:00 PM at Science Center 507 |
| GAUGE THEORY, TOPOLOGY, AND SYMPLECTIC GEOMETRY SEMINAR |
Tom Mark (UNIVERSITY OF VIRGINIA) |
Tight contact structures on positive surgeries |
Motivated by the question of existence of tight contact structures on 3-manifolds, we study the question of whether a contact structure obtained by positive contact surgery along a Legendrian knot in the 3-sphere is tight. If the classical invariants of the knot satisfy a maximality condition, and the surgery coefficient is larger than 2g_4(K) - 1, we prove that the Heegaard Floer contact invariant of a resulting contact structure is nonvanishing; in particular the structure is tight. Our proof applies to integral surgery coefficients, with an extension in progress to rational surgeries. The method uses a generalization of the âcapping offâ procedure for open book decompositions, and may be of further use in studying open books with reducible monodromies. This is joint work with Bulent Tosun" |
November 14, 2014, 3:30 - 4:30 PM at Science Center 507 |
| SPECIAL SEMINAR |
Avi Wigderson (IAS, PRINCETON) |
Points, Lines and Ranks of design matrices |
The Sylvester-Gallai theorem in Euclidean geometry asserts that if a set of points has the property that every line through two of them contains a third point (such lines are called special), then they must all be on the same line, namely, 1-dimensional. There are many proofs, all elementary. When one moves to the complex numbers the same condition can be met in two dimensions, and Kelly s theorem asserts that the points must lie in a 2-dimensional space. The first proof used algebraic geometry, and a later more elementary proof of this fact is still quite complicated. We prove several extensions and quantitative versions of these theorems (and related ones), which are motivated by questions in several areas, including about locally correctable codes, matrix rigidity, and arithmetic combinatorics. In these extensions the assumption about all lines being special, is relaxed to having many special lines in the given point set. As it happens, such weaker conditions still impose considerable structure on the point set! We also address robust versions in which triples of points are only nearly collinear. Our results are obtained via general, tight rank lower bounds on matrices about with certain zero/non-zero pattern of entries. The proofs use an interesting combination of combinatorial, algebraic and analytic tools. In particular, they supply a simple new proof of Kelly s theorem. No special background is assumed. Based on several joint works with Albert Ai, Boaz Barak, Zeev Dvir, Shubhangi Saraf and Amir Yehudayoff." |
November 14, 2014, 11:45 AM at 11:45 AM |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Mu-Tao Wang (COLUMBIA UNIVERSITY) |
Conserved quantities of gravity |
I shall discuss the notion of conserved quantities, including mass, energy, linear momentum, angular momentum, and center of mass at both the quasi-local and total level (for isolated systems). In particular, a definition of quasi-local energy-momentum introduced by S.-T. Yau and myself in 2009 shall be reviewed. This was derived from Hamilton-Jacobi analysis of the Einstein-Hilbert action and a gravitational conservation law. An underlying mathematical tool is the isometric embedding equation for surfaces. In recent joint work with P.-N. Chen and S.-T. Yau, we complement this by the definitions of angular momentum and center of mass at the quasi-local level. The limits of these definitions at spatial and null infinity provide new definitions of total angular momentum and total center of mass that are free of ambiguities and difficulties found in existing definitions, and satisfy some highly desirable properties" |
November 12, 2014, 4:15 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Eyal Lubetzky (NEW YORK UNIVERSITY) |
Information percolation for the Ising model |
We introduce a new method of obtaining sharp estimates on mixing for Glauber dynamics for the Ising model, which, in particular, establishes cutoff in three dimensions up to criticality. The new framework, which considers ``information percolation clusters in the space-time slab, shows that total-variation mixing exhibits cutoff with an O(1)-window around the time at which the magnetization is the square-root of the volume. Furthermore, this method opens the door to understanding the effect of the initial state on the mixing time, showing that starting from the uniform (``disordered ) initial distribution asymptotically halves the mixing time, whereas almost every deterministic starting state is asymptotically as bad as starting from the (``ordered ) all-plus state. Joint work with Allan Sly" |
November 12, 2014, 12:00 - 2:00 PM at Science Center 530 |
| NUMBER THEORY SEMINAR |
N/A () |
**CANCELLED** |
" |
November 12, 2014, at |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Cumrun Vafa (HARVARD UNIVERSITY PHYSICS) |
Twistorial Topological String and tt* Geometry |
" |
November 11, 2014, 4:15 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Daniel Litt (STANFORD UNIVERSITY) |
Non-abelian Lefschetz Hyperplane Theorems |
Work of Lefschetz (in 1924) and Grothendieck (in SGA II) provides many relationships between properties of a smooth projective variety X and an ample divisor D in X. For example, the singular or l-adic cohomology of X agrees with that of D in low degree; X and D have the same Picard group if X has dimension at least 4; and X and D have the same fundamental group if X has dimension at least 3. Iâll describe a general result which encompasses some of these Lefschetz hyperplane theorems and many new ones, comparing maps out of X to maps out of D. The case when the target of these maps is a moduli scheme or stack is of particular interest; for example, one may take the target to be Mg, and thus compare families of curves over X to families over D" |
November 11, 2014, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Oscar Varela (HARVARD UNIVERSITY) |
Towards cohomogeneity-one Nearly-Kahler metrics on the six-sphere |
" |
November 10, 2014, 12:00 PM at Science Center 507 |
| GAUGE THEORY, TOPOLOGY, AND SYMPLECTIC GEOMETRY SEMINAR |
Mark McLean (STONY BROOK) |
Minimal Log Discrepancy of Isolated Singularities and Reeb Orbitis |
Let A be an affine variety inside a complex N dimensional vector space which either has an isolated singularity at the origin or is smooth at the origin. The intersection of A with a very small sphere turns out to be a contact manifold called the link of A. Any contact manifold contactomorphic to the link of A is said to be Milnor fillable by A. If the first Chern class of our link is 0 then we can assign an invariant of our singularity called the minimal discrepancy. We relate the minimal discrepancy with indices of certain Reeb orbits on our link. As a result we show that the standard contact 5 dimensional sphere has a unique Milnor filling up to normalization. This generalizes a Theorem by Mumford" |
November 07, 2014, 3:30PM at Science Center 507 |
| THURSDAY SEMINAR |
Dan Freed (UNIVERSITY OF TEXAS - AUSTIN) |
An application of twisted K-theory to topological band insulators |
" |
November 06, 2014, 4:00 - 6:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Cristian Popescu (UC SAN DIEGO) |
Equivariant Iwasawa theory, Hecke characters and the K-theory of number fields |
In recent work with Greither, we proved a main conjecture in equivariant Iwasawa theory, refining Wiles results on the classical main conjecture over totally real number fields. Via Iwasawa co-descent this permitted us to prove a refinement of the classical Brumer-Stark conjecture (under certain hypotheses.) In joint work with Banaszak, we used these results to construct a family of algebraic Hecke characters for an arbitrary CM number field, generalizing Weil s Jacobi sum Hecke characters. Further, we used certain special values of these Hecke characters to construct Stickelberger splitting maps for the localization sequences in the Quillen K-theory of CM and totally real number fields. We will review these results and constructions and comment on further potential applications to the classical conjectures of Iwasawa and Kummer-Vandiver on class-groups of cyclotomic fields" |
November 05, 2014, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Washington Taylor (MIT) |
String theory vacua and the enumeration of elliptic Calabi-Yau threefolds |
The quest for a systematic understanding of solutions to string theory leads to many interesting classification problems in geometry. A central example is the problem of classifying Calabi-Yau threefold geometries. While it is not known if the number of topological types of CY threefolds is finite, the restricted class of elliptically fibered CY threefolds has been shown by Gross to admit a finite number of distinct topological types (up to birational equivalence). This talk describes recent work in which insights from physics have been combined with basic algebraic geometry and combinatorics to give a systematic approach to bounding and enumerating all elliptically fibered Calabi-Yau threefolds. Empirical evidence suggests that in fact elliptically fibered Calabi-Yau threefolds may constitute the majority of possible CY threefold geometries, particularly at large Hodge numbers. Classification of fourfolds and implications for physics will also be discussed" |
November 05, 2014, 4:15 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Van Vu (YALE UNIVERSITY) |
Random Projections and Applications |
In this talk, we discuss a basic question: How does a projection of a random vector onto a fixed subspace look like? We give a simple and sharp concentration result for this, and present a  series of applications in various areas: random matrices, probability, and statistics. These include determinant of random matrices, concentration of quadratic forms, sharp delocalization of random eigenvectors, sharp local semi-cirle law, clustering (finding hidden communities) problems in statistics and computer science" |
November 05, 2014, 12:00PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Larry Guth (MIT) |
Homotopical effects of k-dilation |
The k-dilation of a map measures how the map stretches k-dimensional areas. If Dil_k f < L, then it means that for any k-dimensional submanifold S in the domain, Vol_k (f(S)) is at most L Vol_k(S). We discuss how the k-dilation restricts the homotopy type of a map. Our main theorem concerns maps between unit spheres, from S^{m} to S^{m-1}. If k > (m+1)/2, then there are homotopically non-trivial maps S^m to S^{m-1} with arbitrarily small k-dilation. I find this somewhat counterintuitive. The construction has a similar flavor to constructions in the h-principle literature with lots of wrinkling. On the other hand, if k is at most (m+1)/2, there every homotopically non-trivial map from S^m to S^{m-1} has k-dilation at least c(m) > 0. So there is a transition at k=(m+1)/2 between flexible behavior and rigid behavior. The first interesting case of the rigid behavior is k=3 and m=2. It was proven by Gromov in the 70 s. The higher-dimensional cases are new. The main difficulty here is to connect the topology and the geometry. To detect that a map S^m to S^{m-1} is homotopically non-trivial requires tools from algebraic topology such as Steenrod squares. We have to connect the Steenrod squares with k-dimensional volumes of k-dimensional surfaces. (For the talk, I won t assume familiarity with Steenrod squares." |
November 04, 2014, 4:15 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Charles Siegel (UNIVERSITY OF PENNSYLVANIA) |
A Modular Operad of Embedded Curves |
Modular operads were introduced by Getzler and Kapranov to formalize the structure of gluing maps between moduli of stable marked curves. We present a construction of analogous gluing maps between moduli of pluri-log-canonically embedded marked curves, which fit together to give a modular operad of embedded curves. This is joint work with Satoshi Kondo and Jesse Wolfson" |
November 4, 2014, 4:00 PM at MIT E17-122 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Kaoru Ikeda (HARVARD UNIVERSITY) |
Symplectic structures of projective flag manifold and the unitary representations |
" |
November 03, 2014, 12:00 - 2:00 PM at Science Center 232 |
| BASIC NOTIONS SEMINAR |
Joe Harris (HARVARD UNIVERSITY) |
Plane Curves |
" |
November 03, 2014, 3:00 PM at Science Center 507 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Nate Bottman (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
Singular quilts and a proposed A-infinity 2-category |
I will describe work-in-progress with Katrin Wehrheim to construct the symplectic A-infinity 2-category `Symp , whose objects are symplectic manifolds and where hom(M,N) is the immersed Fukaya category Fuk(M- x N). The structure maps will be defined by counting moduli spaces of pseudoholomorphic quilts with a figure eight singularity. A formal consequence of Symp is a symplectic analogue of Fourier--Mukai functors. After describing the blueprint for Symp, I will present two analytic results about singular quilts: a removal of singularity for the figure eight singularity, and a Gromov compactness theorem for strip-shrinking. This talk will be based partly on the preprint arXiv:1410.3834 and partly on an upcoming preprint with Wehrheim" |
October 31, 2014, 3:30 PM at Science Center 507 |
| POSTDOC SEMINAR |
Emily Riehl (HARVARD UNIVERSITY) |
On the duality between "free" and "forgetful" constructions |
Groups, rings, and compact Hausdorff spaces have underlying sets and admit free constructions. Moreover, each type of object is completely characterized by the shadow of this free-forgetful duality cast on the category of sets, and this syntactic encoding provides formulas for direct and inverse limits. After we describe a typical encounter with adjunctions, monads, and their algebras, we introduce a new homotopy coherent version of this adjoint duality together with a graphical calculus that is used to define a homotopy coherent algebra" |
October 31, 2014, 2:30 -3:30 PM at Science Center 530 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Ji Oon Lee - *1st speaker* (KAIST) |
Tracy-Widom Distribution for Real Sample Covariance Matrices with General Population |
Consider a sample covariance matrix of the form XX^*. The sample X is an MxN real random matrix whose columns are independent multivariate Gaussian vectors with covariance ÎŁ. We show that the fluctuation of the largest rescaled eigenvalue is given by Tracy-Widom distribution for a large class of general ÎŁ. This is a joint work with Kevin Schnelli" |
October 31, 2014, 12:00 - 2:30 PM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Mykhaylo Shkolnikov - *2nd speaker* (PRINCETON UNIVERSITY) |
Intertwinings, wave equations and beta ensembles |
We will discuss a general theory of intertwined diffusion processes of any dimension. Intertwined processes arise in many different contexts in probability theory, most notably in the study of random matrices, random polymers and path decompositions of Brownian motion. Recently, they turned out to be also closely related to wave equations and more general hyperbolic partial differential equations. The talk will be devoted to this recent development, as well as an algebraic perspective on intertwinings which, in particular, gives rise to a novel intertwining in beta random matrix theory. The talk is based on joint works with Soumik Pal and Vadim Gorin" |
October 31, 2014, 12:00 - 2:30 PM at Science Center 232 |
| NUMBER THEORY SEMINAR |
Jerry Wang (PRINCETON UNIVERSITY) |
Pencils of quadrics and the arithmetic of hyperelliptic curves |
In recent joint works with Manjul Bhargava and Benedict Gross, we showed that a positive proportion of hyperelliptic curves over Q of genus g have no points over any odd degree extension of Q. This is done by computing certain 2-Selmer averages and applying a result of Dokchitser-Dokchitser on the parity of the rank of the 2-Selmer groups in biquadratic twists. In this talk, we will see how arithmetic invariant theory and the geometric theory of pencils of quadrics are used to obtain the 2-Selmer averages" |
October 29, 2014, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
C.F. Jeff Wu (GEORGIA INSTITUTE OF TECHNOLOGY) |
A statistical view of uncertainty quantification: interface between statistics and applied mathematics |
Because of the advances in complex mathematical models and fast computer codes, computer experiments have become popular in engineering and scientific investigations. Statisticians have worked on the design, modeling and computation aspects of computer experiments. Applied mathematicians have approached a closely related class of problem called UQ (uncertainty quantification). Interface between the two approached is made in the talk. Two problems on the statistical side are presented to illustrate this interface. 1. Consider deterministic computer experiments with tuning parameters which determine the accuracy of the numerical algorithm (e.g., mesh density in finite element analysis). To efficiently integrate computer outputs with different tuning parameters, a class of nonstationary Gaussian process models consistent with the knowledge in numerical analysis is proposed to model the integrated output. Estimation is performed by using Bayesian computation. Numerical studies show the advantages of the proposed method over existing methods. A related problem is given to illustrate the interplay between modeling and design. For this and a broader class of models with multi-levels of fidelity, the nested space-filling designs are most suitable. Some examples are given and the underlying mathematics discussed. 2. Calibration parameters in deterministic computer experiments are those attributes that cannot be measured or available in physical experiments or observations. Kennedy-OâHagan (2001) suggested an approach to estimation by using data from physical experiments and computer simulations. We show that a simplified version of the original KO method leads to asymptotically inconsistent calibration. This calibration inconsistency can be remedied by modifying the original estimation procedure. A novel calibration method, called the L2 calibration, is proposed and proven to be consistent and enjoys optimal convergence rate. A numerical example and some mathematical analysis are used to illustrate the source of inconsistency" |
October 29, 2014, 4:15 PM at Science Center 507 |
| HARVARD LOGIC COLLOQUIUM |
Joan Bagaria (UNIVERSITAT DE BARCELONA) |
Reflection phenomena in the set-theoretic universe |
The phenomenon of reflection occurs at different layers of the set-theoretic universe V, and strengthened forms of reflection associated to each layer give rise to natural additional axioms for set theory of different sorts. In this talk we shall review some strong forms of reflection pertaining to different layers such as the class of ordinals, some inner models, V itself, and even the ideal extensions of V provided by the forcing method, while exposing some intriguing connections among the axioms that arise in each case" |
October 29, 2014, 4:30 - 5:30 PM at Logic Center, 2 Arrow St, Rm 408 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Remi Monasson *1st speaker* (LABORATOIRE DE PHYSIQUE THEORIQUE DE LâENS) |
Crosstalk, transitions, and wormholes in an attractor network model of hippocampal place cells |
" |
October 29, 2014, 12:00 - 2:30 PM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Simona Cocco *2nd speaker* (LABORATOIRE DE PHYSIQUE STATISTIQUE DE LâENS) |
Inferring 'interactions' from correlations: application to memory consolidation and cell assemblies in the behaving rat |
" |
October 29, 2014, 12:00 - 2:30 PM at Science Center 232 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Serge Cantat (INSTITUTE FOR ADVANCED STUDY) |
Birational Actions of SL(n,Z) |
Consider a smooth complex projective variety M. Assume that a finite index subgroup of SL(n,Z) acts faithfully on M by birational transformations. Does it follow that the dimension of M is larger than or equal to (n-1)? I shall describe several partial results towards a positive answer to this question" |
October 28, 2014, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Semyon Dyatlov (MIT) |
Resonances in general relativity |
We discuss long time behavior of linear scalar waves on Kerr and Kerr-de Sitter black hole backgrounds and their stationary perturbations. The physical motivation comes from the analysis of gravitational waves emitted during the ringdown stage of a large scale event (such as merging with another black hole). The properties of these waves, and their frequencies, called quasi-normal modes or resonances, depend on the structure of the set of all trapped light rays. In the considered Kerr(-de Sitter) case, the trapped set is r-normally hyperbolic and we can provide a detailed description of quasi-normal modes and long-time behavior of linear waves" |
October 28, 2014, 4:15 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Murad Alim (HARVARD UNIVERSITY) |
Lie algebra and differential rings of tt* geometries of Calabi-Yau sigma models |
" |
October 27, 2014, 12:00 - 2:00 PM at Science Center 232 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Sheng-Fu Chiu (NORTHWESTERN UNIVERSITY) |
Contact non-squeezability and Microlocal category |
This talk focuses on the relation between microlocal categories and symplectic/contact topology. We will briefly describe how to assign a triangulated category to a given geometric object and how this assignment varies under Hamiltonian flows in the ambient manifolds. This allows us to retrieve Hamiltonian invariants from homological data in a systematic way. Finally, we will discuss its application to a contact non-squeezability problem posed by Eliashberg, Kim and Polterovich. This is a joint work with Dmitry Tamarkin" |
October 24, 2014, 3:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Hiro Tanaka (HARVARD UNIVERSITY) |
Fermions |
I will try to give a review of what fermions are, physically, for a mathematical audience not acquainted with the experimental evidence. Then I will go into the mathematical language now popularly used to describe them. The latter part of this talk is supposed to be based on Freed and Moore s paper, Twisted Equivariant Matter." |
October 23, 2014, 4:00 - 6:00 PM at Science Center 507 |
| SPECIAL DIFFERENTIAL GEOMETRY SEMINAR |
Si Li (MSC, TSINGHUA UNIVERSITY) |
Perturbative renormalization and Index theorem |
In this talk, I will build up the equivalence between the deformation quantization on a symplectic manifold and the perburbative BV quantization of a Chern-Simons type theory on its loop space. I will explain how to introduce Ariyah-Bott localization method into exact computation of the correlation functions in the rigorously renormalized theory. As an application, this leads to a simple proof of algebraic index theorem. This is joint work with Qin Li" |
October 22, 2014, 9:30 AM at Science Center 530 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Eric Maskin (HARVARD UNIVERSITY ADAMS UNIVERSITY PROFESSOR) |
Elections and Strategic Voting: Condorcet and Borda |
" |
October 22, 2014, 4:15 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Uzy Smilansky (WEIZMANN INSTITUTE) |
Spectral statistics of Bernoulli matrix ensembles - a random walk approach |
" |
October 22, 2014, 12:00 - 2:00 PM at Science Center 232 |
| NUMBER THEORY SEMINAR |
Alena Pirutka (ECOLE POLYTECHNIQUE, FRANCE, CENTRE DE MATHEMATIQUES LAURENT SCHWARTZ) |
On some counterexamples to the integral Tate conjecture |
In this talk we will discuss some counterexamples to an integral version of the Tate conjecture. In particular, following the approach of Atiyah-Hirzebruch and Totaro, we will use Steenrod operations and classifying spaces of algebraic groups to construct a non-torsion non-algebraic cohomology class. This is a joint work with N.Yagita" |
October 22, 2014, 3:00 PM at Science Center 507 |
| SPECIAL TOPOLOGY SEMINAR |
Shamil Shakirov (UC BERKELEY) |
One-parameter deformation of Chern-Simons theory |
Chern-Simons TQFT is a functor that associates vector spaces to closed oriented surfaces and linear maps to cobordisms. In particular, to closed 3-manifolds with knots inside it associates a number, which is a topological invariant. In the special case of Seifert manifolds with knots wrapping the circle fibers, we define a deformation of this invariant, using the modular S and T matrices first described by A.Kirillov-Jr. We show that for torus knots the resulting deformation is related to Khovanov-Rozansky knot homology, and conjecture the general form of this relation.This talk is based on a joint work with Mina Aganagic" |
October 21, 2014, 3:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Jose Gonzalez (YALE UNIVERSITY) |
The moduli space of stable n-pointed genus zero curves is not a Mori Dream Space when n is at least 13 |
Ana-Maria Castravet and Jenia Tevelev have recently proved that the moduli space of stable n-pointed genus zero curves is not a Mori Dream Space when n is at least 134. We build on their work to obtain the same conclusion when n is at least 13. This talk is a report on joint work with Kalle Karu" |
October 21, 2014, 4:00 PM at MIT E-17-122 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Tristan Collins (HARVARD UNIVERSITY) |
The boundary of the Kahler cone |
We will discuss a geometric characterization of classes of positive volume on the boundary of the Kahler cone of a compact Kahler manifold. As an application, we will show that finite time singularities of the Kahler-Ricci flow always form along analytic subvarieties. Time permitting, we will also discuss some applications to algebraic geometry, specifically to augmented base loci of nef and big line bundles on projective varieties. This work is joint with Valentino Tosatti" |
October 21, 2014, 4:15 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Hector Pasten (HARVARD UNIVERSITY) |
Uniform Diophantine undecidability |
I will discuss a uniform Diophantine undecidability result for certain rings of functions as the characteristic varies (joint work with T. Pheidas and X. Vidaux). This is obtained by means of a uniform interpretation of the integers in these structures. I will also describe a recent generalization to the case of non-Archimedean entire functions which in particular solves the analogue of Hilbert s tenth problem for these rings (joint work with N. Garcia-Fritz)" |
October 20, 2014, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Shu-Heng Shao (HARVARD UNIVERSITY PHYSICS) |
An index formula for supersymmetric quantum mechanics |
" |
October 20, 2014, 12:00 - 2:00 PM at Science Center 232 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Dan Freed (UNIVERSITY OF TEXAS - AUSTIN) |
Chern-Weil forms and abstract homotopy theory |
I will discuss the theorem (joint w/Hopkins) that Chern-Weil forms are the only natural differential forms associated to a connection on a principal G-bundle. We use abstract homotopy theory to eventually reduce the problem to classical invariant theory. In the process we define a generalized manifold which plays the role of EG and whose de Rham complex is precisely the Weil algebra. There is a corresponding geometric interpretation of the Weil model in equivariant de Rham theory" |
October 17, 2014, 3:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Ryan Grady (BOSTON UNIVERSITY) |
Large volume limits and derived mapping stacks: extracting manifold invariants via the BV formalism |
" |
October 16, 2014, 4:00 - 6:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Pham Huu Tiep (UNIVERSITY OF ARIZONA / HARVARD) |
Adequate Subgroups |
The notion of adequate subgroups was introduced by Thorne. It is a weakening of the notion of big subgroups used in generalizations of the Taylor-Wiles method for proving the automorphy of certain Galois representations. Using this idea, Thorne was able to strengthen many automorphy lifting theorems. It was shown recently by Guralnick, Herzig, Taylor, and Thorne that if the degree is small compared to the characteristic then all absolutely irreducible representations are adequate. We will discuss extensions of this result obtained recently in joint work with R. M. Guralnick and F. Herzig. In particular, we show that almost all absolutely irreducible representations in characteristic p of degree less than p are adequate. We will also address a question of Serre about indecomposable modules in characteristic p of dimension less than 2p-2" |
October 15, 2014, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Jack Hanson (INDIANA UNIVERSITY) |
Rate of convergence of the mean for sub-additive ergodic sequences |
If {X_{m,n}} is a sub-additive ergodic process, Kingman s theorem shows convergence of X_{0,n}/n to some nonrandom constant g. In this talk, I will describe results on the rate of convergence of E X_{0,n} / n. The main theorems give bounds on E X_{0,n} - ng in terms of the fluctuations of X_{0,n} about its mean. In particular, if E X_{0,n} - ng is typically of order n^gamma and |X_{0,n} - E X_{0,n}| is typically of order n^chi, we show that gamma is at least chi. The main assumptions are that the process is weakly dependent and that chi is not 1/2. Various models, including first-passage percolation and bin packing, fit into this framework. This is joint work with A. Auffinger and M. Damron" |
October 15, 2014, 12:00 - 2:00 PM at Science Center 232 |
| INFORMAL SEMINAR: NEW RESULTS ON HYPERBOLIC VOLUME |
Curt McMullen & Martin Bridgeman (HARVARD / BOSTON COLLEGE) |
Organizational Meeting / first talk |
Our aim in this seminar is to understand a recent paper of Kojima and McShane that gives explicit and powerful upper bounds for the volume of a 3-manifold that fibers over the circle. Seminar web page: http://math.harvard.edu/~ctm/sem" |
October 15, 2014, 4:00 - 6:00 PM at Science Center 530 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Tianxi Cai (HARVARD SCHOOL OF PUBLIC HEALTH) |
Discovery Research with Electronic Medical Records Data |
" |
October 15, 2014, 4:15 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Baosen Wu (HARVARD UNIVERSITY) |
A construction of stable bundles and reflexive sheaves on Calabi-Yau threefolds |
We will discuss a geometric construction of stable bundles and reflexive sheaves with certain prescribed Chern classes on Calabi-Yau threefolds. We use mainly Serre construction and deformation. We will also discuss application to DRY conjecture on elliptic Calabi-Yau threefolds. This is joint work with S.-T. Yau" |
October 14, 2014, 4:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Jack Huizenga (UNIVERSITY OF ILLINOIS AT CHICAGO) |
Interpolation problems and the birational geometry of moduli spaces of sheaves |
Questions like the Nagata conjecture seek to determine when certain zero-dimensional schemes impose independent conditions on sections of a line bundle on a surface. Understanding analogous questions for vector bundles instead amounts to studying the birational geometry of moduli spaces of sheaves on a surface. We explain how to use higher-rank interpolation problems to compute the cone of effective divisors on any moduli space of sheaves on the plane. This is joint work with Izzet Coskun and Matthew Woolf" |
October 14, 2014, 3:00 PM at Science Center 507 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Tristan Collins (HARVARD UNIVERSITY) |
A tour of Sasakian-Einstein geometry |
I will discuss the problem of finding Sasakian-Einstein metrics, which are a special type of contact metric structures. The primary focus will be connections to algebraic geometry and Kahler geometry, as well as algebro-geometric conditions which imply existence or obstruction of Sasakian-Einstein metrics. I hope to discuss how these conditions lead to the construction of an abundance of Einstein metrics on spheres" |
October 10, 2014, 3:30 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Zongming Ma (THE WHARTON SCHOOL, UNIVERSITY OF PENNSYVANIA) |
Sparse Canonical Correlation Analysis |
Canonical correlation analysis (CCA) is a widely used multivariate statistical technique for exploring the relation between two sets of variables. In this talk we consider the problem of estimating the leading canonical correlation directions in high dimensional settings. Recently, under the assumption that the leading canonical correlation directions are sparse, various procedures have been proposed for many high dimensional applications involving massive data sets. However, there has been few theoretical justification available in the literature. In this talk, we establish rate-optimal non-asymptotic minimax estimation with respect to an appropriate loss function for a wide range of model spaces. Two interesting phenomena are observed. First, the minimax rates are not affected by the presence of nuisance parameters, namely the covariance matrices of the two sets of random variables, though they need to be estimated in the canonical correlation analysis problem. Second, we allow the presence of the residual canonical correlation directions. However, they do not influence the minimax rates under a mild condition on eigengap. A generalized sin-theta theorem and an empirical process bound for Gaussian quadratic forms under rank constraint are used to establish the minimax upper bounds, which may be of independent interest. Time permitting, we will also discuss some efficient algorithm for sparse CCA. This talk is based on joint works with Chao Gao, Zhao Ren and Harrison Zhou" |
October 10, 2014, 1:30 PM at Science Center 232 |
| HARVARD, BRANDEIS, MIT, NORTHEASTERN JOINT COLLOQUIUM AT HARVARD |
Danny Calegari (UNIVERSITY OF CHICAGO) |
Roots, Schottky semigroups, and a proof of Bandt's Conjecture |
In 1985, Barnsley and Harrington defined a Mandelbrot Set M for pairs of similarities ïżœ this is the set of complex numbers z with norm less than 1 for which the limit set of the semigroup generated by the similarities x -> zx and x -> z(x-1)+1 is connected. Equivalently, M is the closure of the set of roots of polynomials with coefficients in {-1,0,1}. Barnsley and Harrington already noted the (numerically apparent) existence of infinitely many small holes in M, and conjectured that these holes were genuine. These holes are very interesting, since they are exotic components of the space of (2 generator) Schottky semigroups. The existence of at least one hole was rigorously confirmed by Bandt in 2002, but his methods were not strong enough to show the existence of infinitely many holes; one difficulty with his approach was that he was not able to understand the interior points of M, and on the basis of numerical evidence he conjectured that the interior points are dense away from the real axis. We introduce the technique of *traps* to construct and certify interior points of M, and use them to prove Bandt s Conjecture. Furthermore, our techniques let us certify the existence of infinitely many holes in M. This is joint work with Sarah Koch and Alden Walker" |
October 09, 2014, 4:30 PM at Science Center Hall A |
| THURSDAY SEMINAR |
Dan Freed (UNIVERSITY OF TEXAS - AUSTIN) |
Remarks on mechanics and symmetry |
" |
October 09, 2014, 4:00 - 6:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Miika Nikula (HARVARD - CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS) |
Geometric properties of critical multiplicative chaos |
We study the geometric measure theory of a certain class of random measures. Loosely speaking, Gaussian multiplicative chaos is a random measure (on a domain in R^n) whose density is given by the exponential of a Gaussian field with a logarithmically singular covariance kernel. The definition is made rigorous by introducing a cut-off parameter to smoothen out the covariance kernel in such a way that the density is a martingale as the cut-off is taken to zero. For a weak enough logarithmic singularity, the martingale limit is nondegenerate and indeed defines a measure. The critical case refers to the situation where the logarithmic singularity is just barely strong enough that the martingale construction degenerates and the limiting measure is identically zero. However, the construction may be renormalized to give a nontrivial limit. We show that the renormalized limit measure does not have point masses but that its mass is carried by a set of Hausdorff dimension 0" |
October 08, 2014, 12:00 - 2:00 PM at Science Center 530 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Salil Vadhan (HARVARD UNIVERSITY SEAS & THE CENTER FOR RESEARCH ON COMPUTATION & SOCIETY) |
The Computational Complexity of Data Privacy |
" |
October 08, 2014, 4:15 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Ronen Mukamel (UNIVERSITY OF CHICAGO) |
Singular moduli and the primes of bad reduction of Teichmuller curves |
Teichmuller curves are algebraic curves which totally geodesically immersed in the moduli space of Riemann surfaces. A growing body of literature demonstrates that Teichmuller curves are remarkable from a variety of perspectives and share extraordinary properties with Shimura curves. We will present the first explicit algebraic models of non-arithmetic Teichmuller curves of positive genus and give evidence drawn from our examples of surprising connections between Teichmuller curves, work of Gross-Zagier on singular moduli and work of Deligne-Pappas on real multiplication in positive characteristics. This is joint work with A. Kumar" |
October 08, 2014, 3:00 - 4:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Christian Schnell (STONY BROOK) |
Kodaira dimension and zeros of holomorphic one-forms |
I will talk about a joint paper with Mihnea Popa; our main result is that on a smooth complex projective variety of general type, every holomorphic one-form has a nonempty zero locus. Although this sounds like a problem in birational geometry, the proof uses results about D-modules on abelian varieties" |
October 07, 2014, 4:00 PM at MIT E-17-122 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Paul Seidel (MIT) |
Steenrod squares and symplectic fixed points |
" |
October 07, 2014, 5:15 PM *note change in time at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Laure Saint-Raymond (ĂCOLE NORMALE SUPĂ©RIEURE ) |
The role of boundary layers in the global ocean circulation |
" |
October 06, 2014, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Vladimir Mitev (HUMBOLDT UNIVERSITY, BERLIN) |
Toda 3-Point Functions from Topological Strings |
Toda field theory is a still unsolved non-rational 2D CFT with applications for both string theory and 4D superconfromal theories. We consider the long-standing problem of computing its 3-point functions. Our main tools are topological strings and the AGT-W relation between gauge theories and 2D CFTs. By computing the superconformal index of the 5D T_N theories, giving a method for taking the 4D limit and by providing the exact AGT-W dictionary, we obtain a prescription for the computation of the partition function of the 4D T_N theories on the four sphere, or equivalently the 3-point Toda structure constants.  Our formula, has the correct symmetry properties, all the zeros that it should and in the semi-degenerate limit, reproduces the formula by Fateev and Litvinov" |
October 06, 2014, 1:00 - 2:00 PM at Science Center 232 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Sobhan Seyfaddini (MIT) |
The displaced disks problem via symplectic topology |
We will show that a C^0-small area preserving homeomorphism of S^2 can not displace a disk of large area. This resolves the displaced disks problem posed by F. BĂ©guin, S. Crovisier, and F. Le Roux" |
October 03, 2014, 3:30 - 4:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
Twisted K-theory |
" |
October 02, 2014, 4:00 - 6:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS RANDOM MATRIX & PROBABILITY THEORY SEMINAR |
Jun Zhang (UNIVERSITY OF MICHIGAN, ANN ARBOR) |
Regularized learning in reproducing Kernal Banach Spaces |
Regularized learning is the contemporary framework for learning to generalize from finite samples (classification, regression, clustering, etc). Here the problem is to learn an input-output mapping f: X->Y given finite samples {(xi, yi), i=1,âŠ,N}. With minimal structural assumptions on X, the class of functions under consideration is assumed to fall under a Banach space of functions B. The learning-from-data problem is then formulated as an optimization problem in such a function space, with the desired mapping as an optimizer to be sought, where the objective function consists of a loss term L(f) capturing its goodness-of-fit (or the lack thereof) on given samples {(f(xi), yi), i=1,âŠ,N}, and a penalty term R(f) capturing its complexity based on prior knowledge about the solution (smoothness, sparsity, etc). This second, regularizing term is often taken to be the norm of B, or a transformation f thereof: R(f) = f(||f||). This program has been successfully carried out for the Hilbert space of functions, resulting in the celebrated Reproducing Kernel Hilbert Space methods in machine learning. Here, we will remove the Hilbert space restriction, i.e., the existence of an inner product, and show that the key ingredients of this framework (reproducing kernel, representer theorem, feature space) remain to hold for a Banach space that is uniformly convex and uniformly Frechet differentiable. Central to our development is the use of a semi-inner product operator and duality mapping for a uniform Banach space in place of an inner-product for a Hilbert space. This opens up the possibility of unifying kernel-based methods (regularizing L2-norm) and sparsity-based methods (regularizing l1-norm), which have so far been investigated under different theoretical foundations." |
October 01, 2014, 12:00 - 2:00 PM at Science Center 232 |
| NUMBER THEORY SEMINAR |
Brian Smithling (JOHNS HOPKINS ) |
An arithmetic transfer conjecture for ramified unitary groups |
The arithmetic fundamental lemma is a conjectural relation proposed by W. Zhang in connection with a relative trace formula approach to the Gan-Gross-Prasad conjectures for (unramified) unitary groups. It asserts a deep relation between the derivative of an orbital integral and an intersection number for cycles in a formal moduli space of p-divisible groups. I will report on an extension of the conjecture to the setting of ramified unitary groups along with, for unitary groups in three variables, its proof. This is joint work with M. Rapoport and W. Zhang" |
October 01, 2014, 3:00 - 4:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM |
Andy Strominger (HARVARD UNIVERSITY) |
Symmetry in Soft Theorem |
" |
October 01, 2014, 4:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Eric Riedl (HARVARD UNIVERSITY) |
Rational Curves on Hypersurfaces |
Let X be a general degree d hypersurface in n-dimensional projective space, and consider the spaces of rational curves on X. Joint with David Yang, following work of Harris, Roth, Starr, Beheshti and Kumar, we prove that the space of degree e rational curves on X is irreducible and we compute its dimension for n > d+1. This resolves all but the n = d+1 case of a conjecture of Coskun, Harris and Starr" |
September 30, 2014, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Chien-Hao Liu () |
D-branes and Azumaya/matrix noncommutative geometry |
" |
September 29, 2014, 12:00 - 2:00 PM at Science Center 232 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Joanna Nelson (COLUMBIA/IAS) |
Cylindrical contact homology in dimension 3 via intersection theory and more |
After reviewing the difficulties in proving dÂČ=0 for dynamically convex contact manifolds, we explain how intersection theory and automatic transversality come to the rescue, as implemented by Hutchings-Nelson. So that these methods do not remain shrouded in mystery, we provide an overview of the relevant ideas from intersection theory for pseudoholomorphic curves in 4-dimensional symplectizations a la Siefring and Hutchings. Time permitting we end with a brief sketch of how to obtain invariance of cylindrical contact homology over Q via nonequivariant formulations, obstruction bundle gluing, domain dependent almost complex structures, and SÂč-equivariant constructions. The discussion of invariance is based on work in progress by Hutchings-Nelson." |
September 26, 2014, 3:30 - 4:30 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Amir Dembo (STANFORD UNIVERSITY) |
Statistical Mechanics on Sparse Random Graphs: Mathematical Perspective |
Theoretical models of disordered materials lead to challenging mathematical problems with applications to random combinatorial problems and coding theory. The underlying structure is that of many discrete variables that are strongly interacting according to a mean field model determined by a random sparse graph. Focusing on random finite graphs that converge locally to trees we review recent progress in validating the `cavity prediction for the limiting free energy per vertex and the approximation of local marginals by the belief propagation algorithm. This talk is based on joint works with Anirban Basak, Andrea Montanari, Nike Sun and Alan Sly" |
September 24, 2014, 12:00 - 2:00 PM at Science Center 232 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS COLLOQUIUM |
Asaf Madi (HARVARD MEDICAL SCHOOL) |
Using big genomic data to analyze inner workings of immune cells |
" |
September 24, 2014, 4:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Alison Miller (HARVARD UNIVERSITY) |
Counting Simple Knots via Arithmetic Invariant Theory |
Certain knot invariants coming from the Alexander module have natural number-theoretic structure: they can be interpreted as ideal classes in certain rings. I will explain the connection between these invariants and the arithmetic invariant theory of Sp_2g acting on its adjoint representation. The associated counting questions have a knot-theoretic interpretation. In fact, they count certain families of high-dimensional knots and related objects. I will give asymptotic answers to these questions in the case of genus 1 assuming standard number-theoretic heuristics" |
September 24, 2014, 3:00 - 4:00 PM at Science Center 507 |
| HARVARD LOGIC SEMINAR |
Gil Sagi (LUDWIG-MAXIMILIANS UNIVERSITY, MUNICH) |
What is a Fixed Term? |
In standard model-theoretic semantics, logical terms are said to be fixed in the system while nonlogical terms remain variable. Much effort has been devoted to characterizing logical terms, those terms that should be fixed, but little has been said on their role in logical systems: on what fixing them precisely amounts to. My proposal is that when a term is considered logical in a system, what gets fixed is its intension rather than its extension. I provide a rigorous way of spelling out this idea. Further, I show that under certain natural assumptions, some paradigmatic examples of nonlogical terms cannot be fixed in a standard system: they require more structure than such a system affords. We thus obtain a precondition for logical terms. I then propose a graded account of logicality: the less structure a term requires, the more logical it is. Finally, I relate this idea to invariance criteria for logical terms. Invariance criteria can be used as a tool in determining how much structure a term needs in order to be fixed. Thus, rather than settling on one criterion for logicality, I use invariance conditions as a measure for logicality." |
September 24, 2014, 4:30 PM at Logic Center, 2 Arrow St, Rm 408 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Hiro Lee Tanaka (HARVARD UNIVERSITY) |
Lagrangian Cobordisms and Fukaya Categories |
Given an exact symplectic manifold with some extra decorations, one can construct two categories whose objects are (exact, decorated) Lagrangians: The Fukaya category, and a category whose morphisms are cobordisms. Both can be triangulated, and there is even a functor between them respecting their triangulated structures. In this talk we discuss some work-in-progress drawing parallels between the two categories, and if time allows, we will discuss the relation of our work with that of Biran-Cornea, or discuss possible applications to the Nearby Lagrangian Conjecture and Heegard-Floer invariants for 2-, 3-, and 4-manifolds" |
September 23, 2014, 4:15 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Gabriel Bujokas (HARVARD UNIVERSITY) |
Covers of an elliptic curve E and curves in ExP^1 |
**This seminar meets at MIT this week*" |
September 23, 2014, 4:00 PM at MIT E-17-122 |
| BASIC NOTIONS SEMINAR |
Benedict Gross (HARVARD UNIVERSITY) |
Singular moduli |
Singular moduli are the values of the modular function j(z) at the points z in the upper half plane that satisfy a quadratic equation with rational coefficients. In other words, they are the j-invariants of elliptic curves with complex multiplication. These j-invariants were studied intensively by the leading number theorists of the nineteenth century. They are algebraic integers, which generate abelian extensions of the imaginary quadratic fields Q(z). This theory was thought to have been brought to a very satisfying completion in the early twentieth century. In the past fifty years it has developed in several directions -- from abelian varieties with complex multiplication to special points on Shimura varieties. I will review the classical theory and discuss the prime factorization of differences of singular moduli" |
September 22, 2014, 3:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS PHYSICAL MATHEMATICS SEMINAR |
Michele Del Zotto (HARVARD UNIVERSITY PHYSICS) |
Progress of Q-Systems |
" |
September 22, 2014, 12:00 - 2:00 PM at Science Center 232 |
| GAUGE THEORY, TOPOLOGY & SYMPLECTIC GEOMETRY SEMINAR |
Emmy Murphy (MIT) |
Existence of overtwisted contact structures on high dimensional manifolds |
The Lutz-Martinet theorem states that any 2-plane field on a 3-manifold is homotopic to a contact structure. This construction lead to Eliashberg s definition of overtwisted contact manifolds, and in this context the existence theorem of Lutz-Martinet can be extended to a uniqueness result: any two overtwisted contact structures which are homotopic as plane fields are in fact isotopic. We discuss a recent extension of these results to contact manifolds of all dimensions. We will focus on showing that any almost contact structure is homotopic to a contact structure, and seeing how this leads to a new definition of overtwistedness in high dimensions. As time allows we will discuss a proof that a homotopy class of almost contact structures is realized by a unique isotopy class of overtwisted contact structure. This project is joint work with Borman and Eliashberg" |
September 19, 2014, 3:30 - 4:30 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Han Liu (PRINCETON UNIVERSITY) |
Transelliptical Graphical Models: Theory and Computation |
We introduce the theory and computation of a semiparametric approach for estimating high dimensional graphical models. There are two main themes of this talk: semiparametric sparsity and statistical optimization. We illustrate the concept of semiparametric sparsity through the transelliptical graphical modeling, and illustrate the concept of statistical optimization through the theoretical analysis of a pathwise coordinate optimization algorithm named PICASA" |
September 17, 2014, 12:30 - 2:00 PM at Science Center 232 |
| NUMBER THEORY SEMINAR |
Hector Pasten (HARVARD UNIVERSITY) |
Counting Squarefree Values of Polynomials with Error Term |
The classical problem of counting squarefree values of polynomials is open in general. An important result of Granville gives an asymptotic formula for this counting problem, conditional to the abc conjecture. The error term is controlled by a density argument and therefore the technique gives no explicit error term. In this talk I will explain a new approach, which gives an asymptotic formula with a concrete error term under abc. A key intermediate result shows that the abc conjecture gives a lower bound for the radical of a polynomial value which not only has explicit dependence on the variable, but also on the polynomial. This is joint work with Ram Murty" |
September 17, 2014, 3:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Aaron Bertram (UTAH) |
Stability Conditions and Polarized Moduli |
Geometric stability conditions on surfaces involve an abelian category of complexes of vector bundles that is NOT the category of coherent sheaves. This begs the following question: Are the functors of quotients (of fixed Hilbert polynomial) of a fixed object representable? I will motivate this question with another observation, which came from work on strange duality over curves by Alina Marian and Dragos Oprea, namely, that when the quot scheme is finite, its degree matches the rank of the space of sections of a determinantal line bundle on moduli. Joint work with my students suggests that their curve result is also true of the projective plane, and may generalize much further" |
September 16, 2014, 3:30 PM at Science Center 507 |
| TOPOLOGY SEMINAR |
Michael Freedman (MICROSOFT AND UCSB) |
Smooth embeddings of closed 3-manifolds in R^4 |
I will present joint work with Ian Agol on smooth 3-manifolds in 4-space. It seems that only fairly primitive arguments obstruct the existence of such embeddings: For example no 3-manifold which embeds in a homology 4-sphere is known not to embed into S^4. I will give some new information on both existence of uniqueness of embeddings. The motivation for this study is that embeddings of 3 manifolds in R^4 impinges on the main open problems of low dimensional topology: The smooth Schoenflies conjecture, the smooth 4D Poincare conjecture, and the Andrews âCurtis conjecture" |
September 15, 2014, 10:20 AM - 12:00 PM at Science Center 232 |
| S.T. YAU'S STUDENT SEMINAR |
Jun Zhang (CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS) |
Information Geometry: Towards a Geometric Framework of Information Sciences |
I will be talking about how notions of differential geometry (metric, conjugate connections, equiaffine geometry, etc.) find their applications in information theory, statistics, machine learning, etc, and how they also pose interesting problems for geometers" |
September 12, 2014, 9:00 - 10:30 AM at Science Center 530 |
| THURSDAY SEMINAR |
Dan Freed (UNIVERSITY OF TEXAS - AUSTIN) |
Algebraic Topology and Mathematical Physics, an Overview |
" |
September 11, 2014, 4:00 - 6:00 PM at Science Center 507 |
| CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS COLLOQUIUM |
Martin Nowak (HARVARD UNIVERSITY) |
Evolution of Cooperation |
" |
September 10, 2014, 4:00 PM at Science Center 507 |
| PRESENTED BY THE CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS: RANDOM MATRIX AND PROBABILITY THEORY SEMINAR |
Laure Saint-Raymond (ĂCOLE NORMALE SUPĂ©RIEURE ) |
The Brownian Motion as Scaling Limit of a Deterministic System of Interacting Particles |
We provide a rigorous derivation of the Brownian motion as the hydrodynamic limit of a deterministic system of hard-spheres as the number of particles N goes to infinity and their diameter Δ simultaneously goes to 0, in the fast relaxation limit NΔdâ 1 â â (with a suitable scaling of the observation time and length). As suggested by Hilbert in his sixth problem, we use Boltzmannâs kinetic theory as an intermediate level of description for the gas close to global equilibrium. Our proof relies on the fundamental ideas of Lanford. The main novelty is the detailed study of the branching process, leading to explicit estimates on pathological collision trees. This is joint work with Thierry Bodineau and Isabelle Gallagher" |
September 10, 2014, 12:00 - 2:00 PM at Science Center 530 |
| PRESENTED BY THE CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS: PHYSICAL MATHEMATICS SEMINAR |
Siu-Cheong Lau (HARVARD UNIVERSITY) |
Generalized SYZ and quivers |
" |
September 08, 2014, 12:00 - 2:00 PM at Science Center 232 |
| PRESENTED BY THE CENTER OF MATHEMATICAL SCIENCES & APPLICATIONS: PROBABILITY THEORY & APPLICATION WORKING SEMINAR |
Jelani Nelson (HARVARD UNIVERSITY SEAS) |
Dimensionality Reduction Via Sparse Matrices |
This talk will discuss sparse Johnson-Lindenstrauss transforms, i.e. sparse linear maps into much lower dimension which preserve the Euclidean geometry of a set of vectors. Both upper and lower bounds will be presented, as well as applications to certain domains such as numerical linear algebra and compressed sensing. Based on various joint works with Jean Bourgain, Daniel M. Kane, and Huy Le Nguyen" |
September 05, 2014, 2:00 PM at Science Center 232 |
| NUMBER THEORY SEMINAR |
Tadashi Tokieda (CAMBRIDGE UNIVERSITY / RADCLIFFE INSTITUTE) |
Toy models |
`Toy here means an object of daily life which you can find/make in minutes, yet which, if played with imaginatively, reveal behaviors that set us thinking for a while. I will show a dozen table-top demos of such toys and discuss mathematics that open up from them" |
May 14, 2014, 3:00 PM at Science Center 507 |
| HARVARD, BRANDEIS, MIT, NORTHEASTERN JOINT COLLOQUIUM AT HARVARD |
Lauren Williams (UC BERKELEY) |
The positive Grassmannian |
The positive Grassmannian is a remarkable subset of the real Grassmannian which has recently arisen in diverse contexts such as integrable systems, scattering amplitudes, and free probability. I will provide an elementary introduction to the positive Grassmannian, focusing on a few intriguing aspects: what it ``looks like, and its connection to shallow water waves (via the KP hierarchy)" |
May 08, 2014, 4:30 PM at Science Center Hall A |
| NUMBER THEORY SEMINAR |
Gopal Prasad (UNIVERSITY OF MICHIGAN) |
Fake projective spaces |
A fake projective plane (fpp) is a smooth projective complex algebraic surface which has same Betti numbers as the complex projective plane. The first example of an fpp was constructed by David Mumford using p-adic uniformization. It was known that there are only finitely many fpp s and their fundamental groups are arithmetic subgroups of PU(2,1). In a joint work with Sai-Kee Yeung, using number theory, Bruhat-Tits theory, and my volume formula for the volumes of symmetric spaces modulo arithmetic groups, we have classified fpp s in 28 nonempty classes. This classification, with extensive computer-assisted computations by Steger and Cartwright, has led to a complete determination of all the fpp s--there are exactly 100 of them. This work has also given us an unexpected algebraic surface. In my talk I will describe the work, and its generalization to higher dimensions. For example, we have found fake analogues of complex projective 4-space. Our results have interesting consequences for the cohomology of arithmetic groups and automorphic forms" |
May 07, 2014, 3:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Jesse Kass (UNIVERSITY OF SOUTH CAROLINA) |
How to make Poincaré Duality into a holomorphic map |
PoincarĂ© Duality of a smooth complex curveâthe duality isomorphism that describes how cycles intersectâcan be realized by a holomorphic map between complex manifolds called the Abel map. Starting with the definition of the Abel map, I review this result and then explain how it extends to singular curves. In doing so, I describe the compactified Jacobian of a curve with ordinary n-fold singularities and, if time permits, discuss some connections with Dima Arinkin s work on autoduality. This work is joint with Kirsten Wickelgren" |
May 06, 2014, 3:00 - 4:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Andrew Morrison (ETH ZURICH) |
On the motive class of the commuting variety |
In 1960, Walter Feit and Nathan Fine discovered an elegant polynomial formula counting the number of Fq points on the commuting variety, i.e. pairs of commuting matrices over the finite field Fq. This formula is in fact valid in the Grothendieck ring of varieties over any base field. We will explain a new geometric proof which leads to several refinements and generalizations of the original result recently used to find the virtual motives of Hilbn(C3)" |
May 06, 2014, 4:00 - 5:00 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Curtis McMullen (HARVARD UNIVERSITY) |
Fibered 3-manifolds and the simplest known surface dynamics |
" |
April 30, 2014, 04:00 PM at Science Center 530 |
| NUMBER THEORY SEMINAR |
Brandon Levin (IAS) |
Moduli of finite flat group schemes and local models |
In Kisinâs work on modularity lifting, he studies flat deformation rings using a moduli space of finite flat group schemes. In turn, the geometry of this space can be related to local models of Shimura varieties. We discuss generalizations of the moduli space, the local models, and the relationship between them" |
April 30, 2014, 3:00 PM at Sci Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Jenia Tevelev (UNIVERSITY OF MASSACHUSETTS AMHERST) |
Birational geometry of moduli of stable rational curves |
I will report on joint work with Castravet on birational geometry of moduli of stable rational curves with n punctures. In particular, we show that it is not a Mori Dream Space when n is at least 134, answering a question of Hu and Keel" |
April 29, 2014, 4:00 PM at Science Center 507 |
| FRIENDS OF THE MATHEMATICS DEPARTMENT AFTERNOON LECTURE |
Barry Mazur, speaking from the MSRI in Berkeley (HARVARD UNIVERSITY) |
PRIMES - based on the book co-authored with William Stein |
The Riemann Hypothesis is one of the great unsolved problems of mathematics and the reward of $1,000,000 of Clay Mathematics Institute prize money awaits the person who solves it. But, with or without money, its resolution is crucial for our understanding of the nature of numbers. There are at least four full-length books recently published, written for a general audience, that have the Riemann Hypothesis as their main topic. A reader of these books will get a fairly rich picture of the personalities engaged in the pursuit, and of related mathematical and historical issues. This is not the mission of this book. We aim, instead, to explain in as direct a manner as possible and with the least mathematical background required, what this problem is all about and why it is so important. For even before anyone proves this hypothesis to be true (or false!), just getting familiar with it and with some of the the ideas behind it, is exciting. Moreover, this hypothesis is of crucial importance in a wide range of mathematical fields; for example, it is a confidence-booster for computational mathematics: even if the Riemann Hypothesis is never proved, its truth gives us an excellent sense of how long certain computer programs will take to run, which, in some cases, gives us the assurance we need to initiate a computation that might take weeks or even months to complete" |
April 25, 2014, 2:00 PM at Science Center 507 |
| FRIENDS OF THE MATHEMATICS DEPARTMENT AFTERNOON LECTURE |
Martin Nowak (HARVARD UNIVERSITY) |
Evolutionary Dynamics and Treatment of Cancer |
Cancer is an evolutionary process. Cancer initiation and progression are caused by somatic mutation and selection of dividing cells. The mathematical theory of evolution can therefore provide quantitative insights into human cancer. I will discuss the role of chromosomal instability (CIN) and the accumulation of drivers and passengers in growing tumors.  I will study success and failure of targeted therapy including combination of different drugs and evolution of resistance. A simple conclusion is that combination treatment can succeed, if the cancer requires at least two point mutations to gain resistance. From the perspective of preventing resistance, simultaneous therapy is highly recommended whereas sequential therapy is a recipe for almost certain treatment failure.Â" |
April 25, 2014, 3:00 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Robert Lipshitz (COLUMBIA UNIVERSITY) |
Hochschild localization and bordered Heegaard Floer homology |
We will discuss an analogue in Hochschild homology of the Smith inequality for a Z/2 action on a topological space. Â We will then apply this theorem to bordered Heegaard Floer homology, to obtain results about the Heegaard Floer homology of double covers, and speculate wildly about other possible extensions and applications. Â This is joint work with David Treumann" |
April 25, 2014, 3:30 PM at Science Center 309 |
| BRANDEIS-HARVARD-MIT-NORTHEASTERN JOINT MATHEMATICS COLLOQUIUM |
Jared Weinstein (BOSTON UNIVERSITY) |
Complex Multiplication from Abel to Zagier |
According to Hilbert, the theory of complex multiplication, which brings together number theory and analysis, is not only the most beautiful part of mathematics but also of all science. Complex multiplication refers to a lattice in the complex numbers (or an elliptic curve) which admits endomorphisms by a ring larger than the integers. We will begin with Kronecker s Jugendtraum -- the use of complex multiplication to solve Hilbert s twelfth problem. This will lead us into a discussion of Heegner points, and the solution of the Birch and Swinnerton-Dyer conjecture in certain cases. We will conclude with some recent work on the modular curve at infinite level, and the unexpected role that complex multiplication plays in its geometry." |
April 24, 2014, 4:30 PM at Sci Center A |
| NUMBER THEORY SEMINAR |
Aaron Pollack (PRINCETON UNIVERSITY) |
Rankin-Selberg integrals associated to nonunique models |
Most known Rankin-Selberg integral representations derive their Euler product structure from the uniqueness of some model, such as the Whittaker model. Â However, there are a few examples of global Rankin-Selberg convolutions which are known to represent L functions, yet don t unfold to a unique model. Â Using an extension of a method devised by Piatetski-Shapiro and Rallis, we will give two new interesting examples of such integrals: one for the exterior square L function on GU(2,2), the other for the Spin L function on GSp(6). Â As I will explain, these integrals deserve to be considered analogues of the integral representation of Kohnen-Skoruppa for the Spin L function on GSp(4). Â This is joint work with Shrenik Shah" |
April 23, 2014, 3:00 PM at Sci Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Dragos Oprea (UC SAN DIEGO) |
Generalized theta functions over abelian surfaces |
The generalized theta functions over an abelian surface are sections of determinant line bundles over moduli spaces of sheaves over the surface. Under general numerical conditions, B. Bolognese, A. Marian, K. Yoshioka and myself showed that the spaces of generalized theta functions have the expected dimension (which had been previously calculated explictly). I will discuss this result, and time permitting, I will also explain several conjectural refinements of the dimension formula taking into account certain natural group actions on the spaces of generalized theta functions" |
April 21, 2014, 4:00 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Christopher Woodward (RUTGERS UNIVERSITY) |
Floer theory and minimal model transitions |
I will discuss a conjecture that a smooth projective variety, considered as a symplectic manifold, has at least as many Floer non-trivial (and so Hamiltonian non-displaceable) Lagrangians as transitions in any minimal model program (mmp) for that variety. The toric case was joint work with E. Gonzalez based on earlier work of Fukaya-Oh-Ohta-Ono. I will discuss some recent results on existence of non-displaceable Lagrangians in blow-ups of certain varieties with effective anticanonical divisors.Â" |
April 18, 2014, 3:30 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Yifeng Liu (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
Bounding Selmer groups via Gross-Kudla-Schoen cycles |
Given an elliptic curve over the field of rationals and another one over a real quadratic field, we construct a motive of rank 8, together with a distinguished class in its Bloch-Kato Selmer group. We show that if the distinguished class is nontrivial, then the dimension of the Bloch-Kato Selmer group is 1. This result can be viewed as the (twisted) triple product version of Kolyvagin s result on bounding Selmer groups of a single elliptic curve via Heegner points" |
April 16, 2014, 3:00 PM at Science Center 507 |
| HARVARD MATH & PHILOSOPHY LOGIC COLLOQUIUM |
Ilijas Farah (YORK UNIVERSITY) |
Logic and operator algebras |
Operator algebras are subalgebras of the algebra of bounded operators on a complex Hilbert space. They are usually in addition assumed to be self-adjoint and norm-closed (C*-algebras) or closed in weak operator topology (von Neumann algebras). Connections between logic and operator algebras in the past century were few and sparse. This has changed radically in the recent years. Several diverse tools from logic were successfully applied to solve long-standing problems in operator algebras and new, purely logical, tools had to be developed to this effect. I will survey some of the most recent developments." |
April 16, 2014, 4:00 PM at HU Logic Center - 2 Arrow Street, Room #420 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Fernando Cukierman (UNIVERSITY OF BUENOS AIRES) |
Families of foliations and varieties of complexes |
We consider differential 1-forms on the complex projective space of dimension r, with homogeneous polynomials of degree d as coefficients, and satisfying the Frobenius integrability condition. The set of all such 1-forms is an algebraic variety, denoted F(r,d). One open problem in this area is to find the irreducible components of F(r,d). In the first part of the talk we plan to describe some of the known irreducible components. Afterwards, we ll discuss a strategy for approaching the problem, via the varieties of complexes. More precisely: let V be a finite dimensional graded vector space and denote by C(V) the corresponding variety of differential complexes, that is, the set of linear endomorphisms of V, of degree one and square zero. We shall review some of the basic geometry of the algebraic variety C(V), including the description of its singular points and irreducible components. Then, we represent F(r,d) as a linear section of a certain C(V), and discuss possible consequences for the problem of enumerating irreducible components of F(r,d), and some generalizations" |
April 15, 2014, 4:30 - 5:30 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
David Jensen (YALE UNIVERSITY) |
Tropical Brill-Noether Theory and the Gieseker-Petri Theorem |
Many problems in algebraic geometry concern the behavior of linear series on general curves. The recently developed theory of specialization of linear series from algebraic to tropical curves provides us with a new set of tools for approaching such problems. We will show how such tools can be used to provide a new proof of the Gieseker-Petri Theorem, which says that the varieties parameterizing linear series on a general curve are smooth" |
April 15, 2014, 3:00 PM **Corrected time** at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Aaron Pixton (HARVARD UNIVERSITY) |
The cohomology of the moduli space of curves |
Let $M_g$ be the moduli space of connected smooth genus g curves. This space has a very complicated cohomology ring $H^*(M_g)$, which is of interest in both algebraic geometry and topology. The tautological ring is an important subring of this cohomology, introduced by Mumford in the 1980s in analogy with the cohomology of Grassmannians. Work of Faber and Faber-Zagier in the 1990s led to two competing conjectural descriptions of the structure of this subring. I will discuss the current status of these two conjectures" |
April 14, 2014, 3:00 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Josh Greene (BOSTON COLLEGE) |
Conway mutation and alternating links |
I will prove that a pair of reduced, alternating link diagrams D and D represent links with homeomorphic branched double covers iff D and D are Conway mutants. The proof relies on combinatorial arguments and a black box from gauge theory (Donaldson s diagonalization theorem). I will also draw mutant knots simultaneously and ambidextrously" |
April 11, 2014, 3:30 PM at Sci Center 507 |
| SPECIAL SEMINAR |
Vladimir Voevodsky (INSTITUTE FOR ADVANCED STUDY) |
Univalent Mathematics in Coq. |
This will be a presentation directed mostly at mathematicians with a demonstration of how to write mathematics (definitions, theorems and proofs) in the proof assistant Coq using the univalent semantics of the Coq language. I will have Coq running on my computer projected to the screen and will show how working with it actually looks like. Those who want to follow me on their laptops can download and install Coq from http://coq.inria.fr " |
April 11, 2014, 3:00 PM at Science Center 232 |
| NUMBER THEORY SEMINAR |
Noam Elkies (HARVARD UNIVERSITY) |
Integer-valued polynomials with slow growth |
For each C there are only finitely many polynomials P \in Z[x] such that |P(n)| < C^n for every integer n>0. On the other hand, there are infinitely many polynomials P in Q[X] that take Z to Z and satisfy |P(n)| < 2^n for all integers n>0: just use P(n) = {n \choose k}. How far below 2^n can we go? That is, what is liminf_P(max_n |P(n)^{1/n}) ? The answer turns out to be the Golden Ratio. This is joint work with Vesselin Dimitrov and David Speyer" |
April 09, 2014, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Ilarion Melnikov (TEXAS A & M UNIVERSITY) |
A (0,2) overview |
I will give a summary of recent developments in obtaining worldsheet-exact results in compactifications of the perturbative heterotic string, focusing on backgrounds preserving N=1 super-Poincare invariance in four dimensions. After discussing the supergravity picture, I will switch to the worldsheet and focus on various localization-based techniques. I will end with a summary of some pressing questions and current directions" |
April 08, 2014, 1:30 - 2:30 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Zsolt Patakfalvi (PRINCETON UNIVERSITY) |
A generic vanishing theorem in positive characteristic |
I will present a generic vanishing type theorem in positive characteristic. I will also introduce a new invariant the S-Kodaira dimension which can be thought of as the Frobenius stable Kodaira dimension. Example application of the above mentioned generic vanishing type theorems, that I will present, are: 1.) if the S-Kodaira dimension of a smooth variety X over an algebraically closed field of positive characteristic is zero then the Albanese morphism of X is surjective. In particular, the first Betti number of X is at most twice the dimension of X. 2.) a characteriztaion of smooth projective varieties birational to ordinary abelian varieties" |
April 08, 2014, 4:00 PM at Science Center 507 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Spaces of Maps between Structured Ring Spectra II |
" |
April 03, 2014, 3:00 - 5:00 PM at Sci Center 507 |
| NUMBER THEORY SEMINAR |
James Maynard (MAGDALEN COLLEGE, OXFORD /UNIVERSITY OF MONTREAL) |
Small gaps between primes |
It is believed that there should be infinitely many pairs of primes which differ by 2; this is the famous twin prime conjecture. More generally, it is believed that for every positive integer $m$ there should be infinitely many sets of $m$ primes, with each set contained in an interval of size roughly $m\log{m}$. Although proving these conjectures seems to be beyond our current techniques, recent progress has enabled us to obtain some partial results. We will introduce a refinement of the `GPY sieve method for studying these problems. This refinement will allow us to show (amongst other things) that $\liminf_n(p_{n+m}-p_n)<\ infty$ for any integer $m$, and so there are infinitely many bounded length intervals containing $m$ primes." |
April 02, 2014, 3:00 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Curtis McMullen (HARVARD UNIVERSITY) |
Constant curvature and Outer space |
" |
April 02, 2014, 4:00 PM at Science Center 530 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
CĂ©sar Lozano Huerta (UNIVERSITY OF ILLINOIS AT CHICAGO) |
Birational Geometry of the Space of Complete Quadrics |
Schubert in the 19th century introduced the moduli space of complete quadrics which has attracted the attention of geometers since. The purpose of this talk is to run the Minimal Model Program on this classical space. I will discuss that this space is a Mori dream space. Then, using classical constructions, I will describe a moduli interpretation for some of its (log) minimal models induced by movable divisors. If time permits, I will mention work in progress which relates this work to representation theory" |
April 01, 2014, 4:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Michele Del Zotto (HARVARD UNIVERSITY) |
Periodicity of the Kontsevich Soibelman operator, singularity theory, and cyclic subgroups of the Cremona groups Cr(n) |
" |
April 01, 2014, 1:30 - 2:30 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Joe Harris (HARVARD UNIVERSITY) |
Uniformity of rational points and the Lang conjecture |
This talk concerns joint work with Lucia Caporaso and Barry Mazur. The question weâll address is very straightforward. Faltingsâ proof of the Mordell conjecture asserts that every curve $C$ of genus $g \geq 2$ defined over a number field $K$ has only a finite number of rational points. The question is, given $g$ and $K$, is there an upper bound on these numbers" |
March 31, 2014, 3:00 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Adam Jacob (HARVARD UNIVERSITY) |
Flat bundles, harmonic metrics and singular affine structures |
There is a natural correspondence between holomorphic bundles over complex manifolds and flat bundles over affine manifolds. More specifically, an elliptic K3 surface can be viewed as a torus fibration over P^1, and away from the singular fibers a torus invariant holomorphic bundle reduces to a flat bundle over punctured P^1. In this talk I will describe and solve the reduction of the Hermitian-Yang-Mills equations to a flat bundle on this Riemann surface, and discuss its relation to twisted harmonic metrics and mirror symmetry. This is joint work with T.C. Collins and S.-T. Yau." |
March 28, 2014, 3:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Spaces of maps between structured ring spectra |
" |
March 27, 2014, 3:00 - 5:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Anders Sodergren (UNIVERSITY OF COPENHAGEN) |
Poisson statistics and the value distribution of the Epstein zeta function |
In this talk I will discuss certain questions concerning the asymptotic behavior of the Epstein zeta function $E_n(L,s)$ in the limit of large dimensions n. In particular, I will describe the value distribution of $E_n(L,s)$ for a random lattice L of large dimension n, giving partial answers to questions raised by Sarnak and Str\ombergsson in their study of minima of $E_n(L,s)$. Some of the key ingredients in our discussion are of independent interest in the geometry of numbers" |
March 26, 2014, 3:00 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Tom Church (STANFORD & MIT) |
Moebius functions and growth rates of groups |
" |
March 26, 2014, 4:00 PM at Science Center 530 |
| LOGIC COLLOQUIUM |
Ralf Schindler (UNIVERSITY OF MĂŒNSTER) |
Martin's Maximum with an asterix |
There are two prominent axioms of set theory which both yield that the continuum be of size \aleph_2, namely Martin s Maximum (MM) and Woodin s (*). In recent years, Jensen s L-forcing has been exploited to verify that many combinatorial consequences of (*) also follow from MM, but the relationship between MM and (*) remains a mystery. We propose and discuss a natural amalgamation of MM and (*), Martin s Maximum with an asterisk." |
March 26, 2014, 4:00 PM at Logic Center, 2 Arrow St, Rm 420 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Roya Beheshti (WASHINGTON UNIVERSITY IN ST. LOUIS) |
Spaces of rational curves on Fano hypersurfaces |
I will discuss some aspects of the geometry of moduli spaces of rational curves on Fano hypersurfaces in projective space and other homogeneous varieties, focusing in particular on some questions regarding the dimension and irreducibility of these moduli spaces" |
March 25, 2014, 4:00 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Mohammed Abouzaid (COLUMBIA UNIVERSITY) |
Formality and Symplectic Khovanov Homology |
I will describe the first (completed) half of a project whose goal is to prove that Khovanov homology agrees with the symplectic analogue. The main result is the formality of the subcategory of the Fukaya category of the nilpotent slice studied by Seidel-Smith which corresponds to Khovanov s arc algebra. They key new ingredient is an abstract criterion for formality due to Seidel, and its implementation using counts of holomorphic curves in a partial compactification of these spaces. This is joint work with I. Smith" |
March 14, 2014, 3:30 - 4:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Inna Zakharevich (INSTITUTE FOR ADVANCED STUDY) |
Filtering the Grothendieck ring of varieties |
" |
March 13, 2014, 3:00 - 5:00 PM at Science Center 507 |
| HARVARD LOGIC COLLOQUIUM |
Paul Larson (MIAMI UNIVERSITY) |
Forcing axioms in âmax extensions |
Martin s Maximum, the maximal forcing axiom, was introduced in the 1980 s by Foreman, Magidor and Shelah, who proved its consistency relative to a supercompact cardinal. In the 1990 s, Woodin introduced âmax, a method for forcing over models of determinacy, and used it produce a new consistency proof for MM(đ ), the restriction of Martin s Maximum to partial orders of cardinality the continuum. Later results of Sargsyan showed that the determinacy hypothesis used in Woodin s result has consistency strength below a Woodin limit of Woodin cardinals. We will discuss a recent attempt to extend Woodin s theorem to partial orders of cardinality đ +. In particular, we will show that in the âmax extension of a suitable determinacy model, certain â» principles fail at both Ï2 and Ï3, significantly reducing the consistency strength upper bound for such a result. Part of the talk will focus on models of determinacy. This is joint work with Caicedo, Sargsyan, Schindler, Steel and Zeman." |
March 12, 2014, 4:00 - 5:00 PM at 2 Arrow Street, Room #420 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Curtis McMullen (HARVARD UNIVERSITY) |
Graphs with expansion < 8 |
" |
March 12, 2014, 4:00 PM at Science Center 530 |
| NUMBER THEORY SEMINAR |
Adriana Salerno (BATES COLLEGE) |
Effective computations in arithmetic mirror symmetry |
In this talk, I will talk about computational approaches to the problem of arithmetic mirror symmetry. One of the biggest questions facing string theorists is the one of mirror symmetry. In arithmetic mirror symmetry, we approach the conjecture from a number theoretic point of view, namely by computing Zeta functions of mirror pairs. I will define all of these terms and then explain our work through a couple of examples of families of K3 surfaces. This is joint work with Xenia de la Ossa, Charles Doran, Tyler Kelly, Stephen Sperber, and Ursula Whitcher" |
March 12, 2014, 3:00 PM at Sci Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Bangere Purnaprajna (UNIVERSITY OF KANSAS) |
Geometry of surfaces of general type |
In this talk I will survey my recent results with my coauthors on varieties of general type with particular emphasis on the case of algebraic surfaces. The first theme will relate the deformation of canonical maps to construction of simple canonical surfaces, addressing a question of Enriques. The framework we develop allows us to describe some components of infinitely many moduli spaces of surfaces of general type. The second theme is to explore a higher dimensional analogue of the uniformization theorem of Riemann and Kobe, the so-called holomorphic convexity of the universal cover of a projective variety, which goes under the name of Shafarevich conjecture. Until recently, this was not known in its full generality for even surfaces fibered by genus two curves. We prove some general statements about fundamental groups of surfaces fibered by hyperelliptic curves of arbitrary genus. Examples show that this is an optimal result. As a byproduct we prove, a stronger form of Shafarevich conjecture for these surfaces, and a very attractive conjecture of Nori on fundamental groups. This also yields statements on second homotopy groups of fibered surfaces" |
March 11, 2014, 4:00 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Yaiza Canzani (HARVARD UNIVERSITY) |
Local geometry of the nodal sets of Laplace eigenfunctions |
Let $(M,g)$ be a compact real analytic surface with no boundary, and let $H$ denote a closed analytic curve in $M$. Write $\varphi_\lambda$ for the eigenfunctions of the Laplacian $\Delta_g$ with eigenvalue $\lambda^2$. When $M$ is the two-torus and $H$ has non-vanishing curvature (Burgain-Rudnick) or when $M$ is an arithmetic surface and $H$ is a geodesic circle (Jung), it has been shown that $H$ is a \emph{good} curve in the sense that $\| \varphi_{\lambda} \|_{L^2(H)} \geq e^{-C \lambda}$ for some $C>0$ and all $\lambda >\lambda_0$. In these cases it was proved that $$ \# \{ \varphi_{\lambda}^{-1}(0) \cap H\}= O(\lambda). \quad \quad (*)$$ In this talk we show that the bound $(*)$ holds on the general surface $(M,g)$ provided $H$ is a good curve. This is joint work with John Toth" |
March 10, 2014, 3:00 PM at Science Center 507 |
| THURSDAY SEMINAR |
Lukas Brantner (HARVARD UNIVERSITY) |
Rezk's Congruence Criterion |
" |
March 06, 2014, 3:00 - 5:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Raman Parimala (EMORY UNIVERSITY) |
Hasse principle over function fields of complete discretely valued fields |
The Brauer-Manin obstruction explains the failure of Hasse principle for the existence of rational points on torsors under connected linear algebraic groups over a number field. Similar questions of Hasse principle have been studied over more general fields, particularly, function fields of curves over complete discrete valued fields. There are several positive results in this direction for connected linear algebraic groups which are rational over function fields of curves over complete discretely valued fields, thanks to the patching techniques developed by Harbater-Hartmann-Krashen. It remained open whether the rationality assumption was necessary for such a Hasse principle to hold. We explain the example of a torus where the failure of the Hasse principle is explained via certain higher reciprocity obstruction analogous to the Brauer-Manin obstruction for number fields (joint work with Colliot-Thelene and Suresh)" |
March 05, 2014, 3:00 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Curt McMullen (HARVARD UNIVERSITY) |
Classification of graphs with small entropy |
" |
March 05, 2014, 4:00 PM at Science Center 530 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Ravi Vakil (STANFORD UNIVERSITY) |
The Chow ring of the moduli space of genus 6 curves |
We determine the Chow ring (with rational coefficients) of the moduli space of curves of genus 6 by showing that all Chow classes are tautological. In particular, all algebraic cohomology is tautological, and the natural map from Chow to cohomology is injective. We rely on results of many others, notably Faber, Vistoli, and Mukai. To show the efficacy of these methods, we give quick derivations of the Chow groups of moduli spaces of curves of lower genus as well. What makes genus $6$ argument tractable (and even short) is the particularly beautiful Brill-Noether theory in this case. This is joint work with Nikola Penev" |
March 04, 2014, 4:00 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Hugh Woodin (HARVARD UNIVERSITY) |
The Continuum Hypothesis and the conception of mathematical infinity |
By middle of the 20th century the problem of the Continuum Hypothesis was widely regarded as one of the prominent problems in all of Mathematics. Remarkably, this question cannot be be solved on the basis of the basic principles (these are the ZFC axioms) on which the entire subject is based. This discovery of Cohen, announced 50 years ago last summer, is arguably one of the major discoveries in the history of modern Mathematics. But does this mean that the question of the Continuum Hypothesis has no answer? Any solution must involve the adoption of new principles but which principles should one adopt? Alternatively, perhaps the correct assessment of Cohen s discovery is that the entire enterprise of the mathematical study of Infinity is ultimately doomed because the entire subject is simply a human invention without any true foundation. In this case, any solution to the Continuum Hypothesis is just an arbitrary (human) choice. Over the last few years a scenario has emerged by which with the addition of a single new principle not only can the problem of the Continuum Hypothesis be resolved, but so can all of the other problems which Cohen s method has been used to show are also unsolvable (and there have been many such problems). Moreover the extension of the basic (ZFC) principles by this new principle would be seen as an absolutely compelling option based on the fundamental intuitions on which the entire mathematical conception of Infinity is founded. However, this scenario critically depends upon the outcome of a single conjecture. If this conjecture is false then the entire approach, which is the culmination of nearly 50 years of research, fails or at the very least has to be significantly revised. Thus the mathematical study of Infinity has arguably reached a tipping point. But which way will it tip" |
March 03, 2014, 3:00 PM at Science Center 507 |
| THURSDAY SEMINAR |
Nathaniel Stapleton (MIT) |
The Morava E-theory of symmetric groups: character theory and Strickland's theorem |
" |
February 27, 2014, 3:00 - 5:00 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Curtis McMullen (HARVARD UNIVERSITY) |
The curve complex of a directed graph |
" |
February 26, 2014, 4:00 PM at Science Center 530 |
| NUMBER THEORY SEMINAR |
François Charles (MIT/UNIVERSITé D'ORSAY) |
Frobenius distribution and exceptional isogenies for pairs of elliptic curves over number fields |
Let E and E be two elliptic curves over a number field. We prove that there exists infinitely many reduction of E and E over finite fields that are geometrically isogenous. This is an analog of a Hodge-theoretic result of Green. The proof relies on dynamical properties of the Hecke correspondences on the modular curve" |
February 26, 2014, 3:00 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Andrew Cotton-Clay (HARVARD UNIVERSITY) |
Weinstein Manifolds |
" |
February 24, 2014, 3:00 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Jen Hom (COLUMBIA UNIVERSITY) |
An infinite rank summand of topologically slice knots |
Let T denote the subgroup of the smooth knot concordance group generated by topologically slice knots. Endo showed that T contains an infinite rank subgroup, and Livingston and Manolescu-Owens showed that T contains a summand of rank three. We show that in fact T contains an infinite rank summand. The proof relies on the knot Floer homology package of Ozsvath-Szabo and the concordance invariant epsilon" |
February 21, 2014, 3:30 - 4:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
Power Operations in K-theory |
" |
February 20, 2014, 3:00 - 5:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Joseph H. Silverman (BROWN UNIVERSITY) |
Canonical Heights, Nef Divisors, and the Arithmetic Complexity of Orbits |
Let f : X --> X be a dominant rational self-map of a smooth projective variety and h an ample Weil height on X. We study the arithmetic degrees a_f(P) = lim h(f^n(P))^{1/n} of algebraic points. Conjecture 1: The limit a_f(P) exists, is an algebraic integer, and takes on only finitely many values as P varies. Conjecture 2: If the f-orbit of P is Zariski dense, then a_f(P) equals the dynamical degree of f. I will discuss the resolution of Conjecture 1 in the case that f is a morphism and Conjecture 2 for isogenies of abelian varieties. The latter proof uses a new non-degeneracy result for canonical heights relative to nef divisors. (Joint work with Shu Kawaguchi" |
February 19, 2014, 3:00 - 4:00 PM at Science Center 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
Curtis McMullen (HARVARD UNIVERSITY) |
Cliques and spectra of graphs |
" |
February 19, 2014, 4:00 PM at Sci Center 530 |
| HARVARD MATH & PHILOSOPHY LOGIC COLLOQUIUM |
Grigor Sargsyan (RUTGERS UNIVERSITY) |
Covering, core model induction and hod mice |
We will discuss recent covering principles and show how they can be used to derive strength from failure of square. Sponsored jointly by the Department of Mathematics and Department of Philosoph" |
February 19, 2014, 4:00 - 5:30 PM at 2 Arrow Street, Room #420 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Tom Church (STANFORD UNIVERSITY) |
A survey of representation stability |
I will give a gentle survey of the theory of representation stability, viewed through the lens of its applications. These applications include: homological stability for configuration spaces of manifolds, including a topological analogue of Vakil-Wood s motivic stabilization; understanding the stable (and unstable) homology of arithmetic lattices; a classification of Hecke eigenclasses in stable mod-p cohomology; uniform generators for congruence subgroups and" |
February 18, 2014, 3:00 PM at Science Center 507 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Units in Morava E-theory |
" |
February 13, 2014, 3:00 - 5:00 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Curt McMullen (HARVARD UNIVERSITY) |
Optimal metrics on graphs |
This talk will begin a discussion of the unsolved problem of the shortest geodesic on moduli space" |
February 12, 2014, 4:00 PM at Science Center 530 |
| NUMBER THEORY SEMINAR |
Kamal Khuri-Makdisi (AMERICAN UNIVERSITY OF BEIRUT) |
Eisenstein series of weight 1 |
In this talk, I will sketch a proof that the ring generated by Eisenstein series of weight 1 on the principal congruence subgroup $\Gamma(N)$ contains all modular forms in weights 2 and above. This means that the only forms that are not seen by polynomials in these Eisenstein series are cusp forms of weight 1. This result gives rise to a systematic way to produce equations for the modular curve $X(N)$" |
February 12, 2014, 3:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Brendan Hassett (RICE UNIVERSITY) |
Families of fibrations of del Pezzo surfaces |
We consider fibrations in quartic del Pezzo surfaces over P^1 with mild singular fibers. There is a fundamental numerical invariant of such a family, known as the height. Our main result is that the family of all del Pezzo surfaces of fixed height is non-empty and irreducible, with the exception of a few small heights. We also show that certain spaces of sections on del Pezzo fibrations parametrize their intermediate Jacobians. (joint work with Kresch and Tschinkel" |
February 11, 2014, 3:00 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Dennis Gaitsgory (HARVARD UNIVERSITY) |
Drinfeld's shtukas and related ideas |
" |
February 10, 2014, 3:00 PM at Science Center 507 |
| TRIVIAL NOTIONS SEMINAR |
Stergios Antonakoudis (HARVARD UNIVERSITY) |
Measured foliations and Riemann surfaces |
We will discuss what meassured foliations and why they are important in the study of Riemann surfaces and their moduli spaces. At the heart of this topic is the fundamental theorem of Hubbard and Masur, which we will explain and, if time permits, we will also outline a simple proof, due to Michael Wol, using harmonic maps" |
February 06, 2014, 12:00 PM at Science Center 112 |
| NUMBER THEORY SEMINAR |
Hossein Movasati (HARVARD UNIVERSITY) |
Modular forms for triangle groups |
In this talk we classify all primes appearing in the denominators of modular forms for triangle groups with a cusp. In particular, we prove that such modular forms are $N$-integral if and only if the triangle group is arithmetic (and hence by Takeuchi s classification it falls into nine cases). As a corollary we show that for the Hecke group of type $(2,m,\infty)$, such modular forms are $p$-integral if and only if $p\equiv \pm 1\pmod m$. The main tool we use is a theorem of Dwork on Gauss hypergeometric functions and its relation to modular forms. This is a joint work with Kh. M. Shokri" |
February 05, 2014, 3:00 PM at Sci Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Tiankai Liu (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
On the Coolidge-Nagata conjecture |
The Coolidge-Nagata conjecture asserts that every rational curve in the complex projective plane that has only cusps (i.e., for which the normalization map is bijective) can be transformed into a line via a birational automorphism of the plane. We will discuss some progress towards this conjecture, and various techniques for studying cuspidal rational curves" |
February 04, 2014, 3:00 PM at Science Center 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Steven Sivek (PRINCETON UNIVERSITY) |
Sutured embedded contact homology is an invariant |
Embedded contact homology (ECH) is an invariant of a closed contact 3-manifold, but proving its invariance is not so straightforward: the only known proof (due to Taubes) is to show that it is isomorphic to monopole Floer homology, which only depends on the underlying manifold. Colin, Ghiggini, Honda, and Hutchings defined a version of ECH for contact 3-manifolds with boundary, which are naturally sutured manifolds, and conjectured that this is also an invariant of the underlying sutured manifold. In this talk I will show that sutured ECH is indeed an invariant and discuss how it can be made into a natural one. This is joint work with Cagatay Kutluhan" |
January 31, 2014, 3:30pm at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Alberto Lopez (TUFTS UNIVERSITY) |
TBA |
" |
January 28, 2014, 3:00 PM at Science Center 507 |
| THURSDAY SEMINAR |
Haynes Miller (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
Dual Brown-Gitler spectra as projective covers |
" |
December 12, 2013, 3:00 - 5:00 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Benedict Gross (HARVARD UNIVERSITY) |
On the arithmetic of hyperelliptic curves |
" |
December 09, 2013, 3:00 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Peter Ozsvath (PRINCETON UNIVERSITY) |
Bordered Floer homology and three-manifolds with torus boundary |
Bordered Floer homology is an invariant for three-manifolds with boundary, which can be used to compute the U=0 specialization of Heegaard Floer homology. In this talk, I will describe an enhancement of bordered Floer homology to the full (unspecialized) Heegaard Floer homology, in the case of three-manifolds with torus boundary. This is joint work with Robert Lipshitz and Dylan Thurston" |
December 06, 2013, 3:30 PM at Science Center 507 |
| HARVARD/MIT LOGIC SEMINAR |
Sam Sanders (GHENT UNIVERSITY) |
Higher-order Reverse Mathematics: Where existence meets computation via infinitesimals |
Classically, the existence of an object tells us very little about how to construct said object. We consider a nonstandard version of Ulrich Kohlenbach s higher-order Reverse Mathematics in which there is a very elegant and direct correspondence between, on one hand, the existence of a functional computing an object and, on the other hand, the classical existence of this object with the same standard and nonstandard properties. We discuss how these results âpotentiallyâ contribute to the programs of finitistic and predicativist mathematics" |
December 06, 2013, 4:30 - 5:30 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Jack Thorne (HARVARD UNIVERSITY) |
The arithmetic of some non-hyperelliptic curves |
We will discuss some new results relating to the arithmetic statistics of a family of non-hyperelliptic genus 3 curves over Q" |
December 04, 2013, 3:00 - 4:00 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Giulio Tiozzo (YALE AND ICERM) |
Galois conjugates of entropies of quadratic maps |
" |
December 04, 2013, 4:00 PM at Sci Center 507 |
| HARVARD/MIT LOGIC SEMINAR |
Lynn Scow (VASSAR COLLEGE) |
|
" |
December 03, 2013, 4:30 - 5:30 PM at Science Center 507 |
| HARVARD/MIT LOGIC SEMINAR |
Brian Wynne (BARD COLLEGE AT SIMON'S ROCK) |
Upper products of existentially closed Abelian â"-groups |
I will start with some background on existentially closed Abelian â-groups, and then discuss my work on upper products, a construction due to Ball, Conrad, and Darnel that generalizes the direct product, the lexicographic product, and the wreath product. In particular, I will present conditions under which the upper product of two existentially closed Abelian â-groups is existentially closed, and some examples" |
November 26, 2013, 4:30 - 5:30 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Arul Shankar (HARVARD UNIVERSITY) |
Counting Binary cubic forms using geometry-of-numbers techniques |
We will present a classical result of Davenport which established asymptotics for the number of $\GL_2(\Z)$-orbits on integral binary cubic forms having bounded discriminant, with a power saving error term. We will then discuss an averaging method of Bhargava s that improves Davenport s power saving error term to an optimal one. Finally, we introduce a refinement that allows us to determine the second main term for this count! (The final refinement is joint work with Bhargava and Tsimerman." |
November 25, 2013, 3:00 - 4:00 PM at Science Center 507 |
| THURSDAY SEMINAR |
Aaron Mazel-Gee (UC BERKELEY) |
Goerss--Hopkins obstruction theory for \infty-categories |
" |
November 21, 2013, 3:00 - 5:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Dennis Gaitsgory (HARVARD UNIVERSITY) |
The work of Vincent Lafforgue on the Langlands conjecture for function fields **Repeat of Nov. 13 Number Theory Seminar** |
Several months ago Vincent Lafforgue settled the Automorphic=>Galois direction in the Langlands conjecture for functions fields. His approach uses the same geometric object as was used by Laurent Lafforgue (and earlier Drinfeld) for GL(n), namely, the moduli space of Shtukas. However, the way it is used is very different. In particular, automorphic representations appear naturally, rather than by comparing traces.  The main new idea that allows to see Galois representations arising from geometry is called excursion operators.  In the talk I ll try to give a rough outline of the ideas of this work. **This is a repeat of the talk I gave at the Number Theory Seminar on Nov. 13**Â" |
November 20, 2013, 2:00 - 3:00 PM at Science Center 232 |
| NUMBER THEORY SEMINAR |
Alexander Goncharov (YALE UNIVERSITY) |
Hodge symmetries |
The classical analogies between arithmetic and complex algebraic geometry tell that mixed Hodge structures are analogs of Galois representations. The Galois action in the l-adic cohomology is derived from the Galois action on the etale site. We suggest a Hodge analog: The role of the Galois group plays (the twistor subgroup of) the Tannakian Galois group of the category of real mixed Hodge structures. This group should act by A-infinity autoequivalences of the category of all holonomic D-modules. We will define such a homotopy action on the subcategory of smooth complexes. It boils down there to construction of certain complex numbers: Hodge correlators of irreducible local systems. The simplest of them turned out to be Rankin-Selberg integrals for special L-values. All of them are encoded as correlators of a certain Feynman integral" |
November 20, 2013, 3:00 - 4:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Diane Maclagan (WARWICK) |
The Cox ring of wonderful compactifications |
The wonderful model of a hyperplane arrangement complement Y is a smooth compactification of Y with normal crossing boundary introduced by DeConcini and Procesi. Examples include the blow-up of P^2 at any number of general points, and the moduli space \overline{M}_{0,n}. I will introduce these varieties, describe an invariant ring description of their Cox rings generalizing the Doran-Giansiracusa description for \overline{M}_{0,n}, and indicate how the Cox ring depends on the realization of the underlying matroid. This is joint work with Florian Block" |
November 19, 2013, 3:00 PM at Science Center 507 |
| HARVARD MATHEMATICS AND PHILOSOPHY LOGIC SEMINAR |
Alexander S. Kechris (CALIFORNIA INSTITUTE OF TECHNOLOGY) |
Topological dynamics and ergodic theory of automorphism of groups of countable structures |
This talk will discuss some aspects of the topological dynamics and ergodic theory of automorphism groups of countable first-order structures and their connections with logic, finite combinatorics and probability theory. This is joint work with Omer Angel and Russell Lyons" |
November 18, 2013, 5:30 - 6:30 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Shing-Tung Yau (HARVARD UNIVERSITY) |
150 Years of Mathematics at Harvard |
Recently, I have written a book on the history of the Mathematics Department of Harvard with my friend Steve Nadis, published by Harvard University Press. When the project started, I was chairman of the department. I was curious about the lives of the great founding fathers of our department. Some of them had changed the course of the development of mathematics, not only through their own research, but also through the students they taught. I thought it would be great if people in other places appreciated how these people worked and built this fine department, in the course of which they also helped to build Harvard University. I believe that the rise of the Harvard Mathematics department from a third-rate department to a world-class leader provides an important chapter that we can learn from. It may help many other universities who hope to build a world-class mathematics department" |
November 18, 2013, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Christoph Keller (RUTGERS UNIVERSITY) |
Conformal Field Theories, Modular Forms and Geometry |
Conformal field theories connect ideas from string theory, quantum field theory, modular forms and Calabi-Yau geometry. I will discuss conformal field theories in two dimensions coming from Calabi-Yau manifolds. Modular invariance allows us to investigate the spectrum of states of such theories. I will discuss how we can rule out classes of theories with large gaps in their spectrum. I will also discuss how such methods may help us understand if there are only finitely many topological types of Calabi-Yau 3-folds" |
November 15, 2013, 1:30 - 2:30 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Eli Grigsby (BOSTON COLLEGE) |
Braids and sutured annular Khovanov homology |
Sutured annular Khovanov homology is a variant of Khovanov homology, due to Asaeda-Przytycki-Sikora, which assigns a triply graded vector space to any link in the solid torus. I will explain why sutured annular Khovanov homology detects the trivial braid but cannot distinguish all pairs of non-conjugate braids. Time permitting, I will also explain why sutured annular Khovanov homology (with coefficients in C) admits the structure of a module over the (universal enveloping algebra of the) Lie algebra sl(2,C), and how this might be useful for understanding the different ways in which links can be realized as braid closures. Portions of this talk are joint with John Baldwin, and other portions are joint with Tony Licata and Stephan Wehrli" |
November 15, 2013, 3:30 - 4:30 PM at Science Center 507 |
| HARVARD, BRANDEIS, MIT, NORTHEASTERN JOINT COLLOQUIUM AT HARVARD |
Sucharit Sarkar (PRINCETON UNIVERSITY) |
Jones polynomial, Khovanov homology, and beyond |
We will start our story with the Jones polynomial, a revolutionary knot invariant introduced by V. Jones in 1984. We will then talk about Khovanov homology of knots, which is a categorification of the Jones polynomial constructed by M. Khovanov. Finally, we will discuss a recent stable homotopy level refinement of Khovanov homology, which is joint work with R. Lipshitz. Along the way, we will mention topological applications of these three knot invariants" |
November 14, 2013, 4:30 PM at Science Center Hall A |
| NUMBER THEORY SEMINAR |
Dennis Gaitsgory (HARVARD UNIVERSITY) |
The work of Vincent Lafforgue on the Langlands conjecture for function fields |
Several months ago Vincent Lafforgue settled the Automorphic=>Galois direction in the Langlands conjecture for functions fields. His approach uses the same geometric object as was used by Laurent Lafforgue (and earlier Drinfeld) for GL(n), namely, the moduli space of Shtukas. However, the way it is used is very different. In particular, automorphic representations appear naturally, rather than by comparing traces.  The main new idea that allows to see Galois representations arising from geometry is called excursion operators.  In the talk I ll try to give a rough outline of the ideas of this work.Â" |
November 13, 2013, 4:15 - 5:15 PM at Science Center Hall E |
| NUMBER THEORY SEMINAR |
Michael Harris (COLUMBIA UNIVERSITY) |
Special values of Rankin-Selberg tensor products for GL(n)xGL(m) |
This is a report on ongoing joint work with Harald Grobner. A cuspidal automorphic representation of GL(n) of cohomological type has two rational structures:  one defined by its cohomological realization and one defined by its Whittaker coefficients.  The ratio between these rational structures is a complex number called the Whittaker period.  We show that, under certain regularity hypotheses, the Whittaker period of a cuspidal cohomological â can be given a motivic interpretation, assuming â is obtained by base change from an automorphic representation Ï of a unitary group. The Whittaker period can also be related to a critical value of the adjoint L-function of Ï.  The resulting expressions for critical values of the Rankin-Selberg and adjoint L-functions are compatible with Deligne s conjecture" |
November 13, 2013, 3:00 - 4:00 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Martin Bridgeman (BOSTON COLLEGE) |
The pressure metric for convex Anosov representations |
" |
November 13, 2013, 4:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Nathan Pflueger (HARVARD UNIVERSITY) |
Brill-Noether theory in low codimension |
Brill-Noether theory studies the existence and deformations of curves in projective spaces; its basic object of study is W(g,r,d), the moduli space of smooth projective genus g curves with a choice of degree d line bundle having at least (r+1) independent global sections. The geometry of W(g,r,d) depends on the number Ï = g-(r+1)(g-d+r). The Brill-Noether theorem, proved by Griffiths and Harris, states that when Ï is nonnegative, the map from W(g,r,d) to M_g is surjective, and a general fiber has dimension Ï. One may naturally conjecture that for Ï<0, W(g,r,d) is finite over a locus of codimension -Ï in M_g. This conjecture fails, but seemingly only when -Ï is large compared to g. I discuss a proof that this conjecture holds for at least one component of W(g,r,d) in cases where 0 < -Ï < r/(r+2) g - 3r" |
November 12, 2013, 3:00 - 4:00 PM at Science Center 507 |
| HARVARD/MIT LOGIC SEMINAR |
Isaac Goldbring (UNIVERSITY OF ILLINOIS AT CHICAGO) |
A survey of the model theory of tracial von Neumann algebras |
Von Neumann algebras are certain algebras of bounded operators on Hilbert spaces. In this talk I will survey some of the model theoretic results about (tracial) von Neumann algebras, focusing mainly on (in)stability, quantifier-complexity, and decidability. No prior knowledge of von Neumann algebras will be necessary. Some of the work presented is joint with Ilijas Farah, Bradd Hart, David Sherman, and Thomas Sinclair." |
November 11, 2013, 4:30 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Jon Bloom (MIT) |
The monopole category and invariants of bordered 3-manifolds I |
Iâll discuss work-in-progress with John Baldwin toward constructing a gauge theoretic analogue of the Fukaya category and monopole Floer theoretic invariants of bordered 3-manifolds. In this talk, I ll describe the basic ideas that go into constructing this category" |
November 08, 2013, 2:15 - 3:15 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
John Baldwin (BOSTON COLLEGE) |
The monopole category and invariants of bordered 3-manifolds II |
Iâll pick up where Jon s talk left off, focusing on the more topological aspects of our construction. In particular, I ll describe a finite set of bordered handlebodies which generate our category. The morphism spaces for this generating set define a finitely generated A-infinity algebra. A bordered 3-manifold then gives rise to a module over this algebra, and a cobordism of bordered 3-manifolds defines a map of modules" |
November 08, 2013, 3:30 - 4:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Soren Galatius (STANFORD UNIVERSITY) |
The Brown-Peterson space BO/l_n |
" |
November 07, 2013, 3:00 - 5:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Jacob Tsimerman (HARVARD UNIVERSITY) |
The Geometry of the Frey-Mazur conjecture |
(Joint w/ B.Bakker) In his landmark paper on the isogeny character, Mazur asked whether for a large prime p, you could have two non-isogenous elliptic curves over Q with isomorphic galois representations on their p-torsion subgroups. This question can be rephrased as being about the existence of rational points on certain arithmetic surfaces. It is therefore natural, both for the function field analogue and the original question, to understand low genus curves on this surface. We explain how one can use hyperbolic methods to attack this question, in the same theme as earlier work of Nadel, Hwang, and To. Our main result is that for a quaternionic order R, and a complex curve C, there exists an integer N=N(R,C) such that if A_1,A_2,A_3 are families of abelian surfaces over C with an R-action, such that their p-torsion group schemes are isomorphic for a prime p>N, then at least 2 of them are isogenous" |
November 06, 2013, 3:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Kiran S. Kedlaya (UNIVERSITY OF CALIFORNIA AT SAN DIEGO) |
Locally analytic vectors from Galois representation: variations on Cherbonnier-Colmez |
The general formalism of p-adic Hodge theory provides a mechanism for converting p-adic Galois representations into representations of the Galois groups of certain p-adic Lie extensions. For instance, Fontaine s usual theory of (phi, Gamma)-modules does this for the Galois group of the p-cyclotomic tower, and the Cherbonnier-Colmez theorem produces an ample supply of locally analytic vectors inside the resulting representation; these are then used by Colmez to exhibit the p-adic Langlands correspondence for GL_2(Q_p). We describe some known and conjectural extensions of this work to other p-adic Lie extensions; this includes joint work with Ruochuan Liu and work in progress with Sarah Zerbes" |
November 06, 2013, 2:00 PM at Science Center Hall A |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Yusuf Mustopa (NORTHEASTERN UNIVERSITY) |
Ulrich Sheaves and Higher-Rank Brill-Noether Theory |
Ulrich sheaves, which are in a sense the nicest ACM sheaves, occur naturally in a wide variety of topics, ranging from Brauer groups to Boij-Soderberg theory. The question of whether a given subvariety of projective space admits an Ulrich sheaf is quite hard in general, and in the case of surfaces an affirmative answer usually solves a Brill-Noether problem for linear series on a special curve. In this talk, I will report on a result obtained jointly with Rajesh Kulkarni and Ian Shipman which shows that the existence of an Ulrich sheaf on a variety of any dimension is equivalent to the solution of a Brill-Noether problem for higher-rank vector bundles on special curves" |
November 05, 2013, 3:00 - 4:00 PM at Science Center 507 |
| JOINT BASIC NOTIONS AND INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Curt McMullen (HARVARD UNIVERSITY) |
The complex hyperbolic geometry of moduli space |
" |
November 04, 2013, 3:00 PM at Science Center 507 |
| SPECIAL EVENT |
Simon Singh () |
The Simpsons and Their Mathematical Secrets |
Author of the bestsellers Fermatâs Enigma, The Code Book and The Big Bang, Simon Singh will discuss his newest book, The Simpsons and Their Mathematical Secrets, which explores how the hit TV show âdrip-feeds morsels of number theory into the minds of its viewersââenough to form the basis of an entire university course" |
November 04, 2013, 7:00 PM at Science Center Hall A |
| THURSDAY SEMINAR |
Michael Andrews (MIT) |
An infinite family in the homotopy groups of spheres |
" |
October 31, 2013, 3:00 - 5:00 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Eriko Hironaka (ICERM AND FLORIDA STATE UNIVERSITY) |
Towards a fibered face theory for free group automorphisms. |
" |
October 30, 2013, 4:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Maarten Derickx (UNIVERSITY OF LEIDEN / UNIVERSITY OF BORDEAUX) |
Finding all points of degree < gonality on Y_1(N) |
Recently Mark van Hoeij and I computed the Q-gonality of the modular curve Y_1(N) for all N < 41. After this work Barry Mazur raised the question of whether there are very sporadic points on Y_1(N), i.e. points of degree < Q-gonality. In this talk I will sketch an approach that allows one to find all very sporadic points on Y_1(N) in certain cases, and report on the very sporadic points found using this approach" |
October 30, 2013, 3:00 - 4:00 PM at Science Center 507 |
| HARVARD/MIT LOGIC SEMINAR **NEW TIME & LOCATION** |
Spencer Breiner (CARNEGIE MELLON UNIVERSITY) |
A scheme construction for logic and model theory |
Although contemporary model theory has been called ``algebraic geometry minus fields , the formal methods of the two fields are radically different. In this talk I will present a theory of ``logical schemes, geometric entities which relate to first-order logical theories in much the same way that algebraic schemes relate to commutative rings. Recall that the affine scheme associated with a commutative ring $R$ consists of two components: a topological space $Spec(R)$ (the spectrum) and a sheaf of rings $\mathcal{O}_R$ (the structure sheaf). Moreover, the scheme satisfies two important properties: its stalks are local rings and its global sections are isomorphic to $R$. In this work we replace $R$ by a first-order logical theory $T$, regarded as a generalized algebraic structure, and then associate the theory with a topological spectrum $Spec(T)$ and a sheaf of theories $\mathcal{O}_T$ which satisfy similar local/global properties. The spectrum of $T$ is a topological \emph{groupoid} built from the semantics of the theory (i.e., $T$-models and isomorphisms); this is based on a construction of Butz \& Moerdijk. The structure sheaf $\mathcal{O}_T$ is then assembled from the Henkin extensions of $T$; the stalk of $\mathcal{O}_T$ over a $T$-model $M$ is the ``elementary diagram of $M$. These stalks satisfy a locality property corresponding to the logical existence and disjunction properties of the Henkin theories. These local theories inherit an action by the groupoid of isomorphisms and, up to a conservative extension $T\subseteq T^\text{eq}$, the isomorphism-stable sections of $\mathcal{O}_T$ recover the original theory. If time allows, I will discuss some constructions from algebraic geometry which generalize to logical schemes. This is joint work with Steve Awodey" |
October 29, 2013, 5:00 - 6:00 PM at Science Center 232 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Margarida Melo (COIMBRA) |
Comparing Toroidal compactifications |
Any polyhehdral decompostion of the cone of positive definite quadratic forms gives rise to a toroidal compactification of the moduli space of abelian varieties. The aim of this talk (based on joint work with Filippo Viviani, arXiv:1106.3291) is to compare two well-known such polyhedral decompositions: the perfect cone decomposition and the 2nd Voronoi decomposition. Using the theory of regular matroids, we determine which cones belong to both the decompositions, thus providing a positive answer to a conjecture of Alexeev and Brunyate. As an application, we compare the two associated toroidal compactifications, each of which has a special role in the geometry of the moduli space of abelian varieties" |
October 29, 2013, 3:00 - 4:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Ricardo Couso Santamaria (UNIVERSITY OF SANTIAGO DE COMPOSTELA) |
Resurgent transseries and the holomorphic anomaly |
Topological string theory is restricted enough to be solved completely in the perturbative sector, yet it is able to compute amplitudes in physical string theory and it also enjoys large N dualities. These gauge theory duals, sometimes in the form of matrix models, can be solved past perturbation theory by plugging transseries ansÀtze into the so called string equation. Based on the mathematics of resurgence, developed in the 80 s by J. Ecalle, this approach has been recently applied with tremendous success to matrix models and their double scaling limits (Painlevé I, etc). A natural question is if something similar can be done directly in the topological closed string sector. In this seminar I will show how the holomorphic anomaly equations of BCOV provide the starting point to derive a master equation which can be solved with a transseries ansatz. I will review the perturbative sector of the solutions, its structure, and how it generalizes for higher instanton nonperturbative sectors. Resurgence, in the guise of large order behavior of the perturbative sector, will be used to derive the holomorphicity of the instanton actions that control the asymptotics of the perturbative sector, and also to fix the holomorphic ambiguities in some cases. The example of local CP^2 will be used to illustrate these results. This work is based on 1308.1695 and on-going research in collaboration with J.D. Edelstein, R. Schiappa and M. Vonk" |
October 29, 2013, 1:30 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Filippo Viviani (ROMA TRE) |
Tropicalizing vs Compactifying the Torelli Map |
We will explain the relationship between the compactified Torelli map (as defined by V. Alexeev) and the tropical Torelli map (as defined by the author in a joint work with S. Brannetti and M. Melo, and furthered studied by M. Chan). This comparison will shed some light on the analogy between the descriptions of the fibers of the two maps, obtained by the author in joint works with L. Caporaso." |
October 29, 2013, 4:00 - 5:00 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Ke Zhu (HARVARD UNIVERSITY) |
Isometric embedding of Riemannian manifolds via the heat kernel |
It was Nash who established the isometric embedding of Riemannian manifolds into Euclidean spaces. However, little can be said about the geometry of the embedding. We produce somewhat canonical isometric embeddings of compact Riemannian manifolds into Euclidean spaces by the heat kernel embedding and GĂŒnther s implicit function theorem. As the heat flow time t->0, the second fundamental form of the embedded images has certain normal form, the mean curvature vectors converge to (large) constant length, and the embeddings satisfy certain universal high-jet relations. These embeddings are canonical in the sense that they are constructed by the eigenfunctions of the Laplacian and intrinsic perturbatio" |
October 25, 2013, 3:30 - 4:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Mark Behrens (MIT) |
bo resolutions |
" |
October 24, 2013, 3:00 - 5:00 PM at Science Center 07 |
| NUMBER THEORY SEMINAR |
Matthew Emerton (UNIVERSITY OF CHICAGO) |
Local-global compatibility in the p-adic Langlands program |
I will describe some recent developments in the p-adic Langlands program, related to the problem of constructing a p-adic Langlands correspondence which satisfies an appropriate form of local-global compatibility. Much of the talk will be based on joint work with Ana Caraiani, Toby Gee, David Geraghty, Vytas Paskunas, and Sug Woo Shin, and also on joint work with Toby Gee and David Savitt" |
October 23, 2013, 3:00 - 4:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Alina Marian (NORTHEASTERN UNIVERSITY) |
The Chern classes of the Verlinde bundles |
The Verlinde bundles are natural vector bundles over the moduli space of curves, associated with theta divisors in relative moduli spaces of sheaves over M_g. Their rank is given by the well-studied Verlinde numbers. I will explain a formula for their entire Chern character, derived jointly with Dragos Oprea and Rahul Pandharipande" |
October 22, 2013, 3:00 PM at Science Center 507 |
| HARVARD/MIT LOGIC SEMINAR |
Cameron Donnay Hill (WESLEYAN UNIVERSITY) |
On Filters in Fraïssé Classes |
I will make several observations about a certain very natural filter on the age of a FraĂŻssĂ© limit. In par- ticular, I will show that several possible properties of classes of finite structures â e.g. zero-one laws and the (algebraic) finite sub-model property â are characterized by the existence of certain extensions of this filter. Time permitting, I will also sketch out some applications in recovering geometry/dimension theory in Ramsey classes and Zero-One classes" |
October 22, 2013, 4:30 - 5:30 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Hiro Tanaka (HARVARD UNIVERSITY) |
Factorization homology and link invariants |
Homology is easy to compute thanks to excision, but isn t very sensitive: If two spaces are homotopy equivalent, but they aren t homeomorphic, homology can t see the difference. In this talk I d like to give one answer to the question: Is there a notion of homology theory for manifolds that s sensitive to more? I will present the definition of factorization homology, which Lurie has also called topological chiral homology. Factorization homology generalizes usual Eilenberg-Steenrod homology, and is expected to be sensitive to more than just the homotopy type of manifolds. The main result will be a classification of all homology theories, namely by giving an equivalence between the category of homology theories and the category of certain kinds of algebras. I will explain how the theorem in turn gives candidates for new sources of invariants of embedding spaces (and in particular, link invariants). If time allows, I can discuss connections to topological field theories, and to Koszul duality. This is joint work with David Ayala and John Francis" |
October 21, 2013, 3:00 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Cliff Taubes (HARVARD UNIVERSITY) |
Extensions of Uhlenbeck's compactness theorem for SL(2;C) connections in dimensions 3 and 4 |
" |
October 18, 2013, 3:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
Brown-Gitler spectra and E_2 algebras |
" |
October 17, 2013, 3:00 - 5:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Igor Rapinchuk (HARVARD UNIVERSITY) |
On Division Algebras with the same maximal subfields |
In this talk, I will address the following question: Let D and T be central division algebras over a field K. When does the fact that D and T have the same maximal subfields imply that D and T are actually isomorphic over K? I will discuss various motivations for this question and some recent results. Time permitting, I will also indicate some variations of this question and its generalizations to algebraic groups. This is joint work with V. Chernousov and A. Rapinchuk." |
October 16, 2013, 3:00 - 4:00 PM at Science Center 507 |
| HARVARD/MIT LOGIC SEMINAR |
Paul Christiano (UC BERKELEY) |
Probabilistic metamathematics and the definability of truth |
No model M of a sufficiently expressive theory can contain a truth predicate T such that for all S, we have M |= T (Sâ) if and only if M |= S. Iâll consider the setting of probabilistic logic, and show that there are probability distributions over models which contain an objective probability function P such that M |= a < P (Sâ) < b almost surely whenever a < P (M |= S) < b. This demonstrates that a probabilistic analog of a truth predicate is possible as long as we allow infinitesimal imprecision. Iâll argue that this result significantly undercuts the philosophical significance of Tarskiâs undefinability theorem, and show how the techniques involved might be applied more broadly to resolve obstructions due to self-reference" |
October 15, 2013, 4:30 - 5:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Brown-Gitler spectra via Dieudonne theory III |
" |
October 10, 2013, 3:00 - 5:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Stefan Patrikis (HARVARD UNIVERSITY / MIT) |
Potential automorphy of regular self-dual motives |
I will describe joint work with Richard Taylor showing that the potential automorphy theorems of Barnet-Lamb, Gee, Geraghty, and Taylor continue to hold with purity hypotheses in place of the usual irreducibility hypotheses. A similar argument yields new results toward `cuspidality implies irreducibility. I will illustrate the potential automorphy theorem by exhibiting many families of regular motives whose L-functions can then be shown to admit meromorphic continuations" |
October 09, 2013, 3:00 - 4:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Ken Ono (EMORY UNIVERSITY) |
Special functions and numbers related to mock modular forms |
Mock modular forms are presently finding new roles all over mathematics. This lecture will include two topics: 1) Freeman Dyson s mock modular form, classical Klein forms, and Zagier s quantum modular forms. 2) Arithmetic of mock modular forms arising from the modularity of elliptic curves" |
October 09, 2013, 4:30 PM at Science Center, Hall E |
| THE HARVARD DEPT OF MATHEMATICS PRESENTS A SPECIAL SCREENING OF |
The Genius of Srinivasa Ramanujan () |
|
A moving one-hour documentary by Nandan Kudhyadi examining the life and legacy of the self-taught Indian number theorist who rose from obscurity to influence the course of modern mathematics. Featuring interviews with prominent mathematicians and footage filmed in locations pivotal to his romantic stor" |
October 09, 2013, 7:30 PM at Science Center Hall C |
| HARVARD MATHEMATICS AND PHILOSOPHY LOGIC COLLOQUIUM |
Rahim Moosa (UNIVERSITY OF WATERLOO) |
The Canonical Base Property and the Zilber Dichotomy Revisited |
The truth of the Zilber dichotomy in several first-order theories of fields with additional operators was behind Hrushovski s dramatic application of model theory to diophantine geometry in the nineties. About ten years ago, abstracting from a theorem in complex-analytic geometry, Pillay introduced a new model-theoretic condition now called the canonical base property (CBP). This condition provides a direct proof of the Zilber dichotomy in various contexts, and has other strong geometric consequences. What seems to be required in establishing the CBP in any given situation is an appropriate notion of" |
October 08, 2013, 4:30 - 5:30 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Amnon Yekutieli (BEN GURION UNIVERSITY) |
Residues and Duality for Schemes and Stacks |
Let K be a regular noetherian commutative ring. I will begin by explaining the theory of rigid residue complexes over essentially finite type K-algebras, that was developed by J. Zhang and myself several years ago. Then I will talk about the geometrization of this theory: rigid residue complexes over finite type K-schemes. An important feature is that the rigid residue complex over a scheme X is a quasi-coherent sheaf in the etale topology of X. For any map f : X â Y between K-schemes there is the ind-rigid trace homomorphism (that usually does not commute with the differentials). When the map f is proper, the ind-rigid trace does commute with the differentials (this is the Residue Theorem), and it induces Grothendieck Duality. Then I will move to finite type Deligne-Mumford K-stacks. Any such stack X has a rigid residue complex on it, and for any map f : X â Y between stacks there is the ind-rigid trace homomorphism. These facts are rather easy consequences of the corresponding facts for schemes, together with etale descent. I will finish with the Residue Theorem, which holds when the map f : X â Y is proper and coarsely schematic; and the Duality Theorem, which also requires the map f to be tame. If there is time I will outline the proofs. Lecture notes are at http://www.math.bgu.ac.il/~amyekut/lectures/resid-stacks/notes.pd" |
October 08, 2013, 3:00 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Siu-Cheong Lau (HARVARD UNIVERSITY) |
Cayley Graph and Mirror Symmetry |
I will talk about a specific class of geometries, namely spheres with three orbifold points, where mirror symmetry can be geometrically explained by counting polygons in a tessellation and elementary graph theory. This is a part of the generalized SYZ program that I am currently working on. The essential outcome is a categorical functor which derives homological mirror symmetry" |
October 04, 2013, 3:30 - 4:30 PM at Science Center 507 |
| TRIVIAL NOTIONS SEMINAR |
Francesco Cavazzani (HARVARD UNIVERSITY) |
ADE Singularities and Slodowy Slices |
" |
October 03, 2013, 1:00 - 2:00 PM at Science Center 507 |
| THURSDAY SEMINAR |
Vesna Stojanoska (MIT) |
Dual Brown-Gitler spectra via realizability of unstable modules over the Steenrod algebra |
" |
October 03, 2013, 3:00 - 5:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Keerthi Madapusi (HARVARD UNIVERSITY) |
The irreducibility of the moduli of polarized K3 surfaces |
We show that the moduli of polarized K3 surfaces of fixed degree is irreducible in characteristic p>2. The key idea is to exhibit p-Hecke correspondences between the ordinary loci of moduli spaces of different degrees and so reduce to the case where the degree is not too divisible by p. For the construction of these correspondences, we make crucial use of the Kuga-Satake correspondence in characteristic p" |
October 02, 2013, 3:00 - 4:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Montserrat Teixidor I Bigas (TUFTS UNIVERSITY) |
Vector bundles with fixed determinant and sections |
Brill-Noether Theory for line bundles has been the main tool for studying Jacobians and moduli spaces of curves. A similar theory can be formulated for vector bundles of higher rank but it is a lot less well behaved. As in the case of line bundles, degeneration techniques can be used to study what happens on the generic curve. I will present some of these techniques and look at how special determinants help explain some of the cases of bad behavior" |
October 01, 2013, 3:00 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Artin Reciprocity via Algebraic K-Theory |
Let K be a number field, let A denote the ring of adeles of K, and let Gal(K) denote the absolute Galois group of K. One of the main results of class field theory asserts the existence of a surjective group homomorphism (the Artin map) from A^* / K^* to the abelianization of Gal(K). In this talk, I will describe recent work of my former student Dustin Clausen, giving a direct construction of the Artin map using ideas from algebraic topology" |
September 30, 2013, 3:00 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Goncalo Oliveira (IMPERIAL COLLEGE) |
Monopoles in Higher Dimensions |
The Monopole (Bogomolnyi) equations are Geometric PDEs in 3 dimensions. In this talk I shall introduce a generalization of the monopole equations to both Calabi Yau and G_2 manifolds. I will motivate the possible relations of conjectural enumerative theories arising from counting monopoles and calibrated cycles of codimension 3. Then, I plan to state the existence of solutions and sketch how these examples are constructed" |
September 27, 2013, 3:30 - 4:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Brown-Gitler spectra via Dieudonne theory II |
" |
September 26, 2013, 3:00 at Sci Center 507 |
| TRIVIAL NOTIONS SEMINAR |
Justin Campbell (HARVARD UNIVERSITY) |
Geometric class field theory after Deligne |
Let X be a smooth projective curve over a finite field. Geometric class field theory classifies abelian covers of X: for example, pulling back the Lang isogeny of the Jacobian of X along an Abel-Jacobi map gives such a cover. In the 1950s Lang and Rosenlicht proved that all unramified abelian covers of X can be obtained from these in a simple way, then around 1974 Deligne found a streamlined proof of this result using l-adic local systems. I will explain Deligne s proof, giving necessary background along the way" |
September 26, 2013, 1:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Arul Shankar (HARVARD UNIVERSITY) |
The average 5-Selmer rank of elliptic curves |
We will compute the average size of the 5-Selmer group of elliptic curves ordered by height, using geometry-of-numbers techniques. We will then see how this result can be used to show that the average rank of elliptic curves is less than 1. This is joint work with Manjul Bhargava" |
September 25, 2013, 3:00 - 4:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Hossein Movasati (IMPA) |
A kind of modular form theory for Calabi-Yau varieties |
Physics literature, and in particular mirror symmetry, gives us many q-expansions which in particular cases are classical (quasi) modular forms but in general they do not belong to the category of automorphic functions. In this talk I will describe the construction of a certain algebra attached to a family of Calabi-Yau varieties which in the particular case of elliptic curves,  it is  the algebra of full (quasi) modular forms. The elements of this algebra have many common features with the algebra of full (quasi) modular forms. The integrality of coefficients, relation with periods and Gauss-Manin connection, the Ramanujan differential equation and etc. are among them. There are also many differences. For instance, strange functional equations, being of transcendental degree seven appearance of two essentially different cusps, the lack of Hecke operators, etc" |
September 24, 2013, 1:30 - 3:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Matthew Woolf (HARVARD UNIVERSITY) |
Effective and Nef Divisors on Moduli Spaces of One-Dimensional Sheaves on the Projective Plane |
The moduli space of one-dimensional sheaves of degree d and Euler characteristic Ï is a fairly natural compactification of the relative Jacobian of lines bundles of Euler characteristic Ï supported on a smooth plane curve of degree d. I will talk about the cones of effective and nef divisors on these moduli spaces. I will mention some of the methods which go into this work, including the theory of interpolation for vector bundles and the theory of Bridgeland stability conditions. I will also show how the study of these cones allows one to determine precisely when two of these moduli spaces are isomorphic" |
September 24, 2013, 3:00 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Joe Harris (HARVARD UNIVERSITY) |
How flexible are curves in projective space? |
" |
September 23, 2013, 3:00 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Daniel Ruberman (BRANDEIS UNIVERSITY) |
Embeddings of non-orientable surfaces in M x I |
We use the correction terms from Heegaard Floer homology and classical signature obstructions to obtain obstructions to embedding closed, non-orientable surfaces in 3- and 4-dimensional manifolds, focusing on embeddings in a lens space or the product of a lens space and an interval. For instance, we show that if a surface embeds nontrivially in L(p, q) x I, then it must also embed in L(p, q). This is joint work with Adam Levine and Saso Strle" |
September 20, 2013, 3:30 - 4:30 PM at Science Center 507 |
| TRIVIAL NOTIONS SEMINAR |
Eric Riedl (HARVARD UNIVERSITY) |
Complete Families of Smooth Curves |
Moduli spaces are a fundamental concept in algebraic geometry, and they continue to be critical in many active areas of research. It is a surprising fact that even algebraic geometers who mostly care about smooth varieties often find singular objects arising naturally in their moduli spaces. This talk will explore an example of that principle. First, I will talk about what a moduli space is in general. Then I will describe a result of Chang and Ran showing that in P^n, a complete family of smooth, generically non-degenerate curves has dimension at most n-1" |
September 19, 2013, 1:00 PM at Science Center 507 |
| THURSDAY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
Brown-Gitler spectra via Dieudonne theory |
" |
September 19, 2013, 3:00 - 5:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Alex Kontorovich (YALE UNIVERSITY) |
Local-Global Principles in Orbits |
We will discuss some natural problems in arithmetic which can be (re)formulated as local-global principles for orbits of certain thin semigroups of integer matrix groups. Applications include partial progress towards Zaremba s conjecture and McMullen s Arithmetic Chaos Conjecture on the ubiquity of low-lying closed geodesics on the modular surface defined over a given number field. The main tools are expander graphs, bilinear forms, and bounds for exponential sums. This is joint work with Jean Bourgain" |
September 18, 2013, 3:00 - 4:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Maksym Fedorchuk (BOSTON COLLEGE) |
Toward GIT stability of syzygies of canonical curves |
I will discuss a Geometric Invariant Theory problem concerning stability of Hilbert and Syzygy points of canonical curves, and explain its solution for the first syzygy point in the generic case (joint with Deopurkar and Swinarski). I will also give motivation and explain applications of this result coming from the minimal model program for the moduli space of curves" |
September 17, 2013, 3:00 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Alex Kontorovich (YALE UNIVERSITY) |
Levels of Distribution |
This will be survey of what a level of distribution means in sieve theory. Time permitting we will discuss some aspects of the work by Yitang Zhang" |
September 16, 2013, 3:00 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Hiro Tanaka (HARVARD UNIVERSITY) |
Lagrangian Cobordisms, Partially Wrapped Fukaya Categories, and a Functor Between Them |
For every symplectic manifold M (equipped with usual Fukaya-categorical set-up), David Nadler and I have defined a category called Lag(M), whose objects are Lagrangian branes, and whose morphisms are certain kinds of cobordisms between branes. (Such categories have also gained interest through the concurrent work of Biran and Cornea.) Nadler and I have conjectured a few relationships between Lag(M) and the partially wrapped Fukaya category of M, and in this talk I ll exhibit a functor between the two. The functor requires an assumption that the analysis of the partially wrapped Fukaya category can be set up, and a conjectural pairing between partially wrapped and infinitesimally wrapped worlds exists. The functor gives us a new result, which says that if two compact branes are cobordant via a compact brane, then they are equivalent in the Fukaya category" |
September 13, 2013, 3:30 - 4:30 PM at Science Center 507 |
| TRIVIAL NOTIONS SEMINAR |
Tom Lovering (HARVARD UNIVERSITY) |
L-functions, Selmer Groups, and Modular Forms |
Since Kummer s striking discovery in 1850 of a relationship between primes dividing Bernoulli numbers and the existence of nontrivial ideal classes in cyclotomic fields, the mysterious relationship between special values of L-functions and Selmer groups has been at the heart of algebraic number theory. In this talk we will review the classical work of Ribet on the ``Converse to Herbrand s Theorem , which uses congruences between modular forms and their Galois representations to give a (relatively) explicit construction Kummer s ideal classes. If we have time we then hope to talk a little about Iwasawa s more refined ``main conjecture (which became a theorem of Mazur-Wiles), and perhaps hint at some of the exciting current work of Skinner-Urban relating more general L-functions and Selmer groups" |
September 12, 2013, 1:00 - 2:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Mark Kisin (HARVARD UNIVERSITY) |
Endomorphisms of abelian varieties and CM liftings |
The classification of abelian varieties over finite fields relies on Tate s theorem on endomorphisms of abelian varieties and Tate-Honda theory which implies that every abelian variety is isogenous to one which has a CM lifting. We will discuss the analogues of these theorems for abelian varieties equipped with a collection of Hodge cycles, and their implication for the structure of the mod p points on a Shimura variety" |
September 11, 2013, 3:00 - 4:00 PM at Science Center 507 |
| SPECIAL SEMINAR |
Yi Tang Zhang (UNIVERSITY OF NEW HAMPSHIRE) |
Bounded gaps between primes |
The speaker proves that there are infinite number of pairs of primes whose difference is bounded by 70 million" |
May 13, 2013, 3:00pm at Science Center 507 |
| HARVARD, BRANDEIS, M.I.T., NORTHEASTERN COLLOQUIUM AT HARVARD |
Mladen Bestvina (THE UNIVERSITY OF UTAH) |
The geometry of Out(F_n) |
The geometry of mapping class groups is very well understood thanks to the work of Masur, Minsky and others. The last couple of years have seen progress in a similar understanding of Out(F_n), the group of outer automorphisms of a free group. In the talk I will review the situation for both groups and point out some of the remaining challenges for Out(F_n)" |
May 09, 2013, 4:30pm at Science Center Hall A |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
David Dumas (UNIVERSITY OF ILLINOIS AT CHICAGO) |
Convex polygons, complex polynomals, and hyperbolic affine spheres |
We describe joint work with Michael Wolf which gives a natural identification between the space of convex polygons in the real projective plane (up to projective transformations) and the space of polynomial holomorphic cubic differentials on the complex plane (up to complex affine transformations). This map arises from a construction in affine differential geometry, and is an analogue for the complex plane of the parameterization by Labourie and Loftin of the space of convex real projective structures on a compact surface by the bundle of cubic differentials over Teichmueller space." |
May 08, 2013, 4:00 PM at Sci Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Daniel Cristofaro-Gardiner (BERKELEY) |
Volume in Seiberg-Witten theory and the asymptotics of embedded contact homology (ECH) capacities |
Abstract: The ECH capacities are a sequence of nonnegative real numbers associated to any symplectic four-manifold that are monotone under symplectic embeddings. I will present recent joint work with M. Hutchings and V. Gripp showing that for any four-dimensional Liouville domain with all ECH capacities finite, these capacities naturally recover the classical symplectic volume in their asymptotic limit. Our proof uses C. Taubes isomorphism between embedded contact homology and Seiberg-Witten Floer cohomology. --Organized by Prof. ST Ya" |
May 06, 2013, 10:00am at Science Center 507 |
| HARVARD/MIT LOGIC SEMINAR |
James Freitag (UNIVERSITY OF CALIFORNIA, BERKELEY) |
Completeness for differential algebraic varieties |
We will discuss the completeness problem for differential algebraic varieties and the partial answers which are known. We will show how the notion can be used to generalize and relate various problems regarding linear independence and generalized Wronskians in differential fields" |
May 06, 2013, 4:30pm at Science Center 507 |
| PROBABILITY SEMINAR |
Dan Stroock (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
Determinants of Green's Functions with Applications to Counting Spanning Trees and Other Things |
" |
May 03, 2013, 1:30 PM at Sci Center 232 |
| PROBABILITY SEMINAR |
Jean-Francois Le Gall (UNIVERSITY OF PARIS -SUD XI ORSAY) |
The harmonic measure of critical Galton-Watson trees |
We consider simple random walk on a critical Galton-Watson tree conditioned to have height greater than n. It is well known that the cardinality of the set of vertices of the tree at generation n is then of order n. We prove the existence of a constant b < 1 such that the hitting distribution of the generation n in the tree by random walk is concentrated with high probability on a set of cardinality approximately equal to n^b . In terms of the analogous continuous model, the dimension of harmonic measure on a level set of the tree is equal to b, whereas the dimension of any level set is equal to 1. The constant b is approximately equal to 0.78 and can be expressed in terms of the asymptotic distribution of the conductance of large critical Galton-Watson trees. This talk is based on joint work with Nicolas Curien" |
May 02, 2013, 3:00 - 4:00 PM at Science Center 232 |
| SPECIAL SEMINAR |
Nils Carqueville (SIMONS CENTER FOR GEOMETRY & PHYSICS, STONY BROOK) |
Orbifold completion of kernel bicategories |
Motivated by topological quantum field theory, one can start from any pivotal bicategory B (i.e. a certain type of 2-category) and construct its orbifold completion B_orb in terms of Frobenius algebras. The completion satisfies the natural properties B \subset B_orb and (B_orb)_orb = B_orb, and it gives rise to various new equivalences and nondegeneracy results. I will explain this construction (which is joint work with Ingo Runkel) along with the necessary algebraic background, and then apply it to the bicategory of Landau-Ginzburg models. Applications include a unified perspective on ordinary equivariant matrix factorisations, a one-line proof of a cousin of the Hirzebruch-Riemann-Roch theorem, and new equivalences for simple singularities. --Organized by Professor Shing-Tung Ya" |
May 01, 2013, 4:15 PM at Science Center 232 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
Charles Smart (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
The Abelian sandpile and Apollonian circle packings |
I will discuss the connection between the Abelian sandpile and Apollonian circle packings discovered in joint work with Lionel Levine and Wesley Pegden. The Abelian sandpile is a deterministic diffusion process on configurations of chips on finite graphs devised by Bak, Tang, and Weisenfeld in 1987. It was recently observed that the Abelian sandpile dynamics has a continuum scaling limit on a large class of graphs -- and this limit is capture by a certain nonlinear elliptic partial differential equation. When the underlying graph is the two-dimensional integer lattice, this PDE has the structure of an Apollonian circle packing. I will discuss the proof of this result and a few additional interesting connections." |
May 01, 2013, 4:00 PM at Sci Center 507 |
| HARVARD/MIT LOGIC SEMINAR |
Haim Gaifman (COLUMBIA UNIVERSITY) |
Epistemic and Ontological Problems Concerning Mathematics |
Philosophy of mathematics is confronted with two major questions: (i) How do we come to know mathematical propositions? (ii) What is the nature of mathematical truth? Attempts to give satisfactory answers to one of the questions have resulted in unsatisfactory accounts regarding the other. I shall outline an approach intended to do justice to both questions. This is an ongoing work" |
April 30, 2013, 4:15 PM at Fong Auditorium (Boylston Hall 110) |
| DIFFERENTIAL GEOMETRY SEMINAR |
Bong Lian (BRANDEIS UNIVERSITY) |
CY bundles on a compact Kaehler manifold |
I will review the notion of a CY bundle (introduced earlier by Yau and me) and its motivations. The notion plays an important role in our recent study on period integrals of CY and general type complete intersections in a complex manifold. I will discuss a construction of a CY bundle for any compact Kaehler manifold. This talk is based on my recent joint work with my student Jingyue Chen. --Organized by Professor S.T. Yau" |
April 30, 2013, 4:15 PM at Science Center 507 |
| JOINT HARVARD/MIT PROBABILITY AFTERNOON: RANDOM MATRICES, RANDOM GEOMETRY |
Nikolai Makarov (CALIFORNIA INSTITUTE OF TECHNOLOGY) |
The support of the equilibrium measure in the random normal matrix model |
" |
April 26, 2013, 3:30 PM at Science Center 309 |
| JOINT HARVARD/MIT PROBABILITY AFTERNOON: RANDOM MATRICES, RANDOM GEOMETRY |
Mark Rudelson (MICHIGAN) |
|
" |
April 26, 2013, 2:30 PM at Science Center 309 |
| JOINT HARVARD/MIT PROBABILITY AFTERNOON: RANDOM MATRICES, RANDOM GEOMETRY |
Jean-François Le Gall (UNIVERSITY OF PARIS -SUD XI ORSAY) |
The Brownian map: A universal model of random geometry |
" |
April 26, 2013, 5:00 PM at Science Center 309 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Tye Lidman (UNIVERSITY OF TEXAS - AUSTIN) |
Monopole Floer homology and covering spaces |
We will show that under certain conditions, monopole Floer homology behaves nicely under covers. Along the way, we establish an isomorphism between monopole Floer homology and the singular homology of Manolescu s Seiberg-Witten Floer spectrum. This is work in progress with Ciprian Manolescu" |
April 26, 2013, 4:00 - 5:00 PM at Science Center 507 |
| PROBABILITY SEMINAR |
Nikolai Makarov (CAL TECH) |
Random normal matrices and Ward indentities |
I will review the method of Ward identities in the context of random normal matrix model. In particular, I will focus on the distribution of eigenvalues near boundary of the support of the equilibrium measure. (Joint work with Y. Ameur and H. Hedenmalm, and with Y. Ameur and N.-G. Kang" |
April 25, 2013, 3:00 at Science Center 232 |
| APPLIED MECHANICS COLLOQUIA |
David Mumford (BROWN UNIVERSITY) |
Winston Chen Lecture: Mathematizing "Shape," from Durer to MRIs |
Describing shape and comparing two shapes are problems that have been studied for a long time by painters and biologists. A mathematicians approach proposed by Riemann is to make a space out of all shapes (e.g. all simple closed plane curves) and to study the geometry of this space. Arnold was the first to compute geodesics and curvature on one such space. More recently his ideas have been extended and applied to analysis of medical images. A zoo of different properties is emerging. I will describe some of the results of this program and connect it with an ancient Chinese map" |
April 24, 2013, 4:00 - 5:00pm at Maxwell Dworkin G115 |
| SPECIAL SEMINAR |
Lydia Bieri (UNIVERSITY OF MICHIGAN) |
From Spacetime Geometry to Gravitational Waves |
Spacetime geometries arising from the Einstein equations coupled to various fields in General Relativity (GR) will be investigated. Foliations of the spacetimes into null hypersurfaces play a crucial role in the discussion. Results on their structure and asymptotic behavior yield insight into gravitational waves. The latter are predicted by the theory of GR and are of major interest in mathematical GR and astrophysics, where we want to describe and finally observe them. D. Christodoulou derived the nonlinear memory effect for gravitational waves displacing test masses permanently. In this talk, we focus on the geometric structure of solutions of the Einstein equations coupled to a null fluid describing a neutrino burst of a typical source of gravitational waves. We then compare this to the case of the Einstein-Maxwell equations. Christodoulou memory will be discussed in these situations. I will present joint work with P. Chen, S.-T. Yau and with D. Garfinkle. --Organized by Professor Shing-Tung Ya" |
April 24, 2013, 2:00 PM at Science Center 232 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
Giulio Tiozzo (HARVARD UNIVERSITY) |
Entropy, dimension and combinatorial moduli for one-dimensional dynamical systems |
We provide a unified framework in which to analyze the dynamics of two seemingly unrelated families of one-dimensional dynamical systems, namely the family of quadratic polynomials and continued fractions. We develop a combinatorial calculus to describe the bifurcation set of both families and prove they are isomorphic. As a corollary, we establish a series of results describing the behavior of entropy as a function of the parameter. One of the most important applications is the relation between the topological entropy of quadratic polynomials and the Hausdorff dimension of sets of external rays landing on veins of the Mandelbrot set" |
April 24, 2013, 3:00PM at Science Center, Hall E |
| NUMBER THEORY SEMINAR |
Yifeng Liu (MIT) |
On refined Gan-Gross-Prasad conjecture for Bessel periods |
In this talk, I will propose a refined version of the global Gan-Gross-Prasad conjecture on the restriction of automorphic representations for classical groups, that is, an explicit formula calculating certain period integrals of Bessel type for an arbitrary pair of orthogonal or unitary groups. This generalizes the work of Ichino and Ikeda in the co-rank 1 case. Moreover, I will provide two new examples supporting such conjecture for the pairs SO(5) x SO(2) and SO(6) x SO(3) using theta lifting, where in particular, the restricted group is neither reductive nor unipotent" |
April 24, 2013, 3:00 pm at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Po-Ning Chen (COLUMBIA UNIVERSITY) |
Minimizing quasi-local mass in general activity |
In this talk, we will discuss some recent joint work with Mu-Tao Wang and Shing-Tung Yau on quasi-local mass in general relativity. In particular, we will discuss the question about finding the isometric embedding that minimizes quasi-local energy for a given surface in a space-time. --Organized by Professor Shing-Tung Ya" |
April 23, 2013, 4:15 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Richard Melrose (MIT) |
Fusion, Loop-Spin and String structures |
There is a Whitehead tower of successive refinements of the structure group of the tangent bundle of a manifold -- orientation, spin and string -- with successive obstructions. String structures are difficult to deal with analytically and work of Witten and others, in the 1980s, indicates that it should be more fruitful to analyse the corresponding transgressed structure over the loop space, loop-orientation for spin and loop-spin for string, and ultimately do analysis (of the Dirac-Ramond operator) there. At a topological level transgression is not in general an isomorphism but this `defect can be repaired, at least in these cases, by adding a fusion condition introduced by Stolz and Teichner. I will describe this and recent work, including that of Redden, Waldorf and ongoing work with Chris Kottke, leading to an equivalence between fusive loop-spin structures and string structures" |
April 22, 2013, 3:00 PM at Science Center 507 |
| LOGIC SEMINAR |
Olivia Caramello (UNIVERSITY OF CAMBRIDGE) |
Fraisse's construction from a topos-theoretic perspective |
We present a topos-theoretic interpretation of (a categorical generalization of) Fraisse s construction in Model Theory, with applications to countably categorical theories. The proof of our main theorem represents an illustration of the role of Grothendieck toposes as bridges for translating properties and results across different mathematical theories; specifically, the three concepts involved in the classical Fraisse s construction (i.e., amalgamation and joint embedding properties, homogeneousness, atomicity) are seen to correspond precisely to three different ways (resp. of geometric, semantic and syntactic nature) of looking at the same classifying topos." |
April 22, 2013, 4:30 PM at Sci Center 507 |
| GAUGE THEORY & TOPOLOGY |
Eli Grigsby (BOSTON COLLEGE, TUFTS UNIVERSITY, HARVARD UNIVERSITY, BRANDIES UNIVERSITY, AND TUFTS UNIVERSITY) |
Categorified invariants and the braid group |
I will describe what various categorified invariants can and cannot tell us about the word and conjugacy problems in the braid group. Parts of this talk describe joint work with D. Auroux and S. Wehrli, and other parts describe joint work with J. Baldwin." |
April 19, 2013, 3:30-4:30 PM at Sci Center 507 |
| HARVARD/MIT LOGIC SEMINAR |
Johanna Franklin (UNIVERSITY OF CONNECTICUT) |
Strongly prompt sets and weak Demuth randomness |
Randomness notions stronger than Martin-Loef randomness can often be described in terms of computational strength. For instance, Downey, Nies, Weber, and Yu showed that the weakly 2-random sequences are precisely the Martin-Loef random sequences that cannot compute any nonrecursive r.e. set, and Ng and I showed that the difference random sequences are precisely the Turing incomplete Martin-Loef random sequences. More recently, Ng and I have characterized the weakly Demuth random sequences as the Martin-Loef random sequences that cannot compute a strongly prompt r.e. set. I ll discuss this result and its consequences and present some open questions in this area" |
April 18, 2013, 4:30 PM at Science Center 310 |
| PROBABILITY SEMINAR |
Mihai Stoiciu (WILLIAMS COLLEGE) |
Transition in the Microscopic Eigenvalue Distribution for Random and Deterministic Unitary Operators |
We consider several classes of random and deterministic unitary operators and investigate their microscopic eigenvalue distribution. We show that these operators exhibit a transition in their microscopic eigenvalue distribution, depending on the properties of the corresponding spectral measures (we investigate random measures and measures associated to hyperbolic reflection groups). In the case of pure point spectral measures, the microscopic eigenvalue distribution is Poisson (no correlation). As the spectral measures approach an absolutely continuous measure, the repulsion between the eigenvalues increases and the microscopic eigenvalue distribution converges to the clock (or picket fence) distribution" |
April 18, 2013, 3:00 - 4:00 PM at Science Center 232 |
| SPECIAL INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Martin Bridgeman, BC/Moon Duchin, Tufts/Vaibhav Gadre, Harvard/Dmitry Kleinbock, Brandeis/Genevieve Walsh, Tufts () |
Pecha Kucha: Dynamics & Geometry, 20x20 |
This seminar will consist of five talks in the areas of Dynamics and/or Geometry. Each speaker will present 20 slides, and each slide will be displayed for 20 seconds" |
April 17, 2013, 4:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Olivia Caramello (UNIVERSITY OF CAMBRIDGE) |
Topological Galois Theory |
We present an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts; such theories are obtained from representations of certain atomic two-valued toposes as toposes of continuous actions of a topological group. Our framework subsumes in particular Grothendieck s Galois theory and allows to build Galois-type equivalences in new contexts, such as for example graph theory and finite group theory" |
April 17, 2013, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Spiro Karigiannis (UNIVERSITY OF WATERLOO) |
A survey of results about G_2 conifolds |
The exceptional properties of the octonion algebra allow us to define the notion of a $G_2$ structure on an oriented spin 7-manifold, which is a certain non degenerate 3-form that induces a Riemannian metric in a nonlinear way. The manifold is called a G_2 manifold if the 3-form is parallel. Such manifolds are always Ricci-flat, and are of interest in physics. More recently, however, there has been interest in G_2 conifolds, which have a finite number of isolated cone-like singularities. After some background on G_2 manifolds and their moduli, we will present (an admittedly biased) survey of some results on G_2 conifolds, and the closely related asymptotically conical G_2 manifolds, including: -- a theorem (K., 2009) on desingularization of G_2 conifolds by glueing, and its implications about the G_2 moduli space -- a new result (K.-Lotay, 2012) on the deformation theory of G_2 conifolds, including several important applications -- a discussion about a potential method of constructing G_2$conifolds, generalizing an existing construction of smooth compact G2 manifolds (K.-Joyce, 2013) --Organized by Professor Shing-Tung Ya" |
April 16, 2013, 4:15 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Albrecht Klemm (UNIVERSITY OF BONN) |
The refined BPS index from stable pair invariants |
We define the refined BPS numbers using a virtual Bialinicki-Birula decomposition on the moduli space of stable pairs in toric Calabi-Yau mainfolds. We explain how to calculate the invariants using localisation or the refined holomorphic anomaly equations. The latter lead to SL(2,Z) quasimodular generating functions for the invariants and extends to non-toric case" |
April 15, 2013, 3:00 PM at Science Center 507 |
| HARVARD/MIT LOGIC SEMINAR |
Antonina Kolokolova (MEMORIAL UNIVERSITY OF NEWFOUNDLAND) |
How hard is proving hardness? A logic approach to barriers in complexity theory |
In spite of much work over the years, the main questions in complexity theory such as P vs. NP remain unresolved. Is this question solvable at all? Is P vs. NP independent of some logical theory? Indeed, on a meta-level, there are several results that state that certain classes of techniques, including Turing s celebrated diagonalization, cannot be used to resolve these questions. Such results we call the barriers of complexity theory. In this talk, we will survey some of the most well-known such barriers (Relativization, Algebrization, Natural Proofs), and talk about how knowledge of such barriers helps evaluate (and, so far, discard) proposed proofs of P vs. NP. The main emphasis will be on using logic-based approaches to pinpoint and formalize these barriers" |
April 15, 2013, 4:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Clark Barwick (MIT) |
The Unicity Theorem, I |
" |
April 11, 2013, 3:00 - 5:00 PM at Science Center 507 |
| SPECIAL SEMINAR |
Yang Hui-He (CITY U, LONDON/NANKAI U, CHINA/MERTON COLLEGE, OXFORD) |
Bipartite Graphs, Quivers and Gauge Theories |
We discuss how bipartite graphs on Riemann surfaces encapture a wealth of information about the physics of large classes of supersymmetric gauge theories, especially those with quiver structure and arising from the AdS/CFT context. The correspondence between the gauge theory, the underlying algebraic geometry of it space of vacua, the combinatorics of dimers and toric varieties, as well as the number theory of dessin d enfants becomes particular intricate under this light. --Organized by Professor Shing-Tung Ya" |
April 11, 2013, 10:00 AM at Science Center 232 |
| PROBABILITY SEMINAR |
Vadim Gorin (MIT) |
2-D Structures of beta-random matrix ensembles and the Gaussian Free Field |
I will present an approach for studying classical beta-random matrix ensembles through (the limits of) Macdonald polynomials and Macdonald difference operators. We will discuss several results along these lines. The main result concerns global fluctuations of multilevel beta-Jacobi ensemble and its degenerations. I will explain that these fluctuations are asymptotically governed by the Gaussian Free Field - 2-D analogue of the Brownian Motion" |
April 11, 2013, 3:00 - 4:00 PM at Science Center 232 |
| SPECIAL SEMINAR |
Claude LeBrun (STONY BROOK) |
Edges, Orbifolds and Seiberg-Witten Theory |
In the Kahler setting, recent work of Donaldson and others has given a new prominence to the existence and uniqueness problems for Einstein metrics with orbifold-like singularities along a submanifold of real codimension 2. This talk will describe obstructions to the existence of more general 4-dimensional Einstein metrics with edge-cone singularities of prescribed angle along a given surface. Our main objective will be to explore the degree to which facts about the Kahler case naturally generalize to the RIemannian setting. --Organized by Professor Shing-Tung Ya" |
April 10, 2013, 11:00 AM - 12:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Jennifer Balakrishnan (HARVARD UNIVERSITY) |
p-adic heights and integral points on hyperelliptic curves |
We give a Chabauty-like method for finding p-adic approximations to integral points on hyperelliptic curves when the Mordell-Weil rank of the Jacobian equals the genus. The method uses an interpretation of the component at p of the p-adic height pairing in terms of iterated Coleman integrals. This is joint work with Amnon Besser and Steffen Mueller" |
April 10, 2013, 3:00 - 4:00 PM at Science Center 507 |
| SPECIAL SEMINAR |
Jun Li (STANFORD UNIVERSITY) |
Moduli space of vector bundles over algebraic surfaces |
" |
April 10, 2013, 1:00 PM at Science Center 411 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Danny Calegari (UNIVERSITY OF CHICAGO) |
Random groups contain surface subgroups |
We show that a random group at density < 1/2 contains a surface subgroup, with probability -> 1 as n -> infinity. In fact, it contains many such subgroups, and they can be taken to be quasiconvex. This is joint work with Alden Walker" |
April 10, 2013, 4:00 - 5:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Mike Roth (QUEEN'S UNIVERSITY) |
Roth's theorem for arbitrary varieties |
If X is a variety of general type defined over a number field k, then the Bombieri-Lang conjecture predicts that the k-rational points of X are not Zariski dense. The conjecture is a prediction that a global condition on the canonical bundle (that it is generically positive ) implies a global condition about rational points. By a well-established principle in geometry we should look for local influence of positivity on the accumulation of rational points. To do that we need measures of both these local phenomena. Let L be an ample line bundle on X, and x â X(kÌ). The central theme of the talk is the interrelations between αx(L), an invariant measuring the accumulation of rational points around x as gauged by L, and the Seshadri constant Δx(L), measuring the local positivity of L near x. In particular, the classic approximation theorem of K.F. Roth on P1 generalizes as an inequality between αx and Δx valid for all projective varieties. This is joint work with David McKinnon" |
April 09, 2013, 3:00 PM at Science Center 507 |
| HARVARD/MIT LOGIC SEMINAR |
John Baldwin (UNIVERSITY OF ILLINOIS AT CHICAGO) |
Constructing atomic Borel structures in the continuum |
I will discuss several applications of a method of Shelah to build a model in the continuum from a countable model satisfying certain geometric conditions. We baptize the notion of Asymptotic Similarity which appeared almost 40 years ago in Shelahâs Classification Theory. We present a template for building atomic Borel structures in the continuum based on this notion. We then survey a wide range of applications of this template" |
April 08, 2013, 4:30 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Chris Wendl (UNIVERSITY COLLEGE LONDON) |
Tight but nonfillable contact manifolds in all dimensions |
Contact topology in dimension three is shaped by the fundamental dichotomy between tight and overtwisted contact structures, and while it is not known whether any such dichotomy exists in higher dimensions, there are certainly contact structures in all dimensions that have all the trappings of overtwistedness (e.g. nonfillability, vanishing contact homology), or tightness (e.g. no contractible orbits, lack of flexibility). In dimension 3, the invariant known as Giroux torsion has played a central role in classifying tight contact structures, and in this talk I will explain how one can generalize it to find the first examples in all dimensions of contact structures that must be considered tight but do not admit any symplectic fillings. A crucial ingredient for this is the existence (also in all dimensions) of symplectic manifolds with disconnected convex boundary, which requires a surprising digression into algebraic number theory. This is joint work with Patrick Massot and Klaus Niederkrueger" |
April 05, 2013, 3:00 - 4:00 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Matt Hedden (MICHIGAN STATE) |
The pillowcase and perturbations of traceless representations of knot groups |
I ll discuss joint work with Chris Herald and Paul Kirk which aims to explicitly understand the generating sets for Kronheimer and Mrowka s singular instanton chain complexes. These generating sets are not finite since they count representations of the knot group that, with the exception of the unknot, come in positive dimensional families. I ll show how to explicitly perturb the Morse functional to ensure non-degeneracy, whilst preserving the desirable feature of being able to identify generators in terms of particular representations of the (augmented) knot group. A feature which arises in this pursuit is a computation of the chain groups in terms of Lagrangian intersection pictures occurring in a pillowcase" |
April 05, 2013, 4:00 - 5:00 PM at Science Center 507 |
| THURSDAY SEMINAR |
Gijs Heuts (HARVARD UNIVERSITY) |
Models for the theory of (â, 1)-operads |
" |
April 04, 2013, 3:00 - 5:00 PM at Science Center 507 |
| PROBABILITY SEMINAR |
Jonathan Novak (MIT) |
An invitation to Weingarten calculus |
The integration of polynomial functions on compact matrix groups is a challenging problem which has a long history in mathematical physics, with various partial results scattered throughout the literature. In recent years, the needs of random matrix theory have led to the development of a structured approach to this problem which has come to be known as Weingarten calculus. This calculus is analogous to Wick-type methods for computing averages of polynomial functions in Gaussian random variables, but it is more involved both combinatorially and algebraically. I ll describe the modern formulation of Weingarten calculus and, if time permits, explain how combining Weingarten calculus and Schwinger-Dyson equations leads to asymptotics for Schur polynomials. This talk is partly based on a book in preparation with Benoit Collins and Sho Matsumoto, and ongoing work with Alice Guionnet." |
April 04, 2013, 3:00 - 4:00 PM at Science Center 232 |
| NUMBER THEORY SEMINAR |
Shouwu Zhang (PRINCETON UNIVERSITY) |
The congruent number problem and special values of L-functions |
A positive and square free integer n is called a congruent number if it is the area of a right angled triangle whose three sides have rational length. A combination of the BSD conjecture and Goldfeld s conjecture asserts that all n = 5, 6, 7 (mod 8) are congruent numbers, and that most n =1,2, 3 (mod 8) are not. In this aspect, Genocchi (1874) showed that all primes p = 3 (mod 8) are not congruent numbers, and Heegner (1952) showed that all primes p = 5 (mod 8) are congruent numbers. Their results have been generalized to certain products of two primes by Feng and Zhao (for non-congruent numbers), and Gross and Monsky (for congruent numbers). In my talk, I will explain how all these results can be extended to certain products of many primes, using systematically the new generalized Waldspurger and Gross--Zagier formulas. This is a joint work with Ye Tian and Xinyi Yuan" |
April 03, 2013, 3:00 - 4:00 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Kasra Rafi (UNIVERSITY OF TORONTO) |
Geometry of Teichmuller Space |
We review recent results about the Teichmueller space equipped with the Teichmueller metric. We give an inductive description of a Teichmueller geodesics using the Teichmueller geodesics of surfaces with lower complexity. We use these results to compare how the Teichmueller space is similar or different from a hyperbolic space" |
April 03, 2013, 4:00 - 5:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
William Meeks (UNIVERSITY OF MASSACHUSETTS AMHERST) |
The Geometry of isoperimetric domains of large volume in simply connected homogeneous 3-manifolds |
Consider a simply connected non-compact homogeneous 3-manifold X. For each V>0, there exists a smooth compact domain D(V) with volume V whose boundary surface area is minimizing and we call such a boundary area minimizing domain an isoperimetric domain of X. One would like to classify all such isoperimetric domains in X for a fixed V up to ambient isometry and to understand the properties of such domains, such as the slope of the isoperimitric profile of X as volume V tends to infinity. In a recent paper with Mira, Perez and Ros, the speaker has obtained an number of such geometric results on these questions. In particular we have been able to show that the Cheeger constant Ch(X) of X is equal to twice the critical mean curvature H(X) of the X. As a consequence of our proof of this relation, for any sequence of isopermitric domains in X with volumes tending to infinity, the constant mean curvatures of their boundary surfaces tend to H(X) and their radii tend to infinity. The difficult case in this study is when X is isometric to universal cover of the Lie group SL(2,R) equipped with a left invariant metric with a 3-dimensional isometry group. These results together with our recent classification of constant mean curvature spheres in X leads to an isoperimetric inequality for smooth compact immersed surfaces in X with 1 boundary component and with absolute mean curvature function less than or equal to Ch(X)/2. --Organized by Professor Shing-Tung Ya" |
April 02, 2013, 4:15 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Alexei Borodin (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
Integrable stochastic particle systems and Macdonald processes |
A large class of one dimensional stochastic particle systems are predicted to share the same universal long-time/large-scale behavior. By studying certain integrable models within this (Kardar-Parisi-Zhang) universality class we access what should be universal statistics and phenomena. In this talk we focus on two different integrable exclusion processes: q-TASEP and ASEP. Using them as a prompt, we will describe the theory of Macdonald processes which unites integrability in various areas of probability including directed polymers, interacting particle systems, growth processes and random matrix theory" |
April 01, 2013, 3:00 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Chung-Jun Tsai (HARVARD UNIVERSITY) |
Dirac spectral flow on contact 3-manifolds |
In Taubes s proof of the Weinstein conjecture, a key ingredient is the spectral flow estimate of a family of Dirac operators, which is used to obtain the energy bound. When the perturbation term is a contact form, much evidence suggests that its spectral flow has better asymptotic behavior. In this talk, I will explain how to study the Dirac spectral flow based on an open book decomposition" |
March 29, 2013, 3:30 - 4:30 PM at Science Center 507 |
| THURSDAY SEMINAR |
Dominic Verity (MACQUARIE UNIVERSITY) |
A Conspectus of Complicial Sets, continued |
" |
March 28, 2013, 3:00 - 5:00 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Alex Wright (UNIVERSITY OF CHICAGO) |
SL(2,R)-orbit closures of translation surfaces |
We will discuss some recent results on the structure of SL(2,R)-orbit closures in the moduli space of translation surfaces. New connections will be presented between the flat geometry of a translation surface and the structure of its orbit closure" |
March 27, 2013, 4:00 - 5:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Jared Weinstein (BOSTON UNIVERSITY) |
p-divisible groups over O_C |
Complex abelian varieties are classified by pairs (V,L), where V is a finite-dimensional complex vector space and L is a lattice in V equipped with a Riemann form. In this talk we discuss a p-adic analogue of this classical result. Let C be a complete and algebraically closed extension of Q_p. We present a classification of p-divisible groups over the ring of integers O_C in terms of linear algebra data. This is joint work with Peter Scholze" |
March 27, 2013, 3:00 - 4:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Noah Giansiracusa (UC BERKELEY) |
Tropical Scheme Theory |
I ll discuss joint work with J.H. Giansiracusa (Swansea) in which we study scheme theory over the tropical semiring T, using the notion of semiring schemes provided by Toen-Vaquie, Durov, or Lorscheid. We define tropical hypersurfaces in this setting and a tropicalization functor that sends closed subschemes of a toric variety over a field with non-archimedean valuation to closed subschemes of the corresponding toric variety over T. Upon passing to the set of T-valued points this yields Payne s extended tropicalization functor. We prove that the Hilbert function of any projective subscheme is preserved by our tropicalization functor, so the scheme-theoretic foundations developed here reveal a hidden flatness in the degeneration sending a variety to its tropical skeleton" |
March 26, 2013, 3:00 PM at Science Center 507 |
| PROBABILITY SEMINAR |
Noureddine El Karoui (UC BERKELEY - STATISTICS) |
Some connections between random matrix theory and high-dimensional statistics |
With data collection and storage easier by the day, statisticians are now working with datasets having many observations and many measurements per observations. This is a radical shift from the classical theory of statistics, where the number of observations (n) is most often assumed to be much bigger than the number of measurements per observations (p). It is therefore important to understand how statistical estimators behave and perform in the setting where both p and n are large. Because random matrices are a key building block of statistics, the theory of high-dimensional random matrices is helpful in shedding light on certain high-dimensional (i.e large p, large n) statistical problems. In this talk, I will discuss some of these problems, as well as potential limitations of the standard models of random matrix theory when used in a statistical setting" |
March 26, 2013, 3:00 - 4:00 PM at Science Center 232 |
| DIFFERENTIAL GEOMETRY SEMINAR |
An Huang (HARVARD UNIVERSITY) |
The tautological system |
The tautological system is a system of differential equations for certain period integrals, that can be regarded as a generalization of the GKZ system. It was introduced by Lian, Song, and Yau in 2011, motivated by ideas from mirror symmetry. I will report our recent progress on this project, based on joint works with Spencer Bloch, Bong Lian, Vasudevan Srinivas, Shing-Tung Yau, and Xinwen Zhu. -- Organized by Professor Shing-Tung Ya" |
March 26, 2013, 4:15 PM at Science Center 507 |
| HARVARD/MIT LOGIC SEMINAR |
Nate Ackerman (HARVARD UNIVERSITY) |
Transferring model-theoretic results about Lâ,Ï to a Grothendieck topos |
One of the most significant discoveries of categorical logic is that for a first order language L the operations of Lâ,Ï(L) can be described categorically. This observation allows us to study models of sentences of Lâ,Ï(L)in categories other than the category of sets and functions. One class of categories which are especially well suited to interpret sentences of Lâ,Ï(L) are Grothendieck toposes, i.e. categories which are equivalent to the category of sheaves on some site. However, while it makes sense to study the model theory of Lâ,Ï(L) in a Grothendieck topos, this model theory can behave very differently than model theory in the category of sets and functions. (For example, in general it will be intuitionistic and need not satisfy the law of excluded middle). A natural question to ask is: If we fix a Grothendieck topos, which results about the model theory of Lâ,Ï(L) in the category of sets and functions have analogs for the model theory of Lâ,Ï(L) in our fixed Grothendieck topos? In this talk we will discuss a method of encoding models of a sentence of Lâ,Ï(L) in a (fixed) Grothendieck topos by models of a sentence of Lâ,Ï(LâČ) in the category of sets and functions, (where LâČ is a language related to L). We will then discuss how to use this encoding to prove analogs in a fixed Grothendieck topos of the downward Löwenheim-Skolem theorem, the completeness theorem as well as Barwise compactness. One of the most significant difficulties we will have to overcome is the fact that sheaves are fundamentally second order objects. We will discuss how our encoding deals with this fact and the tradeoffs which must be made in the final theorems to accommodate the non-first order nature of sheaves and the corresponding models in a Grothendieck topos" |
March 25, 2013, 4:30 PM at Science Center 507 |
| SPECIAL SEMINAR |
Chao Chen (RUTGERS UNIVERSITY - COMPUTER SCIENCE) |
Connecting Homology and Quantification -- Homology Localization and Persistent Homology |
This talk will cover two topics which build connections between homology and quantification. First, we introduce the problem of homology localization, namely, representing homology classes using concise cycles. Several definitions of conciseness will be discussed. We will summarize what is and what is not feasible in terms of computation. Second, we present a tool named persistent homology, followed by its applications in computer vision. Persistent homology creates signatures for scalar functions using homology classes annotated with a quantity, i.e. persistence. Inspired by Morse theory, it reveals useful insight of the topography of functions. --Organized by Professor Shing-Tung Ya" |
March 25, 2013, 4:00 - 5:00 PM at Science Center 530 |
| BASIC NOTIONS SEMINAR |
Mark Kisin (HARVARD UNIVERSITY) |
The Grothendieck p-curvature conjecture |
The Grothendieck p-curvature conjecture says that an algebraic differential equation has a full set of solutions if it has a full set of solution modulo p for almost all primes p. I will explain the conjecture, and survey the methods which have been used to prove some cases of it" |
March 25, 2013, 3:00 PM at Science Center 507 |
| THURSDAY SEMINAR |
Dominic Verity (MACQUARIE UNIVERSITY) |
A Conspectus of Complicial Sets |
" |
March 21, 2013, 3:00 - 5:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Mu-Tao Wang (COLUMBIA UNIVERSITY) |
Surfaces in spacetime and quasi-local mass |
I shall consider the geometry of spacetime 2-surfaces which bound spacelike hypersufaces. These surfaces are of great interest in general relativity because of the connection to the notion of gravitational energy. Several recent results from joint work with PoNing Chen and Shing-Tung Yau will be discussed. --Organized by Professor Shing-Tung Ya" |
March 19, 2013, 4:15 PM at Science Center 507 |
| SPECIAL SEMINAR |
John Loftin (RUTGERS UNIVERSITY) |
Cubic Differentials and Limits of RP^2 Structures |
In a generalization of Thurston s compactication of Teichm\uller space, Anne Parreau, and also Inkang Kim, have described a limit of a family of $RP^2$ structures on a closed surface in terms of the asymptotic eigenvalues of the holonomies around free loops on the surface. One may identify a convex $RP^2$ structure on a closed surface of genus at least 2 with a conformal structure erential. On a given Riemann surface with cubic differential $U$, we investigate the asymptotic data for the convex $RP^2$ structure corresponding to $(\Sigma,\lambda U)$ for $\lambda\to\infty$. For a generic cubic differential $U$ on a Riemann surface $\Sigma$, we explicitly describe the asymptotic information for the $RP^2$ structure corresponding to $(\Sigma,\lambda U)$ in terms of the singular Euclidean metric $|U|^{\frac23}$. We also provide a conjectural formulation for any cubic differential $U$. The proof involves analytic techniques similar to Wolf s approach to Thurston s boundary of Teichm\uller space. This is joint work in progress with Mike Wolf and David Dumas. --Organized by Prof. Shing-Tung Ya" |
March 18, 2013, 2:00 PM at Science Center 507 |
| HARVARD, BRANDEIS, MIT, NORTHEASTERN JOINT COLLOQUIUM AT HARVARD |
Raman Parimala (EMORY UNIVERSITY) |
Period-index questions for the Brauer groups |
For a finite dimensional central division algebra over a number field or a local field, its period and index coincide. There are natural questions concerning bounding indices of division algebras of a given period over finitely generated fields. We shall explain how this question is related to bounding the dimensions of anisotropic quadratic forms over such fields and trace some progress concerning this question" |
March 14, 2013, 4:30 PM at Science Center, Hall A |
| PROBABILITY SEMINAR |
Benoit Collins (UNIVERSITY OF OTTAWA) |
Norm convergence for random matrices and applications |
We will review some recent results about the convergence in the large N limit of the operator norm of random matrix models obtained as non-commutative polynomials in i.i.d unitary Haar distributed matrices. We will describe some applications of these results, in particular to the study of singular values of random subspaces of a tensor product. This talk is based on joint works with S. Belinschi, M. Fukuda, C. Male, I. Nechita" |
March 14, 2013, 3:00 PM at Science Center 232 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Eric Bedford (INDIANA UNIVERSITY) |
Automorphisms of complex manifolds with positive entropy |
We will survey the compact complex surfaces with automorphisms of positive entropy. Then we look at the higher dimensional situation and discuss the existence of pseudo-automorphisms with positive entropy" |
March 13, 2013, 4:00 - 5:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Jochen Gartner (MCGILL UNIVERSITY) |
Massey products in the cohomology of pro-p extensions |
Pro-p extensions of number fields with ramfication restricted to a finite set of primes naturally arise in arithmetic geometry. In the first part of this talk we recall some well-known properties of wildly ramified extensions. We discuss consequences of the Ă©tale K(\pi,1)-property for the associated arithmetic curves in the more difficult tame case due to A. Schmidt and show how the first explicit examples have been obtained by J. Labute using the theory of mild pro-p groups. In the second part we introduce the notion of Massey products in the cohomology of pro-p-groups. These products can be considered as higher analogues of the cup-product and carry some interesting group theoretical information. We give an application of higher Massey products in order to construct mild pro-p groups and discuss arithmetic interpretations of these products in the case of pro-p fundamental groups" |
March 13, 2013, 3:00 - 4:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Brian Lehman (RICE UNIVERSITY) |
Big cycles and volume functions |
The volume of a divisor is an important invariant measuring the positivity of its numerical class. I will discuss an analogous construction for cycles of arbitrary codimension. In particular, this yields geometric characterizations of big cycle classes modeled on the well-known criteria for divisor and curve classes" |
March 12, 2013, 3:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Thomas Lam (UNIVERSITY OF MICHIGAN) |
The projected Richardson stratification of a partial flag variety |
-- Organized by Professor Shing-Tung Ya" |
March 12, 2013, 4:15 PM at Science Center 507 |
| HARVARD/MIT LOGIC SEMINAR |
Rehana Patel and Nate Ackerman (OLIN COLLEGE AND HARVARD UNIVERSITY) |
A Random Walk Through Some First Order 0-1 Laws and Computability of 0-1 Laws |
A class of finite structures has a first order zero-one law if any first order property holds asymptotically almost surely, or almost never, in that class. In this talk, we will focus on first order zero-one laws for classes of graphs that have a fixed finite forbidden subgraph. We will provide a partial catalog, outline some conjectures, and describe approaches to resolving them. 2nd Talk Abstract: In this talk we will consider the abstract operator which takes a complete first order theory T and returns the collection of sentences which are asymptotically almost surely true of all finite substructures of models of T. In particular we will consider the question of how computable the result of this operation can be if we start with a computable collection of Sigma_1-sentences." |
March 11, 2013, 4:30 PM at Sci Center 507 |
| THURSDAY SEMINAR |
Jeremy Hahn (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
From n-fold Segal spaces to n-fold quasi-categories |
" |
March 07, 2013, 3:00 - 5:00 PM at Sci Center 507 |
| PROBABILITY SEMINAR |
Ivan Corwin (MIT) |
From duality to determinants for ASEP |
I will explain duality for the asymmetric simple exclusion process and then solve the associated quantum many body problem for special initial conditions via a contour integral ansatz. Using the resulting formulas I develop generating series which identify particle location distributions and which can be expressed as Fredholm determinants (one of which coincides with the Tracy-Widom ASEP formula). Asymptotics of such expressions are readily computable and lead to Kardar-Parisi-Zhang universality class fluctuations. In essence, this is a rigorous discrete deformation of the physicist s (famously non-rigorous) polymer replica trick. This is based on joint work with Alexei Borodin and Tomohiro Sasamoto" |
March 07, 2013, 3:00 - 4:00 PM at Science Center 232 |
| TRIVIAL NOTIONS SEMINAR |
Francesco Cavazzani (HARVARD UNIVERSITY) |
From 3264 conics to wonderful compactifications |
How many conics in the projective plane are tangent to 5 general conics? We are going to answer to this question, using the beautiful construc- tion of complete conics, already known to Chasles in 1864. Afterwards, we will go through some of the math generated by this construction in the following 150 years; in particular, we are going to describe the construction by De Concini and Procesi of wonderful compactifications of symmetric spaces, and why they deserve to be called this way. The talk will be very Italian style" |
March 07, 2013, 1:00 PM at Science Center 310 |
| SPECIAL INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Benedict Gross, Oliver Knill, Sarah Koch, Barry Mazur, Curtis McMullen and Emily Riehl (HARVARD UNIVERSITY) |
PechaKucha: Mathematics, 20x20 |
PechaKucha is a presentation methodology, popular in design circles, in which speakers show 20 slides for 20 seconds each. This seminar will feature six such talks, on a variety of mathematical topics" |
March 06, 2013, 4:00 PM at Science Center Hall C |
| NUMBER THEORY SEMINAR |
David Zywina (INSTITUTE FOR ADVANCED STUDY) |
Big Monodromy and the Inverse Galois Problem |
By studying the Galois action on etale cohomology groups arising from families of elliptic curves, we will prove several new cases of the regular Inverse Galois Problem. In particular, we will explain why each of the simple groups PSp_4(F_p) occur as the Galois group of a regular extension of the function field Q(t). The key ingredients will be a big monodromy result along with some known cases of the Birch and Swinnerton-Dyer conjecture" |
March 06, 2013, 3:00 - 4:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Matthias Keller (HEBREW UNIVERSITY) |
Intrinsic metrics for Laplacians on graphs |
Although there are many well known analogies between Laplacians on manifolds and on graphs, various recent discoveries show a clear disparity between the both. These differences are most apparent if one considers unbounded operators on graphs. Introducing a new notion of intrinsic distance related to these unbounded operators helps to resolve various of the disparities. (This involves joint work with F. Bauer, S. Haeseler, B. Hua, X. Huang, D. Lenz, J. Masamune, R. Wojciechowski) --Organized by Professor Shing-Tung Ya" |
March 05, 2013, 4:15 PM at Science Center 507 |
| SPECIAL SEMINAR |
Wolfgang Tichy (FLORIDA ATLANTIC UNIVERSITY) |
Constructing initial data for binary neutron stars with spins |
In general neutron stars in binaries are spinning. Thus numerical simulations of the last few orbits and the merger should start from initial conditions that allow for arbitrary spins. We discuss quasi-equilibrium approximations one can make in the construction of binary neutron star initial data with spins. These approximations result in several coupled elliptic equations. To numerically solve these equations we use six different computational domains, which include spatial infinity. Each domain has its own coordinates which are chosen such that the star surfaces always coincide with domain boundaries. Since the data are smooth in each domain we can use an efficient pseudospectral method to solve the elliptic equations. Once the initial data are computed we can perform binary neutron star simulations with our evolution code. --Organized by Professor Shing-Tung Ya" |
March 05, 2013, 2:00 PM at Science Center 232 |
| BASIC NOTIONS SEMINAR |
Dennis Gaitsgory (HARVARD UNIVERSITY) |
Induction of representations and weird Frobenius reciprocity |
The usual Frobenius reciprocity says that the procedure of induction representation (from a subgroup to the ambient group) is right adjoint to the procedure of restriction. We apply it to the ambient group being a reductive group G with the subgroup being a parabolic P, and we consider representations of P that factor through its Levi quotient M. Instead of the usual restriction, the left adjoint procedure is known as the Jacquet (a.k.a. constant term) functor. This works in any of the usual representation-theoretic contexts: e.g., p-adic groups, real reductive groups, finite Chevalley groups. However, in some of the above contexts the following weird phenomenon takes place: the functor of induction also happens to be the *left* adjoint, but to the Jacquet functor with respect to the opposite parabolic. The proof of this fact, say, in the context of p-adic groups, is a cool piece of geometry, where we degenerate the group G to its asymptotic cone. In this talk, after covering some background material (including the phenomenon of weird adjunction for p-adic groups), I ll explain its analog in the context of Geometric Langlands. There it is related to the operation of taking the hyperbolic fiber of a sheaf and Braden s theorem that describes how this operation interacts with Verdier duality." |
March 04, 2013, 3:00 PM at Science Center 507 |
| HARVARD/MIT LOGIC SEMINAR |
Robert Lubarsky (FLORIDA ATLANTIC UNIVERSITY) |
FITTMs, Sigma_3 Determinacy, and nested Sigma_2 Reflection |
Infinite Time Turing Machines are a generalization of classical computability into the transfinite. They are so powerful that the tools of admissible set theory are needed to analyze their strength. Feedback ITTMs are a further extension, which demand for their analysis notions of determinacy, reflection, and non-standard models. I will sketch the theory involved, leading up to the big open conjecture of this topic" |
March 04, 2013, 4:30 PM at Science Center 507 |
| TRIVIAL NOTIONS SEMINAR |
Peter Smillie (HARVARD UNIVERSITY) |
Geometry of Diffeomorphism Groups |
In 1966, on the occasion of the 200th anniversary of Euler s description of the equations of motion of a rigid body, Arnold published a paper in which he showed first how to reinterpret Euler s equations as arising from geodesic flow on the group SO(3), and second how by replacing SO(3) with SDi (D), the group of volume preserving diffeomorphisms of a domain D, one recovers the classical theory of incompressible fluid flow. We ll translate some questions about fluid flow into infinite dimensional Lie geometry, and then answer them" |
February 28, 2013, 1:00 PM at Science Center 310 |
| THURSDAY SEMINAR |
Gijs Heuts (HARVARD UNIVERSITY) |
Toën's axiomatization of the homotopy theory of (infinity,1)-categories |
" |
February 28, 2013, 3:00 - 5:00 PM at Science Center 507 |
| PROBABILITY SEMINAR |
Nalini Anantharaman (UNIVERSITY PARIS SUD / IAS) |
Quantum Ergodicity on Large Regular Graphs |
Quantum ergodicity usually deals with the study of eigenfunctions of the Laplacian on Riemannian manifolds, in the high-frequency asymptotics. The rough idea is that, under certain geometric assumptions (like negative curvature), the eigenfunctions should become spatially uniformly distributed, in the high-frequency limit. I will review the many conjectures in the subject, some of which have been turned into theorems recently. Physicists like Uzy Smilansky or John Keating have suggested looking for similar questions and results on large (finite) discrete graphs. Take a large graph $G=(V, E)$ and an eigenfunction $\psi$ of the discrete Laplacian -- normalized in $L^2(V)$. What can we say about the probability measure $|\psi(x)|^2$ ($x\in V$)? Is it close to uniform, or can it, on the contrary, be concentrated in small sets? I will talk about ongoing work with Etienne Le Masson, in the case of large regular graphs" |
February 28, 2013, 3:00 PM at Science Center 232 |
| NUMBER THEORY SEMINAR |
Sug Woo Shin (MIT) |
Non-emptiness of Newton strata |
A Newton stratum for Shimura varieties (certain moduli spaces of abelian varieties with extra data in characteristic p) is the locus where the p-divisible groups associated with abelian varieties belong to a fixed isogeny class. In case the moduli problem is defined by unitary or symplectic data (which are unramified), Newton strata are known to be nonempty whenever expected by Vasiu and Viehmann-Wedhorn based on earlier work by many, and also recently by Kret. I will explain a different approach to prove the result in the unramified case via Honda-Tate theory and Galois cohomology and some results in the ramified case" |
February 27, 2013, 3:00 - 4:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Yi Zhang (FUDAN UNIVERSITY) |
Smooth toroidal compactifications of Siegel variety from the viewpoint of Kaehler-Einstein metrics |
We try to understand the Kaehler-Einstein properties in algebraic geometry. In particular we study smooth toroidal compactifications of on an arbitrary Siegel varietiy $A_{g,\Gamma}(g>1)$ through the unique group-invariant Kaehler-Einstein metric on $A_{g,\Gamma}.$ We first get a global volume formula，by this formula we then obtain that the K\ahler-Einstein metric on $A_{g,\Gamma}$ endows some restraint combinatorial conditions for all toroidal smooth compactifications $\overline{A}_{g,\Gamma}$ of $A_{g,\Gamma}$ such that the boundary divisor $D_\infty:=\overline{A}_{g,\Gamma}-A_{g,\Gamma}$ is normal crossing. We also study the asymptotic behaviour of logarithmical canonical line bundle on any smooth toroidal compactification of $A_{g,\Gamma},$ we find that the logarithmical canonical bundle degenerate sharply even though it is big and numerically effective. --Organized by Professor Shing-Tung Ya" |
February 26, 2013, 4:15 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Igor Rodnianski (MIT) |
Nonlinear scattering for black holes |
We show the existence of a large class of non-stationary vacuum black hole solutions of the Einstein equations asymptotically converging to a fixed Schwrazschild or Kerr geometry. The spacetimes are constructed by solving a backwards scattering problem with characteristic data prescribed on the horizon and null infinity. We will review the basic concepts, geometry and mathematical tools in General Relativity and will explain some of the elements of the proof of the result" |
February 25, 2013, 3:00 PM at Science Center 507 |
| PROBABILITY SEMINAR |
Raymond Yeung (THE CHINESE UNIVERSITY OF HONG KONG) |
Refinement of Two Fundamental Tools in Information Theory |
In Shannon s original paper and textbooks in information theory, the entropy of a discrete random variable is assumed or shown to be a continuous function. However, we found that all Shannon s information measures including entropy and mutual information are discontinuous in the general case that the random variables take values in possibly countably infinite alphabets. This fundamental property explains why strong typicality and Fano s inequality can only be applied on finite alphabets. Note that strong typicality and Fano s inequality have wide applications in information theory so that it is important to extend them in full generality. In this talk, details about the discontinuity of Shannon s information measures will be given. We will show how these results lead to a new definition of typicality and an inequality tighter than Fano s inequality. Applications in network coding and information theoretic security will be discussed" |
February 22, 2013, 2:00 PM at Science Center 232 |
| PROBABILITY SEMINAR |
Benedek Valko (UNIVERSITY OF WISCONSIN) |
Diffusivity of lattice gases |
We consider one component lattice gases with a local dynamics and a stationary product Bernoulli measure. We give upper and lower bounds on the diffusivity at an equilibrium point depending on the dimension and the local behavior of the macroscopic flux function. We show that if the model is expected to be diffusive, it is indeed diffusive, and, if it is expected to be superdiffusive, it is indeed superdiffusive. (Joint with J. Quastel." |
February 21, 2013, 3:00 - 4:00 PM at Science Center 232 |
| HARVARD, BRANDEIS, MIT, NORTHEASTERN COLLOQUIUM AT HARVARD |
Alex Kontorovich (YALE UNIVERSITY) |
Diophantine problems in thin orbits |
We will discuss several naturally arising problems in arithmetic, including the local-global conjecture for integral Apollonian gaskets and Zaremba s conjecture. While the questions emerge in completely unrelated ways, they boil down to the same issue of determining a Hasse-type principle in a thin orbit. A key role is played by the recent explosion in spectral gap technology in the thin setting" |
February 21, 2013, 4:30 PM at Science Center, Hall A |
| THURSDAY SEMINAR |
Clark Barwick (MIT) |
Models of (â, 1)-categories: a bestiary |
" |
February 21, 2013, 3 - 5PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Jack Thorne (HARVARD UNIVERSITY) |
Symmetric power functoriality for GL(2) |
We discuss some new automorphy lifting theorems, and their application to proving the existence of new cases of Langlands functoriality for GL(2). This is joint work with L. Clozel" |
February 20, 2013, 3:00 - 4:00 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Jayadev Athreya (UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN) |
Gap distributions and homogeneous dynamics |
The Farey sequence F(Q) is the collection of fractions between [0,1] whose denominator (when written in lowest terms) is at most Q. As Q grows, these points become uniformly distributed in the interval, so in some sense, look `random . However, when you look at the gaps between them, they do not behave like those for uniformly distributed random variables, but instead follow an unusual law known as Hall s Distribution. We will explain a proof of this result that uses horocycle flow on the space of lattices SL(2,R)/SL(2, Z), and, time permitting discuss how this picture can be generalized to understanding gaps between directions of saddle connections on Veech surfaces. This talk will include elements from joint work with Y. Cheung, joint work with J. Chaika, and joint work with J. Chaika and S. Lelievre" |
February 20, 2013, 4:00 PM at Science Center 507 |
| SPECIAL SEMINAR |
Can Kozcas (SISSA) |
Extending the Refined Topological Vertex and its Connection to the Refined Chern-Simons Theory |
The refined topological vertex computes the refined topological string amplitudes for the non-compact toric Calabi-Yau threefolds which geometrically engineer supersymmetric gauge theories. Some toric geometries, such as local P^2, have been out of the reach for a direct computation using the refined vertex. A new complimentary vertex is proposed, together with the refined vertex, which computes the refined topological string amplitudes for all non-compact toric Calabi-Yau threefolds. Both of these vertices are intimately connected to the refined Chern-Simons theory introduced by Aganagic and Shakirov. Organized by Professor Shing-Tung Ya" |
February 20, 2013, 3:00 PM at Science Center 232 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Franz Schuster (VIENNA UNIVERSITY OF TECHNOLOGY) |
Affine vs. Euclidean Isoperimetric Inequalities |
The equivalence of the classical Euclidean isoperimetric inequality and the sharp L_1 Sobolev inequality is a beautiful example of the interplay between geometric and analytic inequalities. This remarkable link has been amplified by the recent work on affine isoperimetric and analytic inequalities. An affine isoperimetric inequality is an inequality between geometric functionals which are invariant under volume preserving linear transformations. In contrast to the common misbelief that Euclidean inequalities (that is, inequalities for functionals invariant under rigid motions only) are stronger than affine inequalities, it has become apparent over the last decades that affine isoperimetric inequalities are the most powerful inequalities of (convex) geometric analysis. In this talk we discuss, in particular, one of the most important examples of an affine isoperimetric inequality: Petty s projection inequality. It states that among compact, convex sets of given volume, the ones whose polar projection bodies have maximal volume are precisely the ellipsoids. We will give an overview of the impact over the last decade of this inequality, it s analytic version (the Zhang-Sobolev inequality), and their L_p generalizations by Lutwak-Yang-Zhang and Haberl and myself. We will also shed new light on the special role of Petty s projection inequality in affine geometric analysis by exploiting the fascinating connections between the theory of isoperimetric inequalities and the theory of valuations which were first discovered by Ludwig" |
February 19, 2013, 4:15 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Bernd Sturmfels (UC BERKELEY) |
A Hilbert Scheme in Computer Vision |
Multiview geometry, the study of two-dimensional images of three-dimensional scenes, is foundational for computer vision. We present work with Chris Aholt and Rekha Thomas on the equations that characterize images taken by n cameras. Our varieties are threefolds that vary in a family of dimension 11n-15 when the cameras are moving. Toric geometry and Hilbert schemes are used to characterize degenerations of camera positions" |
February 19, 2013, 3:00 PM at Science Center 507 |
| HARVARD/MIT LOGIC SEMINAR |
Gerald Sacks (HARVARD UNIVERSITY) |
Extensions of Levy-Schoenfield Absoluteness |
" |
February 19, 2013, 5:00 PM at Science Center 112 |
| TRIVIAL NOTIONS SEMINAR |
Gijs Heuts (HARVARD UNIVERSITY) |
Quillen Homology |
In the 60 s, Quillen introduced a very general notion of (co)homology, which gives precise meaning to the idea that taking homology corre- sponds to linearization. His notion reproduces familiar examples such as Hochschild homology (for associative algebras), Lie algebra homol- ogy ( la Chevalley-Eilenberg), group homology, singular homology of spaces and, more interestingly, the cotangent complex of a commuta- tive ring. We ll discuss why Quillen s abstract perspective is a useful one that is applicable to a wide range of settings (a range that is, in fact, still widening today). After that, we might bump into some toy examples of Koszul duality. Or we might not" |
February 14, 2013, 1:00 - 2:00 PM at Science Center 310 |
| PROBABILITY SEMINAR |
Michael Brenner (HARVARD UNIVERSITY SEAS) |
Signal identification from sample covariance matrices with correlated noise |
We find that the spectral characteristics of sample covariance matrices derived from biological datasets (microarrays, RNASeq) are well described by a model in which a signal is corrupted by correlated noise. Such eigenvalue distributions have long tails, and the signal and noise contributions mix with each other in the tails. A mathematical analysis demonstrates that information about the signal can be recovered by finding correlations between large magnitude components of the eigenvectors of the sample covariance matrix. The alignment of such eigenvectors with the signal most likely occurs when the corresponding eigenvalues are close to the signal eigenvalue, with the strength of the alignment being controlled by the ratio of the eigenvalue spacing to the size of typical elements in the sample covariance. Within a long tail of the eigenvalue distribution, the eigenvalue spacing is atypically large, making strong alignment possible" |
February 14, 2013, 3:00 PM at Science Center 232 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Laurent Bartholdi (UNIVERSITY OF GOTTINGEN) |
Computing with branched coverings |
Branched coverings of the sphere manifest themselves in various guises: analytic (as rational maps on the Riemann sphere), topological, or combinatorial (via finite triangulations, subdivision rules, etc.). I will describe a fruitful fourth point of view, via group theory. I will use this language to explain how branched coverings canonically decompose into elementary pieces, similar to the decomposition of 3-manifolds into atoric pieces and the JSJ decomposition of groups into amalgamated free products. This is joint work with Dzmitry Dudko" |
February 13, 2013, 4:00 PM at Science Center 507 |
| HARVARD/MIT LOGIC SEMINAR |
Alice Medvedev (UC BERKELEY) |
Algebraic Dynamics, Number Theory and Model Theory |
Model Theory, a branch of mathematical logic, is a new and useful way to approach number-theoretic conjectures about special points and special subvarieties, such as the Manin-Mumford Conjecture. Algebraic Dynamics, the study of discrete dynamical systems in the category of algebraic geometry, supplies natural generalizations of these conjectures. We use model-theoretic ideas to settle some cases of these dynamical generalizations of number-theoretic conjectures. This talk is mostly about the dynamics of functions of the form F(x1, x2, ... xn) = ( f1(x1), f2(x2), ... fn(xn) ) for univariate polynomials fi over the complex numbers, so it will be accessible to a broad audience. Technical issues will remain under the rug unless probed by the audience." |
February 13, 2013, 4:30 PM at Science Center 232 |
| NUMBER THEORY SEMINAR |
Brandon Levin (STANFORD UNIVERSITY) |
Flat deformations with additional structure |
I will begin with a brief introduction to the deformation theory of Galois representations and its role in modularity lifting. This will motivate the study of local deformation rings and more specifically flat deformations. Next, we will discuss Kisinâs resolution of the flat deformation ring at l = p and describe conceptually the importance of local models of Shimura varieties in analyzing its geometry. In the remaining time, we will address the title of the talk; the additional structure we consider could be a symplectic form, an orthogonal form, or more generally any reductive subgroup G of GL_N. I will describe briefly the role that recent advances in p-adic Hodge theory and local models of Shimura varieties play in this situation" |
February 13, 2013, 3:00 - 4:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Babak Haghighat (HARVARD UNIVERSITY PHYSICS) |
Conifold transitions in Calabi-Yau fourfolds and 3D gauge theories |
Organized by Prof. Shing-Tung Ya" |
February 12, 2013, 4:15 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Mboyo Esole (HARVARD UNIVERSITY) |
The Geometry of Elliptic Fibrations, a String Theory Perspective |
Since the introduction of F-theory by Cumrun Vafa in 1996, string theorists have been looking at the geometry of elliptic fibrations over higher dimensional bases from a completely different perspective leading to surprising results and conjectures. I will present an overview of these ideas and discuss the most recent mathematical results. No prior knowledge of string theory is assumed" |
February 11, 2013, 3:00 PM at Science Center 507 |
| TRIVIAL NOTIONS SEMINAR |
Erick Knight (HARVARD UNIVERSITY) |
Rationality of del Pezzo Surfaces |
In part two of the Eric(k) barrage, del Pezzo surfaces are the central objects. Del Pezzo surfaces are algebraic surfaces whose anti canonical bundle is ample. Over an algebraically closed field, all such surfaces whose anti canonical bundle is ample. Over an algebraically closed field, all such surfaces are rational. However, over non closed fields, the question of rationality is a subtle one and difficult to answer in general. This talk will focus mainly on cubic surfaces, and a couple of criteria to not be rational. If there is time, double covers of P 2 will be discussed as well" |
February 07, 2013, 1:00 - 2:00 PM at Science Center 310 |
| PROBABILITY SEMINAR |
Jason Miller (MIT) |
Imaginary Geometry and the Gaussian Free Field |
The Schramm-Loewner evolution (SLE) is the canonical model of a non-crossing conformally invariant random curve, introduced by Oded Schramm in 1999 as a candidate for the scaling limit of loop erased random walk and the interfaces in critical percolation. The development of SLE has been an exciting area in probability theory over the last decade because Schrammâs curves have now been shown to arise as the scaling limit of the interfaces of a number of different discrete models from statistical physics. In this talk, I will describe how SLE curves can be realized as the flow lines of a random vector field generated by the Gaussian free field, the two-time-dimensional analog of Brownian motion, and how this perspective can be used to study the sample path behavior of SLE. This talk is based on joint work with Scott Sheffield" |
February 07, 2013, 3:00 PM at Science Center 232 |
| NUMBER THEORY SEMINAR |
Bjorn Poonen (MIT) |
Most odd degree hyperelliptic curves have only one rational point |
We prove that the probability that a curve of the form y^2 = f(x) over Q with deg f = 2g+1 has no rational point other than the point at infinity tends to 1 as g tends to infinity. This is joint work with Michael Stoll" |
February 06, 2013, 3:00 - 4:00 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Diana Davis (BROWN UNIVERSITY) |
Cutting sequences on Bouw-Moeller surfaces |
We will investigate a dynamical system that comes from geodesic paths on flat surfaces. We will start with the square torus and the octagon, and then consider a large family of flat surfaces called Bouw-Moeller surfaces, made by gluing together many polygons" |
February 06, 2013, 4:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Gao Da-Peng *NEW SPEAKER* (SIMONS CENTER FOR GEOMETRY & PHYSICS, STONY BROOK UNIVERSITY) |
Asymptotic spectrum of winding states in large volume Calabi-Yau sigma models |
We conjecture that a non-flat D-real-dimensional compact Calabi-Yau manifold, such as a quintic hypersurface with D=6, or a K3 manifold with D=4, has locally length minimizing closed geodesics, and that the number of these with length less than L grows asymptotically as L^{D}. An outline of the physical arguments behind this conjecture is given, which involve the claim that all states in a nonlinear sigma model can be identified as" |
February 05, 2013, *NEW TIME* 1:30 PM at *NEW LOCATION* Science Center 232 |
| BASIC NOTIONS SEMINAR |
Dan Stroock (MIT) |
Randomness and Regularity |
Intuitively speaking, the more random a random variable is, the more regular is its distribution. Unfortunately, this intuition is only approximately correct and is often misleading. On the other, there are circumstances in which it is not only correct but even the origin of a rigorous proof. In this lecture I will show how it can be used to prove that, for any k >1, the highly degenerate heat equation \partial_t u = \partial_{x_1}^2 u + x_1^k \partial_{x_2} u admits a smooth fundamental solution. The existence of such fundamental solution can be proved as an application of L. Hormander s renowned hypoellicity theorem. However, the probabilistic approach has intuitive appeal that more purely analytic proofs lack" |
February 04, 2013, 3:00 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
R. Inanc Baykur (MAX PLANCK INSTITUTE) |
Topological Complexity of Symplectic 4-manifolds and Stein fillings |
Following the ground-breaking works of Donaldson and Giroux, Lefschetz pencils and open books have become central tools in the study of symplectic 4-manifolds and contact 3-manifolds. An open question at the heart of this relationship is whether or not there exists an a priori bound on the topological complexity of a symplectic4-manifold, coming from the genus of a compatible Lefschetz pencil on it, and a similar question inquires if there is such a bound on any Stein filling of a fixed contact 3-manifold, coming from the genus of a compatible open book. We will present our solutions to both questions, making heroic use of positive factorizations in surface mapping class groups of various flavors. This is joint work with J. Van Horn-Morris" |
February 01, 2013, 3:30 PM at Science Center 507 |
| TRIVIAL NOTIONS SEMINAR |
Eric Riedl (HARVARD UNIVERSITY) |
Brauer Groups |
The Brauer Group is an algebraic object with geometric significance. It classifies projective bundles over a base space and is related to central simple algebras. In this talk, we will first talk about what Brauer Groups are, then see one example of how they can be used to understand maps from genus 0 curves to Brauer-Severi varieties" |
January 31, 2013, 1:00 PM at SC 310 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Oleg Ivrii (HARVARD UNIVERSITY) |
Completing the Cardioid |
Recently, McMullen showed that the Weil-Petersson metric on Teichmueller space is the double derivative of the Hausdorff dimension of families of quasi-circles arising from simultaneous uniformization. He noticed that a similar construction can be carried out on spaces of Blaschke products; and so by analogy, one can define a Weil-Petersson metric there. In this talk, we will show that the Weil-Petersson metric is incomplete and describe its completion" |
January 30, 2013, 4:00 - 5:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Si Li (BOSTON UNIVERSITY) |
The Quantum Theory of Landau-Ginzberg B-model |
Given a quasi-homogeneous polynomial with isolated singularity, I will describe a construction of quantum intersection theory on the Jacobian ring via a rigorous perturbative renormalization of a twisted version of Kodaira-Spencer gauge theory. This gives a mathematical theory of Landau-Ginzburg B-model at higher genus, which is expected to mirror to the FJRW theory of orbifold Landau-Ginzburg A-model at all genera. --Organized by Prof. Shing-Tung Ya" |
January 29, 2013, 4:15 PM at Science Center 507 |
| PROBABILITY SEMINAR |
Gaetan Borot (UNIVERSITY OF GENEVA) |
All-order asymptotic of beta ensembles in the multi-cut regime |
The asymptotic behavior for the partition function and various statistics in the one hermitian matrix model has been intensively studied in the past decades. When the eigenvalues condensate on a single segment of the real line, one expects asymptotic expansions in powers of 1/N^2, where N denotes the size of the matrix. Physicists know this under the name of topological expansion since the 70s, and have developed algebro-geometric tools to compute them, culminating in the topological recursion of Eynard and Orantin. From the probabilistic point of view, the existence of such an expansion has been established for off-critical, real-analytic potential by Albeverio, Pastur, Shcherbina (and we will assume those conditions as well). The asymptotic behavior is different when the eigenvalues condensate on several disjoint segments (the so-called multi-cut regime), due to possible tunneling of eigenvalues between the segments. Interferences appear, and most quantities are now expected to have an expansion in 1/N, whose coefficients themselves are bounded functions of N with fast oscillations, given by Theta functions and their derivatives. The heuristic derivation of this behavior has been proposed by Bonnet, David and Eynard. In a joint work with Alice Guionnet, we show how to prove such asymptotic expansions to all orders, by combining rough probabilistic estimates with the analysis of Schwinger-Dyson equations. As a first consequence, we can obtain the all-order asymptotic expansion of orthogonal polynomials outside of the cuts, and of their recurrence coefficients. Our methods provides an alternative to the Riemann-Hilbert techniques to study the leading order, allow more easily to tackle the subleading orders. They also have a wider range of applicability, since they work same in all beta ensembles, where eigenvalues repel each other like the \beta-power of the distance, and the values \beta = 1,2,4 related to integrability have nothing special to this respect" |
January 25, 2013, 2:00 PM at Science Center 232 |
| NUMBER THEORY SEMINAR |
Benson Farb (UNIVERSITY OF CHICAGO) |
The cohomology of SL(n,Z) and its congruence subgroups |
In this talk I will discuss the basic problem of computing the object in the title. Outside the Borel Stability Theorem (proved in the early 70 s), few explicit computations are known except for small n. For large n, we haven t even had a conjectural picture to shoot for. My goal in this talk is to describe some new patterns, some conjectured and some proved, in the cohomology of SL(n,Z) and its congruence subgroups. If time permits I will describe the analogy with the cohomology of the moduli space of Riemann surfaces. This is joint work with Tom Church and Andy Putman, and also with Church, Jordan Ellenberg and Rohit Nagpal" |
December 12, 2012, 3:00 - 4:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Ivan Petrakiev () |
On the homogeneous interpolation problem |
I would like to report some recent results on the homogeneous interpolation problem in p2. Denote by L(d,n,m) the linear system of plane curves of degree d passing through n general points with multiplicity at least m. The classical Nagata s conjecture predicts that, if n ≥ 10 and L(d,n,m) is nonempty, then d/m > \sqrt(n). I will show that, if n=10 and L(d,n,m) is nonempty, then we must have d/m ≥ 2280/721, which is ≈3.0*10-6 away from the conjectured bound" |
December 11, 2012, 3:00 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
John Baldwin (BOSTON COLLEGE) |
A bordered monopole Floer theory |
I ll discuss work-in-progress toward constructing monopole Floer theoretic invariants of bordered 3-manifolds. Roughly, our construction associates an A-infinity algebra to a surface, an A-infinity module to a bordered 3-manifold, and a map of A-infinity modules to a 4-dimensional cobordism of bordered 3-manifolds. I ll focus on the topological and algebraic aspects of our work and, in particular, will indicate how we prove a pairing theorem relating the invariants of two bordered 3-manifolds with that of the manifold obtained by gluing the former together along homeomorphic components of their boundaries. This is joint work with Jon Bloom" |
December 07, 2012, 3:30 PM at Science Center 507 |
| TRIVIAL NOTIONS SEMINAR |
Pei-Yu (HARVARD UNIVERSITY) |
Local new forms for GL(n) |
The L-functions have very good analytic properties and provide abundant arithmetic invariants. In the theory of holomorphic modular forms, one can associate to a Hecke eigenform an L-function. Such an L-function has the Euler product formula and we can hence study what happens at each prime. It is known that those Hecke eigenforms which are newforms can associate to a compatible family of smooth representations of PGL(2,Q_p). We will start from such a representation and study how to find a special element in it to recover back the L-function, or the new form. The key result is that such a new form is arisen from the invariant vectors of Gamma_0(p^m) in the smooth representation of PGL(2,Q_p). The level p^m can be as small as the conductor and the L-function can be recovered by taking zeta integral on a specific invariant vector at this smallest level. This beautiful new form theory has been proven by Casselman in 1970s but people used to have a hard time finding the correct congruence subgroups for more general groups. I will show the generalization to PGL(n) by Jacquet, Piatetski-Shapiro and Shalika to demonstrate the idea of what a possible strategy one can consider to form such a new form theory for general groups. If time permits, I will comment on the generalization to the B_n case, which is my work in progress" |
December 06, 2012, 1:30 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
John Hamal Hubbard (UNIVERSITé DE PROVENCE/CORNELL UNIVERSITY) |
On Hubbard trees, etc. |
" |
December 05, 2012, 4:00 - 5:00 PM at Science Center 507 |
| HARVARD/MIT LOGIC SEMINAR |
Max Weiss (UNIVERSITY OF BRITISH COLUMBIA/HARVARD UNIVERSITY) |
The Logic of the Tractatus |
In his 1921 book the Tractatus, Wittgenstein proposed that every sentence of a language can be represented as the joint denial of some specifiable multiplicity of sentences. Such a representation would determine well-founded ancestries for all sentences, terminating only in sentences whose truth-conditions are fixed independently. The complexity of languages which can be analyzed in this way depends on the strength of the condition that a multiplicity of sentences be specifiable. A natural suggestion is that a multiplicity is specifiable if it is r.e. However, this leads to a computationally intractable syntax. So, we develop a finer analysis of specifiability, based on schematization and iterated substitution. The resulting system strictly extends FOL=, in particular by expressing the concept of transitive closure. This is work in progress, and we conclude with some open questions" |
December 05, 2012, 4:00 PM at Science Center, Rm B-10 |
| NUMBER THEORY SEMINAR |
Tasho Kaletha (INSTITUTE FOR ADVANCED STUDY) |
Epipelagic L-packets and rectifying characters |
We will report on a construction of the local Langlands correspondence for general tamely-ramified p-adic groups and a class of wildly ramified supercuspidal Langlands parameters that have emerged in recent works of Gross-Reeder and Reeder-Yu. The ramification of these parameters introduces two new arithmetic phenomena which were not present in the case of real groups or in the case of tamely-ramified supercuspidal parameters for p-adic groups. We will discuss how these phenomena can be handled and, time permitting, we will give an indication of how the various compatibilities expected of a Langlands correspondence are proved. These include in particular Shahidi s tempered L-packet conjecture, stability, endoscopic transfer, and compatibility with GL_n" |
December 05, 2012, 3:00 - 4:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Giulia Sacca (PRINCETON UNIVERSITY) |
Abelian fibrations from Enriques surfaces |
I will talk about two constructions associating to a linear system on an Enriques surface a fibration in abelian varieties. The first one is the relative compactified Jacobian of the linear system which (in some cases) leads to a smooth odd dimensional Calabi-Yau variety. The second construction (joint work with E. Arbarello and A. Ferretti) is a fibration in Prym varieties and the total space is a singular symplectic variety. I will discuss when these singular symplectic varieties admit a symplectic resolution and show that, when they do, they are deformation equivalent to Hilbn(K3)" |
December 04, 2012, 3:00 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Cumrun Vafa (HARVARD UNIVERSITY) |
Scattering Calabi-Yau Manifolds |
A large class of toric Calabi-Yau threefolds can be described by cubic Feynman graphs. Evaluation of such Feynman graphs corresponds to computing partition function of superconformal theories, and is related to integration over Kahler moduli in the Gromov-Witten theory" |
December 03, 2012, 3:00 PM at Science Center 507 |
| PROBABILITY SEMINAR |
Tanya Shcherbina (INSTITUTE FOR ADVANCED STUDY) |
Universality of the local regime of characteristic polynomials of the 1D Gaussian band matrices |
" |
November 29, 2012, 3:00 PM at Science Center 232 |
| TRIVIAL NOTIONS SEMINAR |
Ryosuke Takahashi (HARVARD UNIVERSITY) |
Maximum Principle for Second Order Fully Nonlinear Elliptic Equations |
The theory of linear or quasi-linear elliptic PDEs has been established for almost a century. However, the developement of the theory for fully nonlinear PDEs is relatively new and difficult. In 1980, L. Evans defined an important type of solutions of fully nonlinear equations which is called viscosity solutions. This new type of solutions was soon studied by M. Crandall, Pierre-Louis Lions and L. Caffarelli and had fertile results. In this talk, I will state the definition of viscosity solutions and show you some comparison theorems and maximum principle of these solutions" |
November 29, 2012, 1:30 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Stefan Patrikis (PRINCETON UNIVERSITY) |
Variations on a theorem of Tate |
Let F be a number field. Tate showed that projective representations of the absolute Galois group of F necessarily lift to actual representations. This talk will discuss some refinements of this result, as well as automorphic and motivic analogues. The automorphic variant is most interesting when one considers its interaction with algebraicity of automorphic representations. The motivic variant leads to a (mostly conjectural) generalization and arithmetic refinement of the classical construction of Kuga-Satake that associates to any complex K3 surface a complex abelian variety." |
November 28, 2012, 3:00 - 4:00 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Yutaka Ishii (KYUSHU UNIVERSITY) |
Trinitas for the Henon Map |
In this talk I relate several combinatorial descriptions of the Julia sets for hyperbolic polynomial diffeomorphisms of C^2: quotients of solenoids by Bedford and Smillie, quasi-automata by Oliva, and Hubbard trees by myself. The notion of iterated monodromy groups, originally introduced for partial self-coverings of arcwise connected spaces, are defined for such polynomial diffeomorphisms and are used to construct quasi-automata from Hubbard trees" |
November 27, 2012, 4:00 - 5:00 PM at Science Center 530 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Koushik Pal (UNIVERSITY OF MARYLAND, COLLEGE PARK) |
Unstable theories with an automorphism |
Kikyo and Shelah showed that if T is a first-order theory in some language L with the strict-order property, then the theory Tσ, which is the old theory T together with an L-automorphism σ, does not have a model companion in Lσ, which is the old language L together with a new unary predicate symbol σ. However, it turns out that if we add more restrictions on the automorphism, then Tσ can have a model companion in Lσ. I will show some examples of this phenomenon in two different context --- the linear orders and the ordered abelian groups. In the context of the linear orders, we even have a complete characterization of all model complete theories extending Tσ in Lσ. This is joint work with Chris Laskowski" |
November 27, 2012, 4:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Yefeng Shen (UNIVERSITY OF MICHIGAN) |
Gromov-Witten theory and cycle-valued modular forms |
A remarkable phenomenon in Gromov-Witten theory is the appearance of (quasi)-modular forms. For example, Gromov-Witten generating functions for elliptic curve, local P2,elliptic orbifold P1 are all (quasi)-modular forms. In this talk, we will discuss modularity property of the Gromov-Witten cycles of elliptic orbifold P1. Since Gromov-Witten cycles live in the cohomology space of moduli of pointed curves, our result gives a geometric realization of a collection of vector-valued (quasi)-modularity forms via Gromov-Witten theory. This work is joint with Todor Milanov and Yongbin Ruan. --Organized by Professor Shing-Tung Ya" |
November 27, 2012, 1:30 - 3:00 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Sukhada Fadnavis (HARVARD UNIVERSITY) |
A Generalization of the Birthday Problem |
The birthday problem states that there is at least half a chance that some two out of twenty-three randomly chosen people will share the same birth date. The calculation for this problem assumes that all birth dates are equally likely. What if the distribution of birth dates is non-uniform and possibly even unknown? Further what if we focus on birthdays shared by two friends rather than any two people? I will present some of our results and conjectures in this generalized setting. I will also show how these results are related to the Stanley-Stembridge poset chain conjecture and the shameful conjecture , two famous conjectures in combinatorics" |
November 26, 2012, 3:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Yaim Cooper (PRINCETON) |
Stable quotients and stable maps: A comparison |
In this talk we will discuss recent results comparing stable quotients and stable maps. We will compare the geometry of the moduli spaces themselves, and also compare the invariants they can be used to define. Specifically, in genus 1 we compare the geometries of M̅1(Pr,d) and Q̅1(Pr,d), and in genus 0 we compare the stable quotient invariants of Fano and Calabi-Yau complete intersections in Pr to the corresponding Gromov-Witten invariants. The latter represents joint work with A. Zinger" |
November 20, 2012, 3:00 - 4:00 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Ngo Viet Trung (HANOI) |
Cohen-Macaulayness of monomial ideals |
I will present a criterium for the Cohen-Macaulayness of a monomial ideal in terms of its primary decomposition. These criteria allow us to use tools of of integer programming to study the Cohen-Macaulayness of monomial ideals which are intersections of powers of prime ideals. As a consequence, we can characterize the Cohen-Macaulayness of every symbolic or ordinary power of a Stanley-Reisner ideal in terms of the simplicial complex. In particular, an ordinary or symbolic power of exponent larger than 2 is Cohen-Macaulay if and only if the simplicial complex is a complete intersection or a matroid, respectively" |
November 20, 2012, 4:30 - 5:30 PM at Science Center 507 |
| PROBABILITY SEMINAR |
Alice Guionnet (MIT) |
About Heavy Tailed Random Matrices |
" |
November 20, 2012, 3:00 PM at Science Center 232 |
| BASIC NOTIONS SEMINAR |
Emily Riehl (HARVARD UNIVERSITY) |
Weighted limits and colimits |
A mathematical object can be completely characterized by a description of the morphisms to or from it qua object of a particular category. Indeed, it is often productive to define an object by means of its universal property, eg, as a limit or colimit of a specific shape. In this talk, we ll introduce, via examples, a more robust notion of shape for a limit or colimit. The corresponding weighted notions of limit and colimit are indispensible for categories whose hom-sets admit some sort of additional structure, but these concepts are productive in the unenriched context as well because they enhance the collection of tools available to define objects with made-to-order universal properties. We will focus in particular on an example with wide applications in algebra and beyond, characterizing the category of algebras for a monad as a weighted limit and using this universal property to replace the classical monadicity theorem with a simple calculation involving the weights. The extension of these results to the quasi-categorical (i.e., oo-categorical) context is joint work with Dominic Verit" |
November 19, 2012, 3:00 PM at Science Center 507 |
| HARVARD, BRANDEIS, MIT, NORTHEASTERN COLLOQUIUM AT HARVARD |
Tom Church (STANFORD UNIVERSITY) |
Representation theory and homological stability |
Homological stability is the remarkable phenomenon where for certain sequences X_n of groups or spaces -- e.g. the special linear group SL(n,Z), the braid group B_n, or the moduli space M_n of genus n Riemann surfaces -- the homology groups H_i(X_n) do not depend on n once n is large enough. But for many analogous sequences, from pure braid groups to congruence matrix groups to Torelli groups, homological stability fails horribly, and H_i(X_n) blows up to infinity. In many of these cases we know very little concretely about H_i(X_n), and it s possible there is no nice closed form for the answers. Representation stability is a program that extends homological stability to situations like these where it s false, by taking the action of symmetry groups into account. This makes it possible to meaningfully talk about the stable homology of the pure braid group or the stable homology of the Torelli group even though the homology never stabilizes. However, it turns out that representation stability is also useful elsewhere in math: it lets us prove and explain a polynomial behavior in the dimensions of vector spaces arising in algebra/combinatorics (coinvariant algebras, free Lie algebras, spaces of harmonic polynomials, etc.) as well as in topology (cohomology of spaces of configurations in a manifold, of pointed curves, of bounded-rank matrices, etc.). Joint work with Benson Farb, Jordan Ellenberg, and Rohit Nagpal" |
November 15, 2012, 4:30 PM at Science Center Hall A |
| TRIVIAL NOTIONS SEMINAR |
Nathan Pflueger (HARVARD UNIVERSITY) |
Rational Normal Scrolls |
" |
November 15, 2012, 1:30 - 2:30 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Stergios Antonakoudis (HARVARD UNIVERSITY) |
On the non-existence of super-Teichmueller disks |
The Bers embedding presents Teichmueller space as a bounded domain in $\mathbb{C}^n$. The complex geodesics (for the Kobayashi metric) provide holomorphic isometric embeddings from the unit ball in $\mathbb{C}$ into the Teichmueller space $T_{g,n}$, called Teichmueller disks. In this talk we will show that super-Teichmueller disks do not exist : If $\Omega$ is a bounded symmetric domain of dimension at least two, then there exists no holomorphic isometry from $\Omega$ into $T_{g,n}$" |
November 14, 2012, 4:00 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Ngo Bao Chau (UNIVERSITY OF CHICAGO) |
Geometric interpretation of automorphic L-functions |
I will recall how automorphic L-functions can be interpreted as a trace and how they appear in the trace formula for certain non-standard test functions. I will also explain how this may be geometrically interpreted in terms of certain moduli space" |
November 14, 2012, 3:00 - 4:00 PM at Science Center 507 |
| PROBABILITY SEMINAR |
Craig A. Tracy (UC DAVIS) |
Bethe Ansatz Methods in Stochastic Integrable Models |
The asymmetric simple exclusion process (ASEP) is not of determinantal class, but it is integrable in the sense that Bethe Ansatz methods lead to an explicit formula for the transition probability for N-particle ASEP. We sketch the proof of this fact. Two variations of ASEP are multispecies ASEP (first, second, etc. class particles) and ASEP on the semi-infinite lattice {1, 2, . . .}. In both cases the standard Bethe Ansatz has to be modified in order to compute the transition probability of the N-particle system. We explain these modifications and indicate how the proof of the main result is changed. This is joint work with Harold Widom." |
November 13, 2012, 1:00 PM at Science Center 232 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Frank Bauer (HARVARD UNIVERSITY) |
On the spectrum of Laplace operators on graphs |
In this talk I will study the spectrum of Laplace operators on graphs. In particular I will focus on the largest eigenvalue of these operators. I will introduce a new graph invariant called the dual Cheeger constant that yields bounds for the largest eigenvalue which are analogous to the bounds for the smallest eigenvalue in terms of the Cheeger constant. Moreover, I will introduce a technique that establishes a connection between estimates for the largest and the smallest eigenvalue by means of random walks on graphs. As one example, I will show how this method can be used to improve known eigenvalue estimates in terms of Ollivier s Ricci curvature. If time permits, I will also talk about the connection of the dual Cheeger constant and the essential spectrum of a graph. --Organized by Professor Shing-Tung Ya" |
November 13, 2012, 4:15 PM at Science Center 507 |
| HARVARD/MIT LOGIC SEMINAR |
Rod Downey (VICTORIA UNIVERSITY WELLINGTON) |
The computability theory of the Finite Intersection Principle |
A family of sets F has the Finite Intersection Property (FIP) if the intersection of any finite subfamily is nonempty. The FIP principle says that any collection of sets has a maximal subcollection with FIP. The reverse maths and effective content of this principle, classically equivalent to choice, was initiated by Dzharfarov and Mummert. They showed, for instance, that there is a computable family with no computable maximal FIP subfamily. We say that a degree a is FIP iff it has the ability to compute a solution to any computable instance of FIP. Dzharfarov and Mummert s result says that 0 is not FIP. Dzharfarov and Mummert showed that each nonzero c.e. degree is FIP, all FIP degrees are hyperimmune, and several classes of 1-generics degree were FIP. We extend these investigations by giving new (shorter) proofs of some of Dzharfarov and Mummert s work, and also showing that all 1-generics are FIP, and showing that, for the degrees below 0 , the FIP degrees are precisely the ones that bound 1-generic degrees. We could hope that this characterization extends to the general hyperimmune case, since hyperimmune degrees resemble those below 0 . However, we can also show that there is a minimal FIP degree that is below 0 . This last result has some technical complexity as it is a full approximation argument constructing a hyperimmune degree below 0 , which does not seem to have occurred in the literature hitherto. Joint work with Diamondstone, Greenberg, and Turetsky." |
November 09, 2012, 3:30 PM at Science Center 411 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Rosa Sena-Dias (INSTITUTO SUPERIOR TECNICO) |
Non-compact scalar-flat K\"ahler toric metrics and their energy |
I will talk about a concrete family of scalar-flat K\ahler toric metrics on non-compact toric surfaces. These generalize some well know Ricci-flat metrics with toric symmetry: the so-called gravitational instantons of Gibbons-Hawking and Kronheimer as well as the Taub-NUT metric. After giving some background and introducing these metrics, I hope to discuss the relation with some recent developments in K\ahler geometry" |
November 09, 2012, 3:30 - 4:30 PM at Science Center 507 |
| PROBABILITY SEMINAR |
Elizabeth Meckes (CASE WESTERN RESERVE UNIVERSITY) |
The spectra of powers of random unitary matrices |
It has long been recognized that the eigenvalues of random unitary matrices look very different from i.i.d. points on the circle: they are very evenly spaced. As you start raising a random unitary matrix to powers, the eigenvalues start to clump together, and by the time you raise a random matrix in U(N) to the Nth power, the eigenvalues look exactly like i.i.d. points on the circle. There is a good reason for this: Rains showed that the distributions are exactly the same, and that there is a kind of smooth interpolation between the two extremes. In joint work with M. Meckes, we quantify this phenomenon by proving sharp non-asymptotic estimates on the means and tails of the L_p Wasserstein distances between spectral measures of powers of random unitary matrices and the uniform measure on the circle. The bounds also allow us to obtain sharp almost-sure convergence rates as the size of the matrix tends to infinity. Along the way, we needed the long-suspected fact that the full unitary group satisfies the same type of log-Sobolev inequality as the special unitary group; I will sketch the proof of this result, which should be of independent interest" |
November 08, 2012, 3:00 PM at Science Center 232 |
| TRIVIAL NOTIONS SEMINAR |
Jeffrey Kuan (HARVARD UNIVERSITY) |
The representation theory and combinatorics behind random partitions |
Various models of random partitions have shown connections to other topics in probability and mathematical physics, such as random matrices and universality of growth processes. We will introduce and motivate a few of these models, and also explain their relationship to the representation theory of symmetric groups and classical Lie groups." |
November 08, 2012, 1:30 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Robert Guralnick (UNIVERSITY OF SOUTHERN CALIFORNIA) |
E8(p) is a Galois group over Q |
Recently, Zhiwei Yun answered a conjecture of Serre showing that E8 is a motivic Galois group over Q. This has the consequence that E8(p) is a Galois group over Q for all but finitely many p. However, the proof did not determine how big one needed to go. Yun suggested that using rigidity with three specific classes should enable a more specific result. Malle and I showed that in fact E8(p) is a Galois group over Q for all p > 5 (i.e. for all good primes). The proof depends on some new results in the character theory of finite reductive groups as well as some new results about subgroups of exceptional groups containing regular unipotent elements. I will discuss some of the ideas and results involved in the proof" |
November 07, 2012, 3:00 - 4:00 PM at Science Center 506 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Matt Bainbridge (INDIANA UNIVERSITY) |
Effective Veech dichotomy |
The Veech dichotomy tells us that the geodesic flow on certain very symmetric flat surfaces has very well-behaved dynamics: every orbit is either periodic or uniformly distributed. In this talk, I will discuss a more effective strengthening of this dichotomy in some cases. The proof involves geometry of numbers and diagonal flows on homogeneous spaces over the Adeles. This is joint work with Martin Moller" |
November 07, 2012, 4:00 - 5:00 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Eric Zaslow (NORTHWESTERN UNIVERSITY) |
Skeleta for Affine Hypersurfaces |
Any smooth affine hypersurface Z of complex dimension n deformation retracts to a cell complex of real dimension n. Starting from the Newton polytope of the defining function, I will give an explicit combinatorial construction of a compact space S, comprised of n-dimensional components, which embeds into Z as a deformation retract. In particular, Z is homotopy equivalent to S. If time allows, I will discuss the relation of this work to the homological mirror symmetry program. This work is joint with Helge Ruddat, Nicolo` Sibilla, and David Treumann. Note: I will be giving the same talk at MIT on the previous day. If there is significant audience overlap, I will adjust accordingly -- e.g., expanding the mirror symmetry discussion. -- Organized by Professor Shing-Tung Ya" |
November 06, 2012, 4:15 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
John Lesieutre (MIT) |
A divisor with non-closed restricted base locus |
I will explain how to construct a pseudoeffective divisor Dλ on the blow-up of P3 at nine very general points which has negative intersections with a set of curves whose union is Zariski dense. It follows that the restricted base locus B-(Dλ) = ∪A ample B(Dλ+A) is not closed and that Dλ does not admit a Zariski decomposition in even a very weak sense" |
November 06, 2012, 3:00 PM at Science Center 507 |
| PROBABILITY AND ANALYSIS SEMINAR |
Hao Jia (UNIVERSITY OF MINNESOTA) |
On scale-invariant solutions to Navier Stokes equation |
Navier Stokes equation has a natural scaling invariance. In this talk I will report on a recent result with Vladimir Sverak that, under natural assumptions every scale-invariant initial data gives global scale-invariant solution to Navier Stokes equation. We do not assume smallness condition on the initial data. The connection with possible non-uniqueness of Leray-Hopf weak solutions will also be discussed" |
November 06, 2012, 1:30 PM at Science Center 232 |
| HARVARD/MIT LOGIC SEMINAR |
Maryanthe Malliaris (UNIVERSITY OF CHICAGO) |
Cofinality spectrum problems in model theory, set theory and general topology |
Recent work of Malliaris and Shelah on model-theoretic questions around saturation of regular ultrapowers has led also to theorems in set theory and general topology, notably the solution of the oldest problem on cardinal invariants of the continuum. The talk will outline the general program and some features of this recent proof" |
November 05, 2012, 4:00 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Gabor Lippner (HARVARD UNIVERSITY) |
Invariant perfect matchings in Cayley graphs |
Measurable graph theory lies at the crossroads of combinatorics and ergodic theory. Results in this field are often related to random processes on discrete groups. I will apply this connection to prove the existence of random perfect matchings with translation invariant distribution in Cayley graphs. In particular we will see that for non-amenable groups such a matching can be constructed as a factor of IID. The key step of the proof is showing that one can always find short augmenting paths in an expander" |
November 05, 2012, 3:00 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Joshua Batson (MIT) |
A link splitting spectral sequence in Khovanov Homology |
The Khovanov homology of a link L is a bigraded abelian group Kh(L) with Poincaré polynomial P_L(q,t), such that P(q,-1) recovers the Jones polynomial. The meaning of the group Kh(L) is topologically obscure, since its definition is resolutely combinatorial, but a suite of spectral sequences abutting to more manifestly three-dimensional homology theories provide some traction. The spectral sequence to singular instanton homology shows that P_L detects the unknot, and the one to Heegaard Floer of the branched double cover shows that P_L detects the two-component unlink. We construct a new spectral sequence from Kh(L) to the tensor product $\otimes_i Kh(K_i)$ of the Khovanov homologies of the components K_1,...,K_n of L. From this we show that P_L detects the n-component unlink for any n, and construct a novel bound on the number of between-component crossing changes required to split a link. This work is inspired by a conjectured spectral sequence in the symplectic theory of Seidel-Smith. Project joint with Cotton Seed" |
November 02, 2012, 3:30 - 4:40 PM at Science Center 507 |
| SPECIAL SEMINAR |
Fan Chung Graham (UC SAN DIEGO) |
Can you hear the shape of a network? New directions in spectral graph theory |
We will discuss some recent developments in several new directions of spectral graph theory, including random walks for directed graphs, graph partitioning and clustering, PageRank methods, graph gauge theory, graph limits and graphlets." |
November 01, 2012, 1:30 PM at Science Center 232 |
| TRIVIAL NOTIONS SEMINAR |
Oleg Ivrii (HARVARD UNIVERSITY) |
Moduli of Curves |
We survey several notions of moduli of curve families and give some applications to conformal mapping of simply-connected and multiply-connected domains" |
November 01, 2012, 1:30 - 2:30 PM at Science Center 507 |
| SPECIAL SEMINAR |
Dan Mangoubi (HEBREW UNIVERSITY) |
Convexity properties of harmonic functions on Riemannian manifolds |
We extend Agmon s theorem on a convexity property of harmonic functions in R^n to convexity property of harmonic functions on Riemannian manifolds. We discover that in pinched negative curvature one has better behavior than in non-negative curvature. We apply the convexity of harmonic functions to give a simple proof of the growth bound on Laplace eigenfunctions on compact manifolds with new curvature-related estimates. -- Organized by Professor Shing-Tung Ya" |
October 31, 2012, 3:00 PM at Science Center 232 |
| **POSTPONED** NUMBER THEORY SEMINAR |
Tasho Kaletha (INSTITUTE FOR ADVANCED STUDY) |
Epipelagic L-packets and rectifying characters |
*check back for rescheduled date* We will report on a construction of the local Langlands correspondence for general tamely-ramified p-adic groups and a class of wildly ramified supercuspidal Langlands parameters that have emerged in recent works of Gross-Reeder and Reeder-Yu. The ramification of these parameters introduces two new arithmetic phenomena which were not present in the case of real groups or in the case of tamely-ramified supercuspidal parameters for p-adic groups. We will discuss how these phenomena can be handled and, time permitting, we will give an indication of how the various compatibilities expected of a Langlands correspondence are proved. These include in particular Shahidi s tempered L-packet conjecture, stability, endoscopic transfer, and compatibility with GLn" |
October 31, 2012, at |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Andres Sambarino (UNIVERSITE PARIS-SUD, ORSAY) |
Convexity and counting |
We will show precise counting results for a class of discrete subgroups of SL(d,\R). This class contains Hitchin representations of surface groups and groups dividing a strictly convex set of P(\R^d)" |
October 31, 2012, 4:00 - 5:00 PM at Science Center 507 |
| SPECIAL PROBABILITY SEMINAR |
Jürg Fröhlich (ETH ZÜRICH) |
What is it that is confusing about Quantum Mechanics |
I will sketch a general algebraic formalism unifying classical and quantum physics. Among other purposes, this formalism serves to highlight the fundamental differences between classical and quantum theories of Nature. I will then attempt to clarify what it is that quantum theories tell us about Nature - in other words, what kind of a theory of Nature quantum mechanics is. With a little luck, I will be able to identify what it is that people find confusing about quantum mechanics and then explain why there is no reason to be confused about this wonderful theory. *Jointly organized by H.T. Yau and Arthur Jaffe" |
October 30, 2012, 1:30 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Yu-Shen Lin (HARVARD UNIVERSITY) |
Discs Counting on Elliptic K3 Surfaces and Wall-Crossing |
Strominger-Yau-Zaslow conjecture suggests that the Ricci-flat metric on Calabi-Yau manifolds might be related to holomorphic discs. In this talk, I will define a new open Gromov-Witten invariants on elliptic K3 surfaces. The new invariant satisfies certain wall-crossing formula and multiple cover formula. I will also establish a tropical-holomorphic correspondence. Moreover, this invariant is expected to be equivalent to the generalized Donaldson-Thomas invariants in the hyperKahler metric constructed by Gaiotto-Moore-Neitzke. Organized by Professor Shing-Tung Ya" |
October 30, 2012, 4:15 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Fan Chung Graham (UC SAN DIEGO) |
Can you hear the shape of a network? - New directions in spectral graph theory |
" |
October 29, 2012, 3:00 PM at Science Center 507 |
| PROBABILITY SEMINAR |
Louis Pierre Arguin (MONTREAL UNIVERSITY) |
Poisson-Dirichlet statistics for the extremes of log-correlated Gaussian fields |
" |
October 26, 2012, 1:30 PM at Science Center 232 |
| HARVARD, BRANDEIS, MIT, NORTHEASTERN COLLOQUIUM AT HARVARD |
Laura DeMarco (UNIVERSITY OF ILLINOIS, CHICAGO) |
Special Curves and postcritically-finite polynominals |
Questions about complex dynamical systems have traditionally been approached with techniques from analysis (complex or geometric). In the last 5 years or so, methods from arithmetic and algebraic geometry have begun to play a central role -- and the result is an active new research area, the arithmetic of dynamical systems (to borrow the title of Silverman s textbook on the subject). The questions themselves have evolved, inspired by results from arithmetic geometry. In this talk, I will present new joint work with Matt Baker, where we study special points and special curves within the moduli space of complex polynomial dynamical systems" |
October 25, 2012, 430 PM at Science Center Hall A |
| TRIVIAL NOTIONS SEMINAR |
Konstantin Matveev (HARVARD UNIVERSITY) |
Limits of Random Surfaces |
We are all familiar with the notion of the limit of a sequence of numbers or functions, but what should be viewed as the limit as $n$ tends to infinity of the sequence of random trees on $n$ vertices or random domino tilings of $2n \times 2n$ square scaled by a factor of $2n$? Or what is the limit of the random self-avoiding walk on a plane hexagonal lattice as the mesh of the lattice tends to zero? In each of these and many other questions correct understanding of the notion and properties of the limiting object sheds light on the asymptotic properties of the involved random structures and unveils a variety of interesting phenomena. I will talk about several instances of limits of random structures including the Brownian motion, Schramm-Loewner evolution, continuum random tree and Gaussian free field" |
October 25, 2012, 130 PM at Science Center 507 |
| THURSDAY SEMINAR |
Clark Barwick (MIT) |
Deligne cohomology (ctd) |
" |
October 25, 2012, 300 - 430 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Abhinav Kumar (MIT) |
Abelian surfaces with everywhere good reduction |
It is a classical theorem of Fontaine and Abrashkin that there are no abelian varieties over Z. On the other hand, there are several examples of elliptic curves over quadratic fields with good reduction everywhere, the first being given by Tate over the field Q(sqrt(29)). I will report on recent joint work with Lassina Dembele, in which we produce several examples of abelian surfaces with real multiplication, defined over a real quadratic field and having good reduction everywhere. It relies on recent explicit equations for Hilbert modular surfaces (due to Elkies and the speaker) and also on efficient computation of Hecke eigenvalues for spaces of Hilbert modular forms (due to Dembele, Donnelly, Voight and Greenberg). Our work also provides some evidence for the Eichler-Shimura conjecture for Hilbert modular forms" |
October 24, 2012, 300 - 400 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Yu-Jong Tzeng (HARVARD UNIVERSITY) |
Enumeration of singular curves with tangency conditions |
How many nodal degree d plane curves are tangent to a given line? The celebrated Caporaso-Harris recursion formula gives a complete answer for any number of nodes, degrees, and all possible tangency conditions. In this talk, I will report my recent work on the generalization of the above problem to count singular curves with given tangency condition to a fixed smooth divisor on general surfaces. I will relate the enumeration to tautological integrals on Hilbert schemes of points and show the numbers of curves in question are given by universal polynomials. As a result, we can obtain infinitely many new formulas for nodal curves and understand the asymptotic behavior for all singular curves with any tangency conditions. --Organized by Professor ST Ya" |
October 23, 2012, 415 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Nathan Ilten (UC BERKELEY) |
Mutations of Laurent polynomials and flat families with toric fibers |
In recent work, I have shown that certain birational transformations mapping a Laurent polynomial to another Laurent polynomial correspond to deformations between the associated toric varieties. I will discuss this result and its relevance in the larger context of mirror symmetry and the classification of Fano varieties" |
October 23, 2012, 300 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Shlomo Sternberg (HARVARD UNIVERSITY) |
Recent incarnations of the Cartan three form |
" |
October 22, 2012, 300 - 400 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Michael Hutchings (UC BERKELEY) |
Existence of two Reeb orbits |
We show that every (possibly degenerate) contact form on a closed three-manifold has at least two geometrically distinct Reeb orbits. The proof uses a relation between contact volume and the asymptotics of the amount of symplectic action needed to represent certain classes in embedded contact homology. This is joint work with Dan Cristofaro-Gardiner and Vinicius Gripp" |
October 19, 2012, 330 - 430 PM at Science Center 507 |
| SPECIAL PROBABILITY SEMINAR |
Claudio Landim (IMPA) |
Action functional and quasi-potential for the Burgers equation in a bounded interval |
Consider the viscous Burgers equation $u_t + f(u)_x = \varepsilon\, u_{xx}$ on the interval $[0,1]$ with the inhomogeneous Dirichlet boundary conditions $u(t,0) = \rho_0$, $u(t,1) = \rho_1$. The flux $f$ is the function $f(u)= u(1-u)$, $\varepsilon>0$ is the viscosity, and the boundary data satisfy $0<\rho_0<\rho_1<1$. We examine the quasi-potential corresponding to an action functional, arising from non-equilibrium statistical mechanical models, associated to the above equation. We provide a static variational formula for the quasi-potential and characterize the optimal paths for the dynamical problem. In contrast with previous cases, for small enough viscosity, the variational problem defining the quasi potential admits more than one minimizer. This phenomenon is interpreted as a non-equilibrium phase transition and corresponds to points where the super-differential of the quasi-potential is not a singleton" |
October 19, 2012, 130 PM at Science Center 232 |
| TRIVIAL NOTIONS SEMINAR |
Ben Stetler (HARVARD UNIVERSITY) |
Information Theory and the Channel Coding Theorem |
Information theory is the quantitative study of the transmission, encoding, and recovery of information. One of the foundational results in the area is thechannel coding theorem, first stated by Claude Shannon in his landmark 1948 paper. The theorem states that for any communication channel with a possibility of transmission error, there is a quantity known as the channel capacity that satisfies the following property at any rate below the channel capacity, information can be transmitted with an arbitrarily low probability of error. We ll discuss the theorem and its converse, providing a brief tour of some of the fundamental concepts of information and coding theor" |
October 18, 2012, 130 PM at Science Center 507 |
| THURSDAY SEMINAR |
Clark Barwick (MIT) |
Deligne cohomology |
" |
October 18, 2012, 300 - 500 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
John Smillie (CORNELL UNIVERSITY) |
Translation surfaces and Teichmueller dynamics |
I will discuss translation surfaces, their moduli spaces and dynamical systems defined on their moduli spaces. I will describe some motivating examples, some known results and some open questions focusing on the role of the horocycle flow and analogs of Ratner theory for unipotent flows" |
October 17, 2012, 400 - 500 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Dennis Gaitsgory (HARVARD UNIVERSITY) |
Arthur parameters for the Langlands correspondence in the geometric setting |
Categorical Geometric Langlands is a conjectural equivalence between the (derived) category of D-modules on the automorphic stack (=the stack of G-bundles over an algebraic curve X) and a certain modification of the (derived) category of quasi-coherent sheaves on the Galois stack (=the stack of local systems on X with respect to the Langlands dual group). This modification has to do with the fact that Langlands parameters (Galois representations) are not enough to account for the automorphic side. Due to the phenomenon of non-temperedness, one has to incorporate the Arthur parameters. In the talk we will explain how this plays out in geometry it turns out that the modification Langlands->Arthur has do to with singularities of the Galois stack, and with the difference that singularities create between coherent sheaves and perfect complexes. This is joint work with D. Arinkin." |
October 17, 2012, 300 - 400 PM at Science Center 507 |
| HARVARD/MIT LOGIC SEMINAR |
Peter Cholak (UNIVERSITY OF NOTRE DAME) |
The computably enumerable sets the tardy sets, the D-maximal sets and the low sets |
We will survey recent work on the computably enumerable sets focusing on a collection of results that implies that the tardy sets break up into in.nitely many orbits and similar for the D-maximal sets. In the tardy case all of the known orbits avoid the complete sets. Can the same be said for the D-maximal sets? At the end we will address the question which sets are automorphic to low sets" |
October 17, 2012, 400 PM at Science Center Hall E |
| DIFFERENTIAL GEOMETRY SEMINAR |
Emanuel Scheidegger (UNIVERSITY OF FREIBURG) |
Topological strings, fibrations and modular forms |
We will explain a conjecture that expresses the Gromov-Witten invariants for elliptically fibered Calabi-Yau threefolds in terms of modular forms. In particular, there is a recursion relation which governs these modular forms. Evidence comes from the polynomial formulation of the higher genus topological string amplitudes with insertions as well as explicit calculcations. --Organized by Professor Shing-Tung Ya" |
October 16, 2012, 130 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Jae Choon Cha (POHANG UNIVERSITY OF SCIENCE & TECHNOLOGY) |
Amenable L2-signatures and cobordism of knots and 3-manifolds |
Recently, new amenable Cheeger-Gromov rho-invariants have been introduced to study homology cobordism of 3-manifolds and concordance of knots and links. This reveals new structures beyond those visible via Cochran-Orr-Teichner type signatures. We introduce the key ideas of amenable L2 methods and some applications. Also, if time permits, we discuss the notion of symmetric Whitney tower cobordism which provides a generalized framework for bordered 3-manifolds and link concordance. Parts of the results in this talk are joint with Kent Orr" |
October 12, 2012, 330 - 430 PM at Science Center 507 |
| PROBABILITY SEMINAR |
Ben Stetler (HARVARD UNIVERSITY) |
Lifshitz tails for spectra of Erdos-Renyi random graphs |
In an Erdos-Renyi random graph, edges are selected independently with probability p/N, where p=p(N) and N is the number of vertices. We can then define the graph laplacian as a random operator on vertex functions. I ll discuss some results that demonstrate that for fixed p, the density of states distributions of these random operators converge weakly to a limiting distribution as N goes to infinity, and that in the subcritical case 0
| October 12, 2012, 130 PM at Science Center 232 | |
| TRIVIAL NOTIONS SEMINAR |
Chao Li (HARVARD UNIVERSITY) |
Mumford Curves |
In the 70s, Mumford discovered p-adic analogues of classical uniformizations of curves and abelian varieties, which generalized Tate s p-adic uniformization of elliptic curves. Besides its significance for moduli, Mumford s construction can be also viewed as a highly nontrivial example of rigid analytic geometry. We shall start by reviewing the classical Schottky uniformization of compact Riemann surfaces and then introduce the dictionary between Mumford curves and p-adic Schottky groups. With the aid of the Bruhat-Tits tree of SL(2), we can illustrate examples of Mumford curves whose geometry and arithmetic are rich, and explain why the answer to life, the universe and everything should be changed" |
October 11, 2012, 130 PM at Science Center 507 |
| THURSDAY SEMINAR |
Kristen Wickelgren (HARVARD UNIVERSITY) |
Esnault and Wittenberg's work on O-cycles and anabelian geometry |
" |
October 11, 2012, 300 - 500 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
David Hansen (BOSTON COLLEGE) |
Eigenvarieties for reductive groups |
I ll describe a general construction of eigenvarieties for connected reductive \bbQ-groups, and explain some of their geometric properties. The main new tool is a pair of" |
October 10, 2012, 300 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Kevin Pilgrim (INDIANA UNIVERSITY) |
Pullback invariants of critically finite rational maps |
Critically finite rational maps f P1 to P1 play a distinguished role in the study of complex analytic dynamical systems. Associated to such a map f are several different combinatorial invariants, each induced via pulling back under f. These invariants, which can be formulated in non-dynamical settings, and which include a virtual endomorphism on a mapping class group, turn out to be harmoniously related to one another. Exploiting these relationships sheds new light on the problems of the classification and the characterization of such maps. This talk will present recent work on these topics, joint with S. Koch and N. Selinger" |
October 10, 2012, 400 - 500 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Tobias Ekholm (UPPSALA UNIVERSITY) |
Exact Lagrangian immersions with a single double point |
We discuss exact Lagrangian immersions of a closed manifold M into complex n-space. By a classical result of Gromov such immersions cannot be injective and thus has at least one double point. We consider the simplest case of immersions with exactly one double point where rigidity and flexibility phenomena live side by side. For example, if n is even, n>4 and the Euler characteristic of M is not equal to -2 then M is necessarily diffeomorphic to the standard sphere. If on the other hand n is odd then any homotopy sphere admits a Lagrangian immersion with a single double point, but if the Maslov index of the double point is not equal to 1 and if the Lagrangian Gauss map of the immersion is homotopically standard, then the homotopy sphere must bound a parallelizable manifold. The talk discusses joint work with Eliashberg, Murphy, and Smith. -- Organized by Prof. ST Ya" |
October 09, 2012, 415 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Shoji Yokura (KAGOSHIMA UNIVERSITY) |
Motivic Hirzebruch class and its Donaldson-Thomas type analogue |
First I will explain the motivic Hirzebruch class, defined on the relative Grothendieck groups of algebraic varieties, which in a sense unifies the three natural transformations of MacPherson s Chern class, Baum-Fulton-MacPherson s Todd class and Cappell-Shaneson s L-class (extending Goresky-MacPherson s L-class). Then I will talk about a naive Donaldson-Thomas type analogue of the motivic Hirzebruch class" |
October 09, 2012, 300 PM at Science Center 507 |
| SPECIAL SEMINAR |
Sergey Grigorian (SUNY STONY BROOK) |
Short-time behaviour of a modified Laplacian coflow of G2 structures |
We first consider the Laplacian co-flow of co-closed G2-structures on compact 7-dimensional manifolds. This is the heat flow for the dual 4-form of a G2-structure. However this flow turns out to be not even weakly parabolic, unlike a similar flow for the G2-structure 3-form. We then modify this flow to make it weakly parabolic in the direction of closed forms and prove short time existence and uniqueness of solutions of this new flow. Organized by Professor S.T. Ya" |
October 09, 2012, 130 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Andy Wand (HARVARD UNIVERSITY) |
Tightness and open book decompostions |
A well known result of Giroux tells us that isotopy classes of contact structures on a closed three manifold are in one to one correspondence with stabilization classes of open book decompositions of the manifold. We will introduce a stabilization-invariant property of open books which corresponds to tightness of the corresponding contact structure. We will mention applications to the classificationof contact 3-folds, and also to the question of whether tightness is preserved under Legendrian surgery" |
October 05, 2012, 330 - 430 PM at Science Center 507 |
| TRIVIAL NOTIONS SEMINAR |
Jie Zhou (HARVARD UNIVERSITY) |
Monodromy, Moduli Spaces and Mirror Manifolds |
Starting by a brief introduction to the topological description (self- automorphisms on local systems) and geometric description (parallel transport via Gauss-Manin connection on at vector bundles) of mon- odromy transformation, we will then calculate the (local) monodromy of some elementary examples using both methods. After that we will proceed to a concise introduction to mirror symmetry from the view- point of the chiral/Frobenius ring structures living on the deforma- tion/tangent spaces, and explain why monodromy is important in the studies of moduli spaces and mirror manifolds. As a byproduct of mir- ror symmetry, we can see how the counting of genus 0 Gromov-Witten invariants on certain CY manifolds could be reduced to the calculation of periods on the mirror CY manifolds" |
October 04, 2012, 130 PM at Science Center 507 |
| THURSDAY SEMINAR |
Aravind Asok (HARVARD UNIVERSITY) |
Homotopy theory of punctured affine spaces |
" |
October 04, 2012, 3 - 5 PM at Sci Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Anders Karlsson (UNIVERSITY OF GENEVA) |
Two extensions of Thurston's spectral theorem of surface diffeomorphisms |
" |
October 03, 2012, 400 - 500 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Brian Conrad (STANFORD UNIVERSITY) |
Minimal Pseudo-reductive Groups |
In recent years, joint work with O. Gabber and G. Prasad led to a general structure theory for pseudo-reductive groups (the definition and arithmetic motivation for which will be reviewed). A lacuna was that over ground fields of characteristic 2 there were some constructions that were poorly understood. More recently, the introduction of a certain notion of minimality has led to a far more satisfactory understanding of those constructions. We will discuss the resulting new classification theorem, and indicate how these minimal groups are related to an old conjecture of Borel and Tits as well as to the proof of a new compactification theorem of Gabber" |
October 03, 2012, 300 - 400 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Alexander Grigorian (BIELEFELD UNIVERSITY) |
Homologies of graphs |
Organized by Professor Shing-Tung Ya" |
October 02, 2012, 415 PM at Science Center 507 |
| TRIVIAL NOTIONS SEMINAR |
Cheng-Chiang Tsai (HARVARD UNIVERSITY) |
Localization to 27 Lines on the Cubic Surface |
Initiated by Kontsevich, localization theorems have been important tools in computing Gromov-Witten invariants, namely counting curves in various spaces. In this talk we aim to introduce the general algorithm for counting curves in complete intersections in projective spaces (or toric varieties) via localization, by restricting our attention to the probably first non-trivial case of counting lines on a general cubic surface in $\mathbb{P}^3$. In particular, we ll give a sketchy review of equivariant cohomology and the Atiyah-Bott localization formula, with which we can go back to our algebro-geometric setting and reduce the computation of lines on a cubic to the above identity." |
September 27, 2012, 130 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Benjamin Howard (BOSTON COLLEGE) |
Gross-Zagier theorems for higher weight modular forms |
Given modular form F of weight n and a Hermitian lattice L of rank n-1, we can form the Rankin-Selberg convolution L-function attached to F and the weight n-1 theta series defined by L. When n=2, Gross and Zagier showed that the central derivative of this L-function is the Neron-Tate height of a Heegner point. Our main result gives an arithmetic interpretation of the central derivative, for all n, in terms of Arakelov theory on unitary Shimura varieties. This is joint work with Jan Bruinier and Tonghai Yang" |
September 26, 2012, 300 - 400 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Hiroshige Shiga (TOKYO INSTITUTE OF TECHNOLOGY) |
Holomorphic families of Riemann surfaces and their degenerations |
We consider holomorphic families of Riemann surfaces parametrized by the punctured disk. It is known that if the monodromy around the puncture is of infinite order, then the degeneration of Riemann surfaces occurs near the puncture. We estimate the degeneration in terms of the hyperbolic geometry of the surface" |
September 26, 2012, 400 - 500 PM at Science Center 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Sam Payne (YALE UNIVERSITY) |
Tropicalization of the moduli space of curves |
The analogy between moduli spaces of stable curves and more recently constructed moduli spaces of tropical curves is explained, canonically and functorially, through a generalized tropicalization map for toroidal embeddings of Deligne-Mumford stacks. This is joint work with D. Abramovich and L. Caporaso. As time permits, I will describe how this precise relation between moduli of curves and moduli of tropical curves is applied, in joint work with S. Galatius, to compute the top weight cohomology of M1;n for all n" |
September 25, 2012, 300 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Siu-Cheong Lau (HARVARD UNIVERSITY) |
Open Mirror Symmetry by using SYZ |
Organized by Professor Shing-Tung Ya" |
September 25, 2012, 415 PM at Science Center 507 |
| BASIC NOTION SEMINAR |
Siu-Cheong Lau (HARVARD UNIVERSITY) |
Mirror symmetry and Fourier transform |
Abstract Mirror symmetry is a duality between symplectic geometry and complex geometry. Its discovery led to non-trivial computations in enumerative geometry. To understand how it works, Strominger-Yau-Zaslow conjectured that the principle behind mirror symmetry is duality between tori. Their insights inspired a lot of interesting results in this direction. In this talk, I will explain how Fourier transform for periodic functions can be incorporated into the SYZ program to cope with quantum corrections by open enumerative invariants" |
September 24, 2012, 3 PM at Science Center 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Ke Zhu (HARVARD UNIVERSITY) |
Thin instantons in G2 manifolds and Seiberg-Witten invariants |
" |
September 21, 2012, 330 - 430 PM at Science Center 507 |
| THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
Totaro's work on algebraic cycles and complex cobordism |
" |
September 20, 2012, 3 - 5 PM at Science Center 507 |
| TRIVIAL NOTIONS SEMINAR |
Omar Antolin Camarena (HARVARD UNIVERSITY) |
No Wandering Domains |
If you re looking to iterate a rational map on the Riemann sphere and figure out what happens to each point, the first distinction you make is between the Fatou set, consisting of points that have the same fate as nearby points, and the Julia set where what happens is wild (and of which you ve most likely seen pretty pictures). Each connected component of the Fatou set is mapped onto another one and you can ask about the trajectories of the components. Dennis Sullivan proved a remarkable conjecture of Fatou s that says that every component of the Fatou eventually falls into a cycle of components, or in slogan form the Fatou set has no wandering domains. I will sketch Sullivan s proof (with some later simplifications by Baker and McMullen), which uses a wandering domain to construct an infinite dimensional space of deformations of the rational map" |
September 20, 2012, 130 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Howard Masur (UNIVERSITY OF CHICAGO) |
Winning sets of foliations for Schmidt games |
A measured foliation F is called Diophantine if for any quadratic differential q whose vertical foliation is F, the corresponding Teichmuller geodesic stays in a compact part of moduli space. In joint work with Jon Chaika and Yitwah Cheung we show that Diophantine foliations are winning for Schmidt games. Schmidt invented this game in the 1970 s played by two players. I will introduce the Schmidt game in this talk and talk about an improvement due to McMullen called absolute winning. Along the way I will talk about how in each Teichmuller disc the Diophantine geodesics are absolute winning" |
September 19, 2012, 400 - 500 PM at Science Center 507 |
| NUMBER THEORY SEMINAR |
Jacob Tsimerman (HARVARD UNIVERSITY) |
O-minimality and Arithmetic Applications |
o-minimality is a model theoretic concept that gives us a notion of a nice Transcendental set. I will introduce this notion and explain the beautiful applications towards transcendence and the Andre-Oort conjecture given by Jonathan Pila. Time permitting, we discuss some potential future applications such as the Ax-Schanuel conjecture for the j-function and the Zilber-Pink conjecture" |
September 19, 2012, 300 - 400 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Andreas Grotz (HARVARD UNIVERSITY) |
Geometric Structures in the Fermionic Operator Approach |
Organized by Professor Shing-Tung Ya" |
September 18, 2012, 415 PM at Science Center 507 |
| BASIC NOTIONS SEMINAR |
Shing-Tung Yau (HARVARD UNIVERSITY) |
Geometry of singular Einstein space |
" |
September 17, 2012, 300 PM at Science Center 507 |
| TRIVIAL NOTIONS SEMINAR |
Ali Daemi (HARVARD UNIVERSITY) |
Infinite Dimensional Morse Theory for Low Dimensional Manifolds |
Morse theory is one of the most important tools in topology and geometry. Among many other applications, Smale used a homology theory based on Morse theory to prove Poincare conjecture in dimension greater than 4. Later Witten gave a more modern formulation of this so called Morse homology, in terms of tunneling effect in physics. Inspired by Witten s work, Floer discovered it is possible to define Morse homology in some interesting infinite dimensional manifolds. After a fast review of Morse theory, I will explain how one can use a Morse function to define Morse homology. Next I will discuss one of the Floer s approaches to carry over Morse homology to certain infinite dimensional manifolds. Nowadays this type of Morse homology is called lagrangian Floer Homology. Ozsvath and Szabo used lagrangian Floer homology to define Heegaard Floer homology which is an invariant assigned to 3-manifolds. A glimpse into this theory will be the finishing part of my talk" |
September 13, 2012, 130 - 230 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Giulio Tiozzo (HARVARD UNIVERSITY) |
Geodesic ray tracking for random walks |
" |
September 12, 2012, 400 - 500 PM at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Adam Jacob (HARVARD UNIVERSITY) |
The Yang Mills Flow and the Atiyah-Bott Formula on Kahler Manifolds |
" |
September 11, 2012, 400 - 530 PM at Science Center 507 |
| HARVARD MIT ALGEBRAIC GEOMETRY SEMINAR |
Curt McMullen (HARVARD UNIVERSITY) |
Moduli spaces of isoperiodic forms on Riemann surfaces |
" |
September 11, 2012, 300 - 400 PM at Science Center 507 |
| PARTIAL DIFFERENTIAL EQUATION SEMINAR |
Zhen Lei (HARVARD UNIVERSITY) |
Introduction to Navier-Stokes equations |
" |
September 11, 2012, 130 PM at Science Center 232 |
| PROBABILITY SEMINAR |
Alan Hammond () |
The Multi-line Airy Process and it's Brownian-Gibb Property |
Consider a large number N of one-dimensional Brownian bridges define on the interval [-N,N] and conditioned by mutual avoidance. The curves become ordered under the conditioning, with the highest one reaching a mean value of 2N at the midpoint 0. A parabolic scaling in x and y about the point (0,2N) - dilating the y-direction by N^{1/3} and the x-direction by N^{1/3} - leads in a weak limit in high N to a process supported on infinitely many non-intersecting curves. This process appears as a scaling limit of the height profile of natural models for growing interfaces. In joint work with Ivan Corwin, we prove that this multi-line Airy process is supported on continuous curves, and that it satisfies a Gibbs resampling property which is a natural counterpart to a resampling property enjoyed by a finite system of Brownian bridges. This probabilistic means of analysing a scaling limit object in the KPZ universality class is a rather different tool to the exact solution approaches which are often used; it yields several new results, and furnishes the final element in a proof of Johansson that the normalized lateral fluctuation of the geodesic in geometric first passage percolation has a limiting law" |
September 07, 2012, 130 PM at Science Center 232 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
Ronen Mukamel (STANFORD UNIVERSITY) |
Fundamental domains and generators for lattice Veech groups |
" |
September 05, 2012, 4 PM at Science Center 507 |
| SUMMER TOPOLOGY SEMINAR |
Geoffroy Horel () |
Topological Calculus |
Abstract If A is an associative algebra, the pair consisting of its Hochschild cohomology and its Hochschild homology has a lot of structure Hochschild cohomology is a Gerstenhaber algebra, Hochschild homology has a degree one differential, moreover there is an action of the cohomology on homology which behaves nicely with respect to this structure. There is a (2-colored) operad encoding these operations the calculus operad. Kontsevich and Soibelman described a topological operad whose homology is the calculus operad and acting on the pair (Hochschild cochains, Hochschild chains). In this talk we will use factorization homology to prove Kontsevich and Soibleman s result in the topological setting. We will also give higher dimensional analogue of that result" |
August 16, 2012, 2 PM at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
X. Buff / C. McMullen (UNIVERSITY OF TOULOUSE & ICERM / HARVARD UNIVERSITY) |
Antipode-preserving cubic rational maps & Cascades in the dynamics of surface foliations |
Double Feature!" |
June 6, 2012, 300 p.m. at Science Center, room 530 |
| PROBABILITY SEMINAR |
Omer Angel (UNIVERSITY OF BRITISH COLUMBIA) |
Linearly reinforced random walks |
We prove that the linearly reinforced random walk on a bounded degree graph with sufficiently small initial weights is recurrent. On non-amenable graphs we also establish transience for sufficiently large initial weights. The vertex reinforced jump process is also treated. Joint with Nicholas Crawford and Gady Kozma" |
May 11, 2012, 130PM at Science Center 232 |
| NUMBER THEORY SEMINAR |
Ellen Eischen () |
An Eisenstein measure for unitary groups |
One approach to constructing certain p-adic L-functions relies on construction of a p-adic family of Eisenstein series. I will explain how to construct such a family for certain unitary groups. As part of the talk, I will explain how to p-adically interpolate certain values of both holomorphic and non-holomorphic Eisenstein series. I will also mention some applications to number theory and beyond" |
May 9, 2012, 300 pm at Science Center, room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
Milena Hering (UCONN STORR) |
|
" |
May 8, 2012, 300 pm at MIT (2-147) |
| GAUGE THEORY & TOPOLOGY |
Cagatay Kutluhan (HARVARD UNIVERSITY) |
Holonomy filtration and knots |
Motivated by the construction of the isomorphism between Heegaard Floer and Seiberg--Witten Floer homologies (joint with Yi-Jen Lee and Clifford H. Taubes), I will describe a doubly filtered Floer homology for null-homologous knots in closed oriented 3-manifolds in the context of Seiberg-Witten theory. I will also explain how the aforementioned construction leads to an isomorphism between the latter and Ozsvath-Szabo s knot Floer homology" |
May 4, 2012, 330 pm at Science Center, room 507 |
| BRANDEIS - HARVARD-MIT-NORTHEARSTERN COLLOQUIUM AT HARVARD |
Peter May (UNIVERSITY OF CHICAGO) |
What is equivariant cohomology and what is it good for? |
Let G be a topological group and let G act on a space X. What can one deduce about the G-fixed point space X^G and the orbit space X/G from information about X? I will explain classical cohomological results, P.A. Smith theory and the Connor conjecture, that give quite remarkable answers to these questions. I will use modern proofs of these results to describe equivariant cohomology theory, which means different things to different people. The proof of the Connor conjecture will lead us directly to the idea that cohomology should be graded on the real representation ring of G rather than just on the integers. In turn, this will lead us to a remarkable relationship between Mackey functors in algebra and equivariant stable homotopy groups. All concepts will be defined." |
May 3, 2012, 430 pm ( Tea to start at 400 ) at Talk at 317 Goldsmith Hall, Tea at 300 Goldsmith Hall |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Amie Wilkinson (UNIVERSITY OF CHICAGO) |
Conservative diffeomorphisms from a C^1 generic perspective |
" |
May 2, 2012, 400 pm at Science Center, room 507 |
| NUMBER THEORY SEMINAR |
Wei Zhang (COLUMBIA UNIVERSITY) |
Local character expansion and L-values |
A theorem of Harish-Chandra asserts that, in a small neighborhood of the origin, the character of a representation of p-adic reductive group can be expanded as a sum of Fourier transform of nilpotent orbital integrals. We will show a (truncated) version of this result in a relative setting and apply to a conjecture of Ichino-Ikeda and N. Harris that refines the Gan-Gross-Prasad conjecture" |
May 2, 2012, 300 p.m. at Science Center, room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
John Ottem (CAMBRIDGE) |
Ample subvarieties and q-ample divisors |
We introduce a notion of ampleness for subschemes of higher codimension using the theory of q-ample line bundles. We also investigate certain geomet- ric properties satisfied by ample subvarieties, e.g. the Lefschetz hyperplane theorems and numerical positivity. Using these properties, we also construct a counter example to the converse of the Andreotti-Grauert vanishing theorem." |
May 1, 2012, 300 p.m. at Harvard University Science Center, room 507 |
| RANDOM MATRIX & PROBABILITY SEMINAR |
Bertrand Duplantier (INSTITUTE FOR THEORETICAL PHYSICS, SACLAY (FRANCE)) |
SLE, KPZ and Liouville Quantum Gravity |
When two boundary arcs of a Liouville quantum gravity random surface are conformally welded to each other (in a boundary quantum-length-preserving way) the resulting interface is a random curve described by the Schramm-Loewner evolution (SLE). This allows to develop a theory of quantum fractal measures, consistent with the Knizhnik-Polyakov-Zamolochikov relation (KPZ), and to analyze their evolution under conformal welding maps related to SLE. As an application, one can construct quantum length and boundary intersection measures on the SLE curve itself (Joint work with Scott Sheffield (MIT)" |
May 1, 2012, 300 pm at Science Center, room 232 |
| GAUGE THEORY & TOPOLOGY |
Tatyana Kobylyatskaya (HARVARD UNIVERSITY) |
Symplectic embeddings of rational homology balls |
We will begin with a description of the rational homology balls appearing in Fintushel and Stern s rational blow-down operation for smooth 4-manifolds, a generalization of the standard blow-down. We will then discuss various smooth and symplectic embedding results of these rational homology balls. Time permitting, we will also give some explicit constructions of such symplectic embeddings." |
April 27, 2012, 330 pm at Science Center, room 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Samuel Lelievre (UNIVERSITE' PARIS-SUD) |
Flat surfaces with no convex presentation (joint work with Barak Weiss) |
A translation surface is obtained from the union of one or several disjoint polygons in the plane, by gluing by translations pairs of parallel same length sides with opposite orientations. The collection of polygons used for this, or presentation of the surface, is not unique, since one can cut along polygonal lines, translate and reassemble pieces. Baby example a flat torus presented as a square with opposite sides identified. Cutting the square along a diagonal leads to a presentation as two triangles; assembling these along other sides give parallelogram presentations. These are a few of infinitely many presentations for the same translation surface. Starting from an octagon made of a regular pentagon assembled to its mirror image along one of its sides, let us glue opposite sides. We get a translation surface of genus two. Veech showed it has no convex presentation. What translation surfaces have no convex presentation? How can a good understanding of the dynamics of SL(2,R) on moduli spaces of translation surfaces help answer that question" |
April 26, 2012, 400 pm at Science Center, room 530 |
| BRANDEIS-HARVARD-MIT-NORTHEASTERN JOINT COLLOQUIUM |
Balazs Szegedy (UNIVERSITY OF TORONTO, INSTITUTE FOR ADVANCED STUDY) |
Higher order Fourier analysis |
Abstract In a famous paper Timothy Gowers introduced a sequence of norms U(k) defined for functions on abelian groups. He used these norms to give quantitative bounds for Szemeredi s theorem on arithmetic progressions. The behavior of the U(2) norm is closely tied to Fourier analysis. In this talk we present a generalization of Fourier analysis (called k-th order Fourier analysis) that is related in a similar way to the U(k+1) norm. Ordinary Fourier analysis deals with homomorphisms of abelian groups into the circle group. We view k-th order Fourier analysis as a theory which deals with morphisms of abelian groups into algebraic structures that we call k-step nilspaces. These structeres are variants of structures introduced by Host and Kra (called parallelepiped structures) and they are close relatives of nil-manifolds. Our approach has two components. One is an uderlying algebraic theory of nilspaces and the other is a variant of ergodic theory on ultra product groups. Using this theory, we obtain inverse theorems for the U(k) norms on arbitrary abelian groups that generalize results by Green, Tao and Ziegler. As a byproduct we also obtain an interesting limit theory for functions on abelian groups in the spirit of the recently developed graph limit theory" |
April 26, 2012, 430pm at Science Center, Hall A |
| RANDOM MATRIX SEMINAR |
R. Nadakuditi (( MICHIGAN )) |
Phase transitions in spiked random matrices |
We consider the eigenvalues and eigenvectors of finite, low rank perturbations of random matrices (aka spiked random matrices) and bring into sharp focus an interesting phase transition phenomenon whereby the large matrix limit of the extreme eigenvalues of the perturbed matrix differs from that of the original matrix if and only if the eigenvalues of the perturbing matrix are above a certain critical threshold. Our analysis reveals the connection between the threshold and integral transforms of the spectral measure arising from free probability theory." |
April 26, 2012, 300 pm at Science Center, room 232 |
| NUMBER THEORY SEMINAR |
Nicolas Ojeda Bar (HARVARD UNIVERSITY) |
Towards a cohomological construction of Breuil-Kisin modules |
We will present an approach to the construction of Breuil-Kisin modules using crystalline cohomology. Along the way, we will define a new PD-base for crystalline cohomology that seems to improve upon the ring S used by Breuil" |
April 25, 2012, 300 at Science Center, room 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Dierk Scheicher (JACOBS UNIVERSITY) |
News about Newton global dynamics and efficient root finding |
Newton s method as a root finder is locally very fast, but the global dynamics seemed difficult to understand, even for complex polynomials in one variable. In particular, there may be open sets of starting points that converge to no roots (but to attracting cycles of higher periods). We describe how to turn Newton s method into an efficient root finder that, in the expected case, needs no more than $O(d^2 \log^5d + d\log|\log \eps |$ iterations to find all roots of a degree d polynomial with precision $\eps$. We also answer a question by Smale to classify all polynomials for which there are attracting cycles of higher periods (joint with Mikulich)." |
April 25, 2012, 400 pm at Science Center, room 507 |
| HARVARD/MIT GRAD STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
Dennis Gaitsgory (HARVARD UNIVERSITY) |
Factorization algebras attached to quantum groups, continuation |
" |
April 24, 2012, 530pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
Arend Bayer (UCONN STORR) |
Projectivity and birational geometry of Bridgeland moduli spaces |
I will present a construction of a nef divisor for every moduli space of Bridgeland stable complexes on an algebraic variety. In the case of K3 surfaces, we can use it to prove projectivity of the moduli space, generalizing a result of Minamide, Yanagida and Yoshioka. Its dependence on the stability condition gives a systematic explanation for the compatibility of wall-crossing of the moduli space with its birational transformations; this had first been observed in examples by Arcara-Bertram. This is based on joint work with Emanuele Macrì" |
April 24, 2012, 300 - 400 p.m. at MIT (2-147) |
| BASIC NOTIONS SEMINAR |
Paul Bourgade (HARVARD UNIVERSITY) |
The circular law |
The normalized spectral distribution of a large square random matrix with iid centered entries is asymptotically given by the uniform measure on the unit disk. This is the non-Hermitian counterpart of Wigner s semicircle law for random matrices with symmetry conditions, but its proof is more technical because of the spectrum of non-Hermitian operators is unstable. I will review the history of the circular law and recent progress towards precise versions of it." |
April 23, 2012, 300 pm at Science Center, room 507 |
| GAUGE THEORY & TOPOLOGY SEMINAR |
Ethan Street (HARVARD UNIVERSITY) |
Towards an Instanton Floer Homology for Tangles |
Abstract In this thesis defense, I will motivate and study the problem of computing the cohomology rings of a class of moduli spaces of flat connections on orbifold Riemann surfaces. I will then discuss the parallel problem of computing the instanton Floer homology ring of a product link in product 3-manifold. Complete results in the case of genus 0 will be given. I will briefly discuss the application of these ideas to defining of instanton Floer homology for a tangle in a sutured 3-manifold. Emphasis will be on elementary ideas related to the moduli spaces rather than Floer homology" |
April 20, 2012, 330pm at Science Center, Room 507 |
| BRANDEIS - HARVARD-MIT-NORTHEARSTERN COLLOQUIUM AT HARVARD |
Ravi Vakil (STANFORD UNIVERSITY) |
Limits of discriminants in algebraic geometry |
We consider the ``limiting behavior of discriminants, by which we mean informally the closure of the locus in some parameter space of some type of object where the objects have certain singularities. Examples include configuration spaces of points on a variety (such as a complex projective manifold), and hypersurfaces on a variety. The classes of the discriminants in the ring of motives tend to a limit (in some appropriate sense) as the number of points (or the degree of the hypersurface) goes to infinity. (This ring is not scary, and I will define everything from scratch.) The limits have remarkable structure, in terms of motivic zeta values (which will be defined in the talk). The results parallel a number of results in both arithmetic and topology, and suggest a number of conjectures in both. (Two motivating classical facts the chance of an integer being square free is 1 / zeta(2). The space of polynomials over C with no triple root has two non-zero rational cohomology groups h^0=1 and h^3=1.) I will also present a conjecture (motivated by results in arithmetic and topology) suggested by our work. Although it is true in important cases, Daniel Litt has shown that it contradicts other hoped-for statements. This is joint work with Melanie Wood" |
April 19, 2012, 430 pm at Harvard University Science Center, Hall A |
| RANDOM MATRIX & PROBABILITY SEMINAR |
Philippe Di Francesco (INSTITUT DE PHYSIQUE THEORIQUE DU C.E.A., SACLAY, FRANCE AND M.S.R.I, BERKELEY) |
Discrete Integrable Systems and Cluster Algebras |
Recursive systems arising from integrable quantum spin chains, such as Q,T and Y-systems display remarkable combinatorial properties. These are actually part of a more general mathematical structure called Cluster Algebras, introduced by Fomin and Zelevinsky around 2000, which has found a host of mathematical applications so far, ranging from the theory of total positivity, invariants in algebraic geometry, to the representation theory of quantum groups. A cluster algebra is a sort of dynamical system describing the mutation of a vector of data along the edges of an infinite tree, with rules guaranteeing that only Laurent polynomials of the initial data are generated. A longstanding conjecture of Fomin and Zelevinsky states that these have non-negative integer coefficients. In this talk, we will describe the very simple example of discrete integrable systems, and use their exact solutions in terms of paths on graphs or networks to explain this positive Laurent phenomenon. Non-commutative extensions will also be discussed. (Based on work in collaboration with Rinat KEDEM)." |
April 19, 2012, 300 pm at Science Center, room 232 |
| NUMBER THEORY SEMINAR |
Nicolas Templier (PRINCETON UNIVERSITY) |
Harmonic families of automorphic representations |
We consider certain families of automorphic representations of reductive groups over number fields. We establish a general Plancherel equidistribution theorem for the local parameters of these families. This generalizes and improves many earlier results, notably by Serre and others for GL(2), and on the asymptotics of Betti numbers, limit multiplicities of the automorphic spectrum and Sato-Tate equidistribution for families. The theorem is strong enough to shed new light on the Katz-Sarnak heuristics on zeros of L-functions and eigenvalues of random matrices. In particular we find an interesting connection between the conjectured Symmetry Type attached to families and Arthur Classification. This is joint work with Sug-Woo Shin." |
April 18, 2012, 300 p.m. at Science Center, room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
Izzet Coskun (UIC) |
Bridgeland stability |
I will report on joint work with Daniele Arcara, Aaron Bertram and Jack Huizenga on the birational geometry of the Hilbert scheme of points in the plane. We study the stable base locus decomposition of the effective cone of the Hilbert scheme. We describe the models and give them modular interpretations in terms of moduli spaces of Bridgeland stable objects. This talk will build on Jack s thesis defense, also on Tuesday at 100 at Harvard (Science Center 110)." |
April 17, 2012, 300 pm at Harvard University Science Center, room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
Dennis Gaitsgory (HARVARD UNIVERSITY) |
Factorizations algebras attached to quantum groups |
" |
April 17, 2012, 530 pm at MIT room 2-190 |
| BASIC NOTIONS SEMINAR |
Alex Bloemendal (HARVARD UNIVERSITY) |
Continuum limits of random matrices at the spectral edge |
A recurring theme in probability theory is to study the asymptotic properties of a large discrete random system by constructing an appropriate limit object. In a recent development in random matrix theory, such an approach has led to novel and unified descriptions of the universal local eigenvalue statistics. I will tell the story at the spectral edge, where the limit takes the form of a continuum random Schrödinger operator; the law of its ground state energy coincides with the widely occurring Tracy-Widom distribution. By considering rank-one perturbations and an associated linear PDE, I will sketch a way to reconcile this description with the classical ones in terms of a Fredholm determinant or a Painlevé transcendent" |
April 16, 2012, 300 pm at Science Center, room 507 |
| GAUGE THEORY & TOPOLOGY |
Thomas Koberda (HARVARD UNIVERSITY) |
Mapping class groups, homology and finite covers of surfaces |
Please note This is also Thomas Koberda s thesis defense" |
April 13, 2012, 330 pm at Science Center, room 507 |
| TRIVIAL NOTIONS |
Yu-Shen Lin (HARVARD UNIVERSITY) |
Mirror Symmetry from SYZ |
Mirror symmetry is a rather new field from physics. It first astonished mathematicians by predicting the number of rational curves of degree d in quintic Calabi-Yau 3-folds by a rather simple calculation related to the mirror. We will have a brief story of classical mirror symmetry and SYZ perspective. The SYZ viewpoint provides a way to predict how symplectic geometry on one Calabi-Yau manifold X relates to complex geometry of its mirror \check{X}. Hopefully, we can see from a local example how might holomorphic discs with boundary on Lagrangians in X be related to the correction of complex structure of \check{X" |
April 12, 2012, 200 p.m. at Science Center, room 310 |
| PROBABILITY SEMINAR |
Naor, A. (NYU) |
Grothendieck's inequality and the propeller conjecture. |
We will start with a description of the classical Grothendieck inequality, and the corresponding Grothendieck constant. We will then indicate a few of the numerous applications of the Grothendieck inequality, and review the work on the problem of estimating the Grothendieck constant. In particular, we will describe the 1977 Krivine conjecture on the exact value of the Grothendieck constant, and a related conjecture of Koenig, on maximizers of a certain oscillatory kernel, that was made as a step towards proving the Krivine conjecture. The main new result that we will discuss is the solution of Krivine s conjecture (joint with M. Braverman, K. Makarychev and Y. Makarychev). While Krivine asked for a specific counter example showing that his bound is sharp, we will obtain an improved Grothendieck inequality for all matrices, showing that the Grothendieck constant is strictly smaller than Krivine s bound. The main new probabilistic contribution here is establishing the usefulness of higher dimensional randomized rounding schemes, and we will discuss their impact on approximation algorithms. We will also discuss recent works (one joint with Khot and the other joint with Heilman and Jagannath) on a useful extension of the Grothendieck inequality that relates to a conjectured sharp estimate for the expected maximum of Gaussian vectors. This conjecture, called the propeller conjecture, has been recently proved in R^3" |
April 12, 2012, 300 pm at Science Center, room 232 |
| NUMBER THEORY SEMINAR |
Jayce Getz (MCGILL UNIVERSITY) |
An approach to nonsolvable base change for GL(2) |
I will describe an approach to base change for automorphic representations of GL(2) along nonsolvable Galois extensions of number fields. Parts of the talk are based on joint work with N. Templier" |
April 11, 2012, 300 pm at Science Center, room 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Nathan Dunfield (UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN) |
Integer homology 3-spheres with large injectivity radius |
Conjecturally, the amount of torsion in the first homology group of a hyperbolic 3-manifold must grow rapidly in any exhaustive tower of covers (see Bergeron-Venkatesh and F. Calegari-Venkatesh). In contrast, the first betti number can stay constant (and zero) in such covers. Here exhaustive means that the injectivity radius of the covers goes to infinity. In this talk, I will explain how to construct hyperbolic 3-manifolds with trivial first homology where the injectivity radius is big almost everywhere by using ideas from Kleinian groups. I will then relate this to the recent work of Abert, Bergeron, Biringer, et. al. In particular, these examples show a differing approximation behavior for L^2 torsion as compared to L^2 betti numbers. This is joint work with Jeff Brock" |
April 11, 2012, 400 pm at Science Center, room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
Jorge Vitorio Pereira (IMPA) |
Singular foliations with trivial canonical class |
I will discuss the structure of singular codimension one foliations with numerically trivial canonical bundle on complex projective manifolds. To expose the particular features of this class of foliations I will use reduction modulo p and deformation of free morphisms along foliations among other techniques. The talk will be based on a joint work with Frank Loray and Frederic Touzet" |
April 10, 2012, 300 - 400 p.m. at MIT (2-147) |
| BASIC NOTIONS SEMINAR |
Yum-Tong Siu (HARVARD UNIVERSITY) |
Multiplier Ideal Scheaves |
ABSTRACT Multiplier ideal sheaves identify the jet directions where estimates for partial differential equations fail. The concept originated in complex analysis. The techniques developed for them have become useful tools in algebraic and complex geometry. Will discuss some recent results and open problems." |
April 9, 2012, 300 - 400 pm at Science Center, room 507 |
| GAUGE THEORY & TOPOLOGY |
Nathan Dunfield (UIUC) |
Twisted Alexander polynomials of hyperbolic knots |
I will discuss a twisted Alexander polynomial naturally associated to a hyperbolic knot in the 3-sphere via a lift of its holonomy representation to SL(2, C). It is an unambiguous symmetric Laurent polynomial whose coefficients lie in a number field coming from the hyperbolic geometry. The polynomial can be defined as the Reidmeister torsion of a certain acyclic chain complex, namely the first homology of the knot exterior with coefficients twisted by the holonomy representation tensored with the abelianization map. This polynomial contains much topological information, for instance about the simplest surface bounded by the knot. I will present computations showing that for all 313,209 hyperbolic knots in S^3 with at most 15 crossings it in fact gives perfect such information, in contrast with a related polynomial coming from the adjoint representation of SL(2, C) on it s Lie algebra. This is joint work with Stefan Friedl and Nicholas Jackson" |
April 6, 2012, 330 pm at Science Center, room 507 |
| RANDOM MATRIX & PROBABILITY SEMINAR |
Bourgade, P (HARVARD UNIVERSITY) |
Strong Szegö asymptotics for L-functions |
Montgomery s conjecture states that, at the microscopic scale, the zeros of L-functions have the same statistics as the eigenvalues of random matrices from the Gaussian unitary ensemble. The repulsion of these zeros also appears through the limit of their linear statistics, at the mesoscopic scale they converge to a Gaussian field, in the same way as in the strong Szegö theorem, known for Toeplitz operators and random matrix theory. This is joint work with Jeffrey Kuan" |
April 5, 2012, 300 pm at Science Center, room 232 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Tom Sharland (UNIVERSITY OF WARWICIK) |
Polynomial matings and rational maps with cluster cycles |
" |
April 4, 2012, 400 pm at Science Center, room 507 |
| LOGIC COLLOQUIUM |
Tony Martin () |
Exploring the Frontiers of Incompleteness (Ninth Presentation) Completeness or Incompleteness of Basic Mathematical Concepts |
httplogic.harvard.ed" |
April 4, 2012, 400 pm at The Fong Auditorium, Harvard University |
| NUMBER THEORY SEMINAR |
Bianca Viray (BROWN UNIVERSITY) |
A strengthened Gross-Zagier formula for singular moduli |
In 1985, Gross and Zagier gave an elegant formula for the factorization of J(d_1, d_2) under the assumption that d_1 and d_2 are fundamental and relatively prime. (J(d_1,d_2) is a product of differences of j(tau_i) s, where tau_i is an element in the upper half plane of discriminant d_i). We strengthen their result to give a complete factorization for any two fundamental discriminants, and obtain at least a partial factorization for any two quadratic imaginary discriminants. This is joint work with Kristin Lauter" |
April 4, 2012, 300 pm at Science Center, room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
Paolo Aluffi (FLORIDA STATE) |
Chern classes of hypersurface arrangements |
We propose a formula comparing the Chern class of the sheaf of diwith loga- rithmic poles along the components of a free divisor and the Chern class of the complement of the divisor (in the sense of MacPherson). We prove that this formula holds for free hyperplane arrangements and, more generally, for certain arrangements of hypersurfaces in nonsingular varieties. In the case of arbitrary hyperplane arrangements, we show that the Chern class of the complement is essentially determined by the combinatorics of the arrangement, and relate this information to other invariants such as the Segre class of the singularity subscheme of the arrangement" |
April 3, 2012, 300 pm at Harvard University Science Center, room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
Dustin Clausen () |
Koszul duality and Verdier duality |
" |
April 3, 2012, 530 pm at MIT room 2-190 |
| BASIC NOTIONS |
Keerthi Madapusi Pera (HARVARD UNIVERSITY) |
p-adic uniformization and Hodge cycles on abelian varieties |
" |
April 2, 2012, 300 pm at Science Center, room 507 |
| PROBABILITY SEMINAR |
Chatterjee, S. (NYU) |
Invariant measures and the soliton resolution conjecture |
The soliton resolution conjecture for the focusing nonlinear Schrodinger equation (NLS) is the vaguely worded claim that a global solution of the NLS, for generic initial data, will eventually resolve into a radiation component that disperses like a linear solution, plus a localized component that behaves like a soliton or multi-soliton solution. Considered to be one of the fundamental problems in the area of nonlinear dispersive equations, this conjecture has eluded a proof or even a precise formulation till date. I will present a theorem that proves a statistical version of this conjecture at mass-subcritical nonlinearity. The proof involves a combination of techniques from large deviations, PDE, harmonic analysis and bare hands probability theory." |
March 30, 2012, 130 **special time** at Science Center, room 232 |
| GAUGE THEORY & TOPOLOGY |
Max Lipyanskiy (COLUMBIA UNIVERSITY) |
Gromov-Uhlenbeck Compactness |
We introduce an analytic framework that, in special circumstances, unites Yang-Mills theory and the theory of pseudoholomorphic curves. As an application of these ideas, we discuss the relation between instanton Floer homology and Lagrangian Floer homology of representation varieties" |
March 30, 2012, 330 pm at Science Center, room 507 |
| TRIVIAL NOTIONS |
Aliakbar Daemi (HARVARD UNIVERITY) |
Lie geometry |
Lie groups and Lie algebras form two important concepts in mathematics. There are some old results attempting to understand these objects. For example Cartan in a well-known theorem proved that any simple Lie group up to conjugacy has a unique maximal compact subgroup. Classical approaches to attack these problems need a good deal of theory. In this talk we will see how geometry helps us to prove generalizations of some of these theorems. Specifically I ll prove results about the structure of simple Lie algebras and Lie groups using methods of geometric invariant theory and Riemannian geometry" |
March 29, 2012, 200 p.m. at Science Center, room 310 |
| NUMBER THEORY SEMINAR |
Eddie Herman (UNIVERSITY OF CHICAGO) |
Beyond Endoscopy for the Symmetric Cube L-function |
We will discuss the idea of Langlands paper Beyond Endoscopy, and give several recent examples. From there we give a detailed study of a beyond endoscopy approach to the symmetric cube L-function for a certain family of automorphic representations. In this family, we can show the symmetric cube L-function is analytic to the left of Re(s)=1. The key idea being an exponential sum identity of Katz-Patterson, which has some connection to the Fundamental Lemma. All these ideas require the use of analytic number theory, which is quite unlike the treatment of endoscopy and the stable trace formula." |
March 28, 2012, 300 pm at Science Center, room 507 |
| LOGIC COLLOQUIUM |
John Steel () |
Exploring the Frontiers of Incompleteness (Eighth Presentation) The Triple Helix |
httplogic.harvard.ed" |
March 28, 2012, 400 pm at The Fong Auditorium, Harvard University |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Kathryn Lindsey (CORNELL UNIVERSITY) |
Invariant components of translation surfaces |
Abstract A holomorphic 1-form on a compact Riemann surface defines a flat metric on the complement of a finite set of points in the surface; such a surface, together with the flat metric, is called a translation surface. Geodesic flow in a fixed direction on a translation surface decomposes the surface into finitely many invariant subsets (components) in which the dynamics are either periodic or minimal. The moduli space of translation surfaces has a natural stratification based on the number and order of the zeros of the 1-form, and each stratum has at most three connected components. I will present tight upper bounds on the number of periodic and minimal invariant sets a surface can have, with the bound taken over all surfaces in any connected component of a stratum of the moduli space." |
March 28, 2012, 400 pm at Science Center, room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
() |
NO SEMINAR ON THIS DATE |
No seminar ( MIT Spring break" |
March 27, 2012, at |
| BASIC NOTIONS |
Sophie Morel (HARVARD UNIVERSITY) |
Langlands Functoriality |
I will attempt to present a non-trivial case of the Langlands functoriality principle from scratch. No prior knowledge of Shimura varieties is necessary to understand this talk." |
March 26, 2012, 300 pm at Science Center, room 507 |
| TRIVIAL NOTIONS |
Gabriel Bujokas () |
Poncelet's Porism |
Say we have two plane conics C and C . Poncelet s Porism says that if there is a n-sided polygon inscribed by C and circumscribed by C , then there are infinitely many such polygons. We will prove this classical theorem by relating it to the group law on elliptic curves. Then, we are going to look at an analogue of Poncelet s porism in space, due to Griffiths and Harris" |
March 22, 2012, 200 p.m. at Science Center, room 310 |
| LOGIC COLLOQUIUM |
James Cummings () |
Exploring the Frontiers of Incompleteness (Seventh Presentation) / Some Challenges for the philosophy of set theory |
http;//logic.harvard.edu" |
March 21, 2012, 400 pm at The Fong Auditorium, Harvard University |
| NUMBER THEORY SEMINAR |
Samit Dasgupta (UNIVERSITY OF CALIFORNIA - SANTA CRUZ) |
On Greenberg's conjecture for symmetric square p-adic L-functions |
We report on work in progress on the conjecture of Ralph Greenberg on the trivial zero of the p-adic L-function associated to the symmetric square of a modular form. Underlying our approach is a factorization formula for p-adic Rankin L-series. This factorization takes place outside the range of interpolation and is inspired by Gross s factorization formula for the Katz p-adic L-function of an even Dirichlet character" |
March 21, 2012, 300 pm at Science Center, room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
Alina Marian (NORTHEASTERN) |
Verlinde sheaves and strange duality for K3 and abelian surfaces |
I will discuss aspects of a conjectural duality, first proposed by J. Le Potier, in the geometry of determinant line bundles over spaces of sheaves on a complex surface. I will describe progress in the case of K3 and abelian surfaces, based on joint work with D. Oprea." |
March 20, 2012, 300 - 400 pm at Science Center, room 507 |
| RANDOM MATRIX & PROBABILITY SEMINAR |
Martin Hairer (UNIVERSITY OF WARWICK) |
Solving the KPZ equation |
The KPZ equation was originally introduced in the eighties as a model of surface growth, but it was soon realised that its solution is a universal object describing the crossover between the Gaussian universality class and the KPZ universality class. The mathematical proof of its universality however is still an open problem, in particular because of the lack of a good approximation theory for the equation. Indeed, the only known way so far to mathematically interpret solutions to the KPZ equation is to reduce it to a linear stochastic PDE via a non-linear transformation called the Cole-Hopf transform. Unfortunately, the resulting linear equation does itself lack a good approximation theory and many microscopic models do not behave well under the Cole-Hopf transform. In this talk, we present a new notion of solution to the KPZ equation that bypasses the use of the Cole-Hopf transform. Our approach also allows to factorise the solution map into a universal (i.e. independent of initial condition) measurable map, composed with a solution map with good continuity properties. This lays the foundations for a robust approximation theory to the KPZ equation, which is needed to prove its universality. As a byproduct of the construction, we obtain very detailed regularity estimates on the solutions, as well as a new homogenisation result" |
March 20, 2012, 300 - 400 pm at Science Center, room 232 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR ON GEOMETRIC REPRESENTATION THEORY |
Jacob Lurie (HARVARD UNIVERSITY) |
Verdier and Koszul duality for factorization algebras |
" |
March 20, 2012, 530 pm at Science Center, room 507 |
| BASIC NOTIONS SEMINAR |
Vaibhav Gadre (HARVARD UNIVERSITY) |
Word and relative metrics along random geodesics. |
For a non-uniform lattice G in SL(2,\R) cusps of the quotient hyperbolic surface S= \mathbb{H}^2/ G give a relative metric on G in which group elements g_1 and g_2 are distance 1 if they belong to the same coset of a parabolic subgroup. We will outline a comparison of word and relative lengths along a random geodesic in \mathbb{H}^2, where we consider two different notions of random first, with respect to the Lebesgue measure on S^1 and second, with respect to a harmonic measure on S^1 coming from a random walk on G. Time permitting, we will describe analogous results in Teichmuller theory" |
March 19, 2012, 300 pm at Science Center, room 507 |
| PROBABILITY SEMINAR |
Ivan Corwin (MICROSOFT RESEARCH, MIT) |
Gibbsian line ensembles |
Gibbsian line ensembles are naturally in growth models, directed polymers, certain stochastic PDEs, random matrix theory, and tilings. Roughly speaking, a Gibbsian line ensemble is a collection of indexed curves which have a certain spatial generalization of the standard Markov property. The purpose of this talk is to show how this Gibbsian perspective complements as well as ties in with the exact solvability approach often taken in studying these ensembles and their related probabilistic models. I will highlight a few interesting questions on the universality and uniqueness of line ensembles with an infinite number of lines." |
March 16, 2012, 130 pm at Science Center, room 232 |
| PROBABILITY SEMINAR |
J. Lee Harvard () |
Directed polymer at weak disorder |
" |
March 9, 2012, 130 pm at Science Center, room 232 |
| GAUGE THEORY & TOPOLOGY |
Cliff Taubes (HARVARD UNIVERSITY) |
SL(2;C) connections with L^2 bounds on curvature |
" |
March 9, 2012, 330 pm at Science Center, room 507 |
| TRIVIAL NOTIONS |
Giulio Tiozzo (HARVARD UNIVERSITY) |
Apollonian circle packings |
Configurations of mutually tangent circles go as far back as Descartes, and even Apollonius. In such a configuration one can ask how many circles of a given size there are, or if all the reciprocals of the radii are integers, how many of these reciprocals are prime? We will see how these elementary counting questions, admit a beautiful dynamical interpretation in terms of Kleinian groups, hyperbolic 3-space and equidistribution of horospheres. No previous knowledge of any of these words is required" |
March 8, 2012, 200 p.m. at Science Center, room 310 |
| RANDOM MATRIX & PROBABILITY SEMINARN |
R. Movassagh () |
Density of States of Quantum Spin Systems from Isotropic Entanglement |
We propose a method which we call Isotropic Entanglement (IE), that predicts the eigenvalue distribution of quantum many-body (spin) systems (QMBS) with generic interactions. We interpolate between two known approximations by matching fourth moments. Though, such problems can be QMA-complete, our examples show that IE provides an accurate picture of the spectra well beyond what one expects from the first four moments alone. We further show that the interpolation is universal, i.e., independent of the choice of local terms" |
March 8, 2012, 300 pm at Science Center, room 232 |
| RANDOM MATRIX & PROBABILITY SEMINAR |
J. Lee Harvard () |
Density of States of Quantum Spin Systems from Isotropic Entanglement |
We propose a method which we call Isotropic Entanglement (IE), that predicts the eigenvalue distribution of quantum many-body (spin) systems (QMBS) with generic interactions. We interpolate between two known approximations by matching fourth moments. Though, such problems can be QMA-complete, our examples show that IE provides an accurate picture of the spectra well beyond what one expects from the first four moments alone. We further show that the interpolation is universal, i.e., independent of the choice of local terms" |
March 8, 2012, 300 pm at Science Center, room 232 |
| THE THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
Cohomology of formal groups |
" |
March 8, 2012, 300 pm at Science Center, room 507 |
| NUMBER THEORY SEMINAR |
Jacob Tsimerman (HARVARD UNIVERSITY) |
Lower bounds for Galois orbits and the Andre-Oort Conjecture |
It is classically known that the degrees of the fields of definition of CM elliptic curves are essentially equal to sizes of class groups of imaginary quadratic fields, and can thus be controlled by Siegel s theorem. We generalize this to CM abelian varieties, giving lower bounds on these degrees and more generally for sizes of Galois orbits of CM points in Shimura Varieties. We will also discuss the applications (joint with J.Pila) to the Andre-Oort conjecture" |
March 7, 2012, 300 pm at Science Center, room 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Scott Wolpert (UNIVERSITY OF MARYLAND) |
Infinitesimal deformations of nodal stable curves |
For families of compact Riemann surfaces, holomorphic quadratic differentials provide the dual to infinitesimal deformations. For families of nodal stable curves, we describe that the direct image of a subsheaf of the square of the relative dualizing sheaf provides the dual to infinitesimal deformations. The description begins with the construction of Kuranishi families and the Hubbard-Koch universal property. Applications include an analytic description of the moduli cotangent bundle for the Deligne-Mumford stable curve compactification and a description of the normal sheaf of the compactification divisor. A formula for comparing zw=t plumbing family constructions is a further application" |
March 7, 2012, 400 pm at Science Center, room 507 |
| GEOMETRIC REPRESENTATION THEORY SEMINAR |
Jacob Lurie (HARVARD UNIVERITY) |
Factorization structures in topology -- III |
" |
March 6, 2012, 530 pm at MIT room 2-190 |
| BASIC NOTIONS SEMINAR |
Wilfried Schmid (HARVARD UNIVERSITY) |
Mixed Hodge modules |
" |
March 5, 2012, 300 pm at Science Center, room 507 |
| PROBABILITY SEMINAR |
I. Corwin (MIT/ MICROSOFT) |
Quantum many body systems solvable via a new integral ansatz |
The attractive delta Bose gas arises naturally in studying the moments of the stochastich heat equation, or a continuum polymer partition function. I will explain how variants of this many body system arise naturally from an interacting particle system called q-TASEP (particles jump on Z to the right at rate 1-q^gap where gap is the number of holes to a particle s right before the next particle), and from a semi-discrete polymer which arises as a limit of q-TASEP. I will then introduce an integral ansatz to solve for the propegrator of the many body system without appealing to the Bethe Ansatz. This provides a purely probabilistic and PDE means to rederive some of the formulas found in my work on Macdonald Processes with Borodin, and also leads to some new moment formulas which should enable the calcuation of multipoint statistics for the KPZ equation" |
March 2, 2012, 130 pm at Science Center, room 232 |
| GAUGE THEORY & TOPOLOGY |
Sushmita Venugopalan (RUTGERS UNIVERSITY) |
Yang-Mills heat flow on gauged holomorphic maps |
Abstract We study the gradient flow lines of a Yang-Mills-type functional on the space of gauged holomorphic maps $\mathcal{H}(P,X)$, where $P$ is a principal bundle on a Riemann surface $\Sigma$ and $X$ is a Kahler Hamiltonian $G$-manifold. For compact $\Sigma$, possibly with boundary, we prove long time existence of the gradient flow. The flow lines converge to critical points of the functional. So, there is a stratification on $\mathcal{H}(P,X)$ that is invariant under the action of the complexified gauge group. Symplectic vortices are the zeros of the functional we study. When $\Sigma$ has boundary, similar to Donaldson s result for the Hermitian Yang-Mills equations, we show that there is only a single stratum - any element of $\mathcal{H}(P,X)$ can be complex gauge transformed to a symplectic vortex. This is a version of Mundet s Hitchin-Kobayashi result on a surface with boundary" |
March 2, 2012, 330 pm at Science Center, room 507 |
| RANDOM MATRIX SEMINAR |
Michael Damron (PRINCETON UNIVERSITY) |
A simplified proof of the relation between scaling exponents in first - passage percolation. |
Abstract In first passage percolation, we place i.i.d. non-negative weights on the nearest-neighbor edges of Z^d and study the induced random metric. A long-standing conjecture gives a relation between two scaling exponents one describes the variance of the distance between two points and the other describes the transversal fluctuations of optimizing paths between the same points. This is sometimes referred to as the KPZ relation. In a recent breakthrough work, Sourav Chatterjee proved this conjecture using a strong definition of the exponents. I will discuss work I just completed with Tuca Auffinger, in which we introduce a new and intuitive idea that replaces Chatterjee s main argument and gives an alternative proof of the relation. One advantage of our argument is that it does not require a certain non-trivial technical assumption of Chatterjee on the weight distribution" |
March 1, 2012, 300 pm at Science Center, room 232 |
| HARVARD-MIT-NORTHEASTERN COLLOQUIUM AT HARVARD |
Harvey Friedman (OHIO STATE UNIVERSITY) |
Maximality and incompleteness |
Abstract We show how the usual axioms for mathematics (ZFC) are insufficient even in transparent countable and finite contexts. We begin with the familiar every countable binary relation contains a maximal square - (an A x A). The proof is entirely constructive. We formulate every nice binary relation contains a nice maximal square, using ambient spaces with modest structure. I.e., every invariant binary relation on rational [0,16]^32 contains an invariant maximal square. This statement can be analyzed for purely order theoretic notions of invariance that treat 1,...,16 as distinguished. We discuss cases that can only be proved by going well beyond the usual ZFC axioms" |
March 1, 2012, 430 at Science Center, Lecture Hall A |
| TRIVIAL NOTIONS |
Carl Erickson (HARVARD UNIVERSITY) |
The Siegel Zero |
The zeros of L-functions encode the distribution of various arithmetic objects. Restrictions on these zeros, such as the Riemann Hypothesis, have pleasant consequences for these distributions. In particular, number theorists are concerned with Siegel zeros which are real zeros between 0 and 1. These are so named because C. L. Siegel proved in 1935 a beautiful result on L-functions, restricting such zeros. However, his method of proof is to allow the existence of one zero in order to show that there cannot be any even worse zeros. We will not assume familiarity with L-functions, but will build up enough facts to outline Siegel s proof. We will also show how Siegel s result gives a strong result on Gauss class number problem, but is ineffective because of the quasi-circularity of the proof" |
March 1, 2012, 200 p.m. at Science Center, room 310 |
| NUMBER THEORY SEMINAR |
Xinwen Zhu (HARVARD UNIVERSITY) |
Local models of Shimura varieties |
I will report some recent progress in the study of local models of Shimura varieties, including the proof of the coherence conjecture of Pappas-Rapoport and the Kottwitz conjecture" |
February 29, 2012, 300 pm at Science Center, room 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Dzmitry Dudko (JACOBS UNIVERSIRTY) |
Matings with laminations |
" |
February 29, 2012, 400 pm at Science Center, room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR ON GEOMETRIC REPRESENTATION THEORY |
Jacob Lurie (HARVARD UNIVERSITY) |
Factorization structures in topology, continuation |
" |
February 28, 2012, 530 pm at Harvard University Science Center, room 507 |
| BASIC NOTIONS SEMINAR |
Barry Mazur (HARVARD UNIVERSITY) |
Statistics in the arithmetic of elliptic curves |
" |
February 27, 2012, 300 pm at Science Center, room 507 |
| NUMBER THEORY SEMINAR **NOTE DIFFERENT TIME, PLACE, & DAY** |
Bharghav Bhatt (UNIVERSITY OF MICHIGAN) |
Comparison theorems in p-adic Hodge theory |
A basic result in classical Hodge theory is the isomorphism between de Rham and Betti cohomology for complex manifolds. The p-adic analogue of this comparison was the subject of a series of conjectures made by Fontaine in the early 80s. In the last three decades, these conjectures have been proven by various mathematicians, and have had an enormous influence on arithmetic algebraic geometry. In my talk, I will discuss some work in progress that leads to a simple proof of these conjectures based on general principles in derived algebraic geometry (namely, derived de Rham cohomology), and some classical geometry with curve fibrations. The work presented builds on ideas of Beilinson who proved the de Rham comparison conjecture this way (discussed in this seminar roughly one year ago). The key new result that allows us to extend this story to the (log) crystalline setting is a comparison isomorphism between derived de Rham and crystalline cohomology for lci varieties in characteristic p, as well as a relative version for lci maps of p-adic schemes." |
February 24, 2012, 330 pm at Science Center, room 232 |
| GAUGE THEORY & TOPOLOGY |
Max Lipyanskiy (COLUMBIA UNIVERSITY) |
Gromov-Uhlenbeck Compactness- (CANCELLED) |
CANCELLED -- TO BE RESCHEDULE" |
February 24, 2012, at |
| TRIVIAL NOTIONS |
Ethan Street (HARVARD UNIVERSITY) |
The Dzhanibekov Effect, or The Tennis Racket Theorem |
Abstract The goal of the talk is to, from absolute first principles, derive the striking result that rotating rigid bodies in space behave chaotically, and in special cases exhibit highly counter-intuitive behavior. No physics background is required we will literally start with Newton s 3 laws and lazily proceed to develop Euler s equations for rigid body motion. There will be a video in Russian, live demonstrations, and precious little actual mathematics. If time permits (which it likely will), I will throw books at the audience" |
February 23, 2012, 200 p.m. at Science Center, room 310 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Giulio Tiozzo (HARVARD UNIVERSITY) |
Entropy and dimension of real sections of the Mandelbrot set |
" |
February 22, 2012, 400 pm at Science Center, room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
Samual Grushevsky (STONY BROOK) |
Pairs of real normalized differentials, cohomology of Mg, and cusps of plane curves |
We use a pair of meromorphic differentials on a Riemann surface with all periods real to construct real foliations of Mg with complex leaves. This structure allows us to bound the possible number of common zeroes of these two differentials. One application of this is a new proof of vanishing of some tautological classes in cohomology. Another application is a new bound for the maximal number of cusps of plane curves. Joint work in progress with Igor Krichever" |
February 21, 2012, 300 pm at Harvard University Science Center, room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
Jacob Lurie (HARVARD UNIVERSITY) |
Factorization structures in the topological setting |
** PLEASE NOTE The above seminar is out of sequence at MIT, and the start time is later than usual." |
February 21, 2012, 545 pm at MIT room 2-190 |
| GAUGE THEORY & TOPOLOGY |
John Pardon (STANFORD UNIVERSITY) |
Totally disconnected groups (not) acting on three-manifolds |
Hilbert s Fifth Problem asks whether every topological group which is a manifold is in fact a (smooth!) Lie group; this was solved in the affirmative by Gleason and Montgomery--Zippin. A stronger conjecture is that a locally compact topological group which acts faithfully on a manifold must be a Lie group. This is the Hilbert--Smith Conjecture, which in full generality is still wide open. It is known, however (as a corollary to the work of Gleason and Montgomery--Zippin) that it suffices to rule out the case of the additive group of $p$-adic integers acting faithfully on a manifold. I will present a solution in dimension three. The proof uses tools from low-dimensional topology, for example incompressible surfaces, minimal surfaces, and a property of the mapping class group" |
February 17, 2012, 330 at Science Center, room 507 |
| PROBABILITY SEMINAR |
David R. Nelson (HARVARD UNIVERSITY (DEPARTMENT OF PHYSICS)) |
Competition and Cooperation at Frontiers |
Species often expand from where they first evolved, invade into favorable habitats or move in response to climate changes, or gradients in nutrients, salinity, ambient temperature, etc., in the case of biofilms. Recent microbial experiments on bacteria and yeast have uncovered a remarkable genetic demixing phenomenon at the frontier of a two-dimensional range expansion. Simple models of asexual biological evolution at expanding frontiers can explain both the spatio-genetic correlations that develop for neutral competitions and the effect of natural selection. However, new questions arise when two or more species (or genetic variants of the same species) display cooperative or antagonistic growth strategies. For example, can mutualism prevent demixing? Evidence for a phase transition at a critical degree of cooperativity for mutualists will be presented in a one dimensional stepping stone model" |
February 16, 2012, 300 pm at Science Center, room 232 |
| TRIVIAL NOTIONS |
George Boxer () |
Crystals, Young Tableaux, Littelmann Paths, and Representation Theory |
A Kashiwara crystal is a combinatorial structure that can be associated to a finite dimensional representation of a complex semisimple Lie algebra. There are combinatorial operations on crystals that correspond to operations on representations, such as taking tensor products. Crystals were originally discovered by Kashiwara and Lusztig within the theory of quantum groups. In this talk I will give elementary combinatorial definitions of crystals and the basic operations on them. Then I will explain the connection between crystals of type A_n and Young Tableaux. Time permitting, I will introduce Littelmann s path model which gives a uniform combinatorial description of the crystals of all finite dimensional representations of all complex semisimple Lie algebras, as well as a generalization of the Littlewood-Richardson rule to all Cartan types" |
February 16, 2012, 200 p.m. at Science Center, room 310 |
| NUMBER THEORY SEMINAR |
Keerthi Madapusi Pera (HARVARD UNIVERSITY) |
The Tate conjecture for K3 surfaces over finite fields of odd characteristic |
Using recent advances in the theory of integral models of Shimura varieties, mainly due to Kisin, and the classical Kuga-Satake construction, we show that K3 surfaces over finite fields of odd characteristic p satisfy the Tate conjecture, as long as they admit a polarization of degree prime-to-p" |
February 15, 2012, 300 pm at Science Center, room 507 |
| LOGIC COLLOQUIUM |
Philip Welch () |
Exploring the Frontiers of Incompleteness (Sixth Presentation) / Global Reflection Principles |
httplogic.harvard.ed" |
February 15, 2012, 400 pm at The Fong Auditorium, Harvard University |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
Dennis Gaitsgory (HARVARD UNIVERSITY) |
Factorizable gerbes |
" |
February 14, 2012, 530 pm at MIT room 2-190 |
| BASIC NOTIONS SEMINAR |
Benedict Gross (HARVARD UNIVERSITY) |
Discriminants and root discriminants |
" |
February 13, 2012, 300 pm at Science Center, room 507 |
| GAUGE THEORY & TOPOLOGY |
Adam Levine (BRANDEIS) |
Bordered Floer homology and splicing knot complements |
We use bordered Floer homology to study 3-manifolds obtained by gluing together two knot complements (gluing meridian to longitude). If the knots are non-trivial knots in S^3, we show that the Heegaard Floer homology of the resulting manifold has rank greater than one. By extending this approach to knots in arbitrary three manifolds, we hope to obtain a new proof of Eftekhary s claimed result that a manifold whose Heegaard Floer homology has rank one cannot contain an essential torus. This is joint work in progress with Matt Hedden" |
February 10, 2012, 330 pm at Science Center, room 507 |
| RANDOM MATRIX & PROBABILITY SEMINAR |
Ivan Corwin (MICROSOFT RESEARCH NEW ENGLAND AND MIT) |
Macdonald processes and solvability in the KPZ universality class |
Abstract The goal of the talk is to survey recent progress in understanding statistics of certain exactly solvable growth models, particle systems, directed polymers in one space dimension, and stochastic PDEs. A remarkable connection to representation theory and integrable systems is at the heart of Macdonald processes, which provide an overarching theory for this solvability. This is based off of joint work with Alexei Borodin" |
February 9, 2012, 300 pm at Science Center, room 232 |
| TRIVIAL NOTIONS |
Nathan Kaplan (HARVARD UNIVERSITY) |
Incidence Problems in the Plane |
Abstract How many incidences can we have between n points and m lines in the plane? Given n points in the plane, how many distinct distances must occur between them? What is the largest number of pairs of points that can be distance one apart? The answer to the first of these problems is given by the famous Szemerédi-Trotter Theorem. We will describe several different proofs of this result and give an application to number theory. We will then talk about the second of these problems, the Erdös Distinct Distance Problem, which was recently almost completely solved by Guth and Katz using the polynomial method . We will also discuss some related unsolved problems, such as the last of these three, the Erdös Unit Distance Problem. We will see several different techniques that are used in this area, including ideas from graph theory, combinatorics, algebra, and ham sandwiches" |
February 9, 2012, 200 p.m. at Science Center, room 310 |
| NUMBER THEORY SEMINAR |
Matthew Emerton (UNIVERSITY OF CHICAGO) |
A new perspective on the Breuil--Mezard conjecture |
In this talk I will explain a geometric perspective on the Breuil--Mezard conjecture. The basic idea is to construct p-adic formal schemes parameterizing semi-stable n-dimensional representations of a local Galois group, which admit specialization maps to a variety in characteristic p which parameterizes mod p n-dimensional representations of the same Galois group. The Breuil--Mezard conjecture can then be reinterpreted as a statement about the multiplicities of these specializations maps. This is joint work-in-progress with Toby Gee" |
February 8, 2012, 300 pm at Science Center, room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
TBA () |
TBA |
The Harvard-MIT graduate student seminar in geometric representation theory will resume next week. Our plan for the first half of the semester is to study the point of view on the category of representations of the Quantum Group via factorization. In the process we will recover the Finkelberg-Schechtman equivalence between u_q-mod with the category of factorizable sheaves, and the Schechtman-Varchenko picture for U_q(n) as cohomology of certain local systems on configuration spaces. The ultimate goal is to use this point of view to connect with representations of affine algebras at the negative level and thereby reprove the KL equivalence. For the first few weeks the material will have a significant intersection with what was discussed at the Talbot workshop in 2008. Some notes have been posted on the seminar webpage." |
February 7, 2012, 530 pm at Science Center, room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
Dennis Gaitgory (HARVARD UNIVERSITY) |
Quantum groups and factorizable sheaves an overview |
" |
February 7, 2012, 530 pm at |
| BASIC NOTIONS SEMINAR |
Hong-Tzer Yau (HARVARD UNIVERSITY) |
Random Matrix, Beta ensembles, and Dyson Brownian Motion |
The Wigner-Dyson-Gaudin-Mehta conjecture asserts that the local eigenvalue statistics of large random matrices in the bulk exhibit universal behavior depending only on the symmetry class of the matrix ensemble. For invariant matrix models, the eigenvalue distributions are given by a log gas with a potential $V$ and inverse temperature $\beta = 1, 2, 4$, corresponding to the orthogonal, unitary and symplectic ensembles. The universality conjecture for invariant ensembles asserts that the local eigenvalue statistics are independent of $V$ for all positive real $\beta$. In this talk, we review our recent solution to the universality conjecture for both invariant and non-invariant ensembles. The special role played by the logarithmic Sobolev inequality and Dyson Brownian motion will be discussed" |
February 6, 2012, 300 pm at Science Center 507 |
| RANDOM MATRIX & PROBABILITY SEMINAR |
Vershynin, R. U. (MICHIGAN, ANN ARBOR) |
Random hyperplane tessellations and embeddings into metric spaces |
Abstract How many hyperplanes in R^n does one need in order to cut a given set K into small pieces (say, of diameter at most 0.1)? We will see that (a) random hyperplanes are almost ideal for this problem, and (b) the optimal number of hyperplanes depends on a single global geometric parameter of K, namely the mean width. We will explore some connections of this type of problems with geometric functional analysis (Euclidean sections of convex sets), stochastic geometry (random tessellations), and information theory (dimension reduction, embedding into metric spaces, and compressed sensing). This is a joint work with Yaniv Plan (UM)." |
February 2, 2012, 300 pm at Science Center, room 232 |
| NUMBER THEORY SEMINAR |
Joseph Rabinoff (HARVARD UNIVERSITY) |
The Skeleton of the Jacobian and the Jacobian of the Skeleton |
Let K be a complete non-Archimedean field, let X be a smooth, complete, connected algebraic K-curve with split semistable reduction, and let J(X) be its Jacobian. Berkovich has defined a notion of the skeleton of X, which is a metric graph \Sigma(X) onto which the analytification X^an deformation retracts, as well as a notion of the skeleton of J(X), which is a real torus \Sigma(J(X)) onto which J(X)^an deformation retracts. Following earlier work of Baker and others, we develop a theory of the Jacobian J(\Gamma) of a metric graph \Gamma, which is again a real torus, and we show that \Sigma(J(X)) = J(\Sigma(X)) canonically. If K is discretely valued then this gives a method of calculating the component group of the Néron model of J(X) without appealing to Raynaud s theorem, and if K is algebraically closed then this gives a powerful tool for constructing meromorphic functions on X with prescribed absolute value. This work is joint with Matt Baker" |
February 01, 2012, 300 pm at Science Center, room 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Thomas Koberda (HARVARD UNIVERSITY) |
Mapping class groups, homology and finite covers of surfaces |
Abstract I will discuss various ways of analyzing the action of a pseudo-Anosov homeomorphism on the homology of a finite cover of a surface" |
February 1, 2012, 400 pm at Science Center, room 507 |
| PROBABILITY SEMINAR |
Pierre Nolin (ETH ZüRICH) |
Two-dimensional percolation and self-organized criticality |
In two dimensions, the percolation model features a phase transition at a certain value of the macroscopic parameter (density of open sites), and for this specific critical value, it displays a strong conformal invariance property, as proved by Smirnov (2001). This property has important consequences for discrete models, at and near criticality. In particular, we discuss the formation of universal random shapes, observed in various concrete situations (chemical etching, erosion...) fractal interfaces with dimension 7/4, coming from density fluctuations, arise spontaneously. It is possible to establish rigorously this observation for a set of particles diffusing independently. As the particles evolve, a concentration gradient appears, and we see random interfaces that look like the so-called SLE (Schramm-Loewner Evolution) process with parameter 6 - a process that describes the boundaries of percolation clusters at criticality" |
January 31, 2012, 300 pm at Science Center, room 530 |
| NUMBER THEORY SEMINAR |
Joël Bellaïche (BRANDEIS UNIVERSITY) |
A universal Galois representation attached to modular forms of level 1 modulo 2 |
Recently, Nicolas and Serre determined the structure of the algebra generated by the action of Hecke operators on modular forms of level 1 modulo 2 it is an algebra of formal series in two variables over the field with two elements. Serre asked whether there existed a two-dimensional Galois representation over that algebra, unramified outside 2, with trace sending the Frobenius element at any odd prime to the corresponding Hecke operator. We shall give an affirmative answer to this question, and discuss several properties, and the significance, of this Galois representation." |
January 25, 2012, 300 pm at Science Center, room 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
JON CHAIKA (UNIVERSITY OF CHICAGO) |
Badly approximable directions on flat surfaces |
In this talk we show that directions on flat surfaces which are poorly approximated by saddle connection directions are a winning set for Schmidt s game. This extends a result of Schmidt for the torus and strengthens a result of Kleinbock and Weiss. We will state some consequences of the result. This is joint work with Yitwah Cheung and Howard Masur" |
December 14, 2011, 430 pm at Science Center, room 507 |
| NUMBER THEORY SEMINAR |
JACK THORNE (HARVARD UNIVERSITY) |
Some canonical constructions in arithmetic invariant theory |
In recent work, Bhargava and Shankar have given a bound for the average rank of an elliptic curve defined over the field of rational numbers. Results of this kind rely on the construction of correspondences between Selmer classes and algebraic objects, such as binary quartic forms. I will discuss a representation-theoretic construction of correspondences of this type." |
December 14, 2011, 300 pm at Science Center, room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
MAXIM ARAP (UNIVERSITY OF GEORGIA) |
Classification of smooth weak Fano threefolds of Picard number two |
Smooth Fano threefolds have been classified through the works of Fano, Iskovskikh, Shokurov, Mori and Mukai. Threefolds whose anti-canonical class is nef and big, but not ample, are called weak Fano (or almost Fano). The aim of this seminar is to briefly review the classification of smooth Fano threefolds and to report the recent results on the classi- fication of smooth weak Fano threefolds of Picard number two" |
December 13, 2011, 300 pm at MIT, room 2-146 |
| GAUGE THEORY & TOPOLOGY |
LIAM WATSON () |
L-spaces and left-orderability |
A group is left-oderable if it admits a strict total order of its elements that is invariant under multiplication on the left; an L-space is a rational homology sphere with simplest possible Heegaard Floer homology. It has been conjectured that an irreducible rational homology sphere is an L-space if and only if it has non-left-orderable fundamental group. While this conjecture seems very optimistic, I will discuss some of the evidence for it. This will centre around joint projects with S. Boyer and C. Gordon and with A. Clay" |
December 9, 2011, 330 pm at Science Center, room 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
IAN BIRINGER (YALE UNIVERSITY) |
Geometry of Hyperbolic 3-Manifolds with Constrained Rank |
With the recent resolution of Thurston s geometrization conjecture by Perelman, it is now known exactly when a closed 3-manifold M admits a hyperbolic metric. Mostow s rigidity theorem states that such a metric is unique if it exists, so a natural goal is to describe its geometry in terms of the topology of M. We are interested in the geometric constraints imposed by one of M s simplest topological invariants its `rank , i.e. the number of elements needed to generate its fundamental group. We will explain how closed hyperbolic 3-manifolds with constrained rank and injectivity radius have a geometric decomposition with bounded complexity. Applications to arithmetic manifolds, rank vs Heegaard genus, and the group theory of Kleinian groups may be given." |
December 7, 2011, 430 pm at Science Center, room 507 |
| NUMBER THEORY SEMINAR |
JUNECUE SUH (HARVARD UNIVERSITY) |
Parity in the cohomology of varieties over finite fields |
An old question of Serre, which also appeared in Deligne s Weil II, asks if the odd-degree l-adic Betti numbers of a proper smooth variety over a field are always even. We give an answer (in the affirmative) and then discuss some later, finer questions of Serre and of Katz." |
December 7, 2011, 300 pm at Science Center, room 507 |
| LOW DIMENSIONAL NOTIONS |
CAGATAY KUTLUHAN () |
Embedded contact homology |
I will describe Hutchings s embedded contact homology and a variant of it used as a mediator in the construction of the isomorphism between Heegaard Floer and Seiberg--Witten Floer homologies" |
December 6, 2011, 1200 pm at Science Center, room 530 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
DENNIS GAITSGORY (HARVARD UNIVERSITY) |
Recovering the full Kazhdan-Lusztig tensor product |
Please note This is the last Harvard-MIT graduate student seminar on Geometric Representation Theory of the fall semester." |
December 6, 2011, 530 pm at Science Center, room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
PATRICK BROSNAN () |
TBA |
" |
December 6, 2011, 300 pm at Harvard University Science Center, room 507 |
| GAUGE THEORY & TOPOLOGY |
DAVID SHEA VELA-VICK (COLUMBIA UNIVERSITY) |
Contact structures and knot Floer homology |
I plan to discuss a general method for building the minus version of knot Floer homology using sutured Floer homology and contact structures. I will also show how contact geometric constructions can be used to recover many of the naturally defined maps connecting the various version of Heegaard Floer theory. Time permitting, I will also discuss generalizations of these techniques to the study of tight contact structures on non-compact 3-manifolds with cylindrical ends" |
December 2, 2011, 330 pm at Science Center, room 507 |
| THURSDAY SEMINAR |
CHRIS SCHOMMER-PRIES () |
Invertible Conformal Nets |
" |
December 1, 2011, 300 pm at Harvard University Science Center, room 507 |
| RANDOM MATRIX & PROBABILITY SEMINAR |
J. LEBOWITZ (RUTGERS UNIVERSITY) |
Time Evolution and Stationary States of Macroscopic Systems Classical and Quantum |
I will review both old and recent work about the time dependence and steady states of isolated macroscopic systems. This will include a discussion of the micro/macro connection in quantum mechanics. The derivation of a master equation for open systems will also be considered" |
December 1, 2011, 300 pm at Science Center, room 232 |
| NUMBER THEORY SEMINAR |
DAVID BROWN (EMORY UNIVERSITY) |
Random Dieudonne Modules and the Cohen-Lenstra conjectures |
Knowledge of the distribution of class groups is elusive - it is not even known if there are infinitely many number fields with trivial class group. Cohen and Lenstra s heuristic models the p-part of a class group by a random finite abelian p-group, correctly predicting many strange experimental observations. While proof of the Cohen-Lenstra conjectures remains inaccessible, the function field analogue -- distribution of class groups of quadratic extensions of Fp(t) -- is more tractable. Friedman and Washington modeled the l-power part (with l not p) of such class groups as random matrices and derived heuristics which agree with experiment. Achter later refined these heuristics, and many cases have been proved (Achter, Ellenberg and Venkatesh). When l = p, the l-power torsion of abelian varieties, and thus the random matrix model, goes haywire. I will explain the correct linear algebraic model -- Dieudonne modules. Our main result is an analogue of the Cohen-Lenstra/Friedman-Washington heuristics -- a theorem about the distributions of class numbers of Dieudonne modules (and other invariants particular to l = p). Finally, I ll present experimental evidence supporting our heuristics." |
November 30, 2011, 300 pm at Science Center, room 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
JOSHUA BROWN (SUNY STONY BROOK) |
Rock-paper-scissors in the complex world |
http//www.math.harvard.edu/~kochs/seminar.htm" |
November 30, 2011, 430 pm at Science Center, room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR ON GEOMETRIC REPRESENTATION THEORY |
DENNIS GAITSGORY (HARVARD UNIVERSITY) |
Local definition of the KL tensor product |
" |
November 29, 2011, 530 pm at MIT, room 2-190 |
| LOW DIMENSIONAL NOTIONS |
CAGATAY KUTLUHAN () |
Pseudoholomorphic curves and monopoles |
I will give an overview of Taubes s strategy to establish correspondences between symplectic and Seiberg--Witten invariants of low-dimensional manifolds. This talk will be a gentle first step towards understanding the isomorphism between Heegaard Floer and Seiberg-Witten Floer homologies of closed oriented 3-manifolds" |
November 29, 2011, 1200 pm at Science Center 530 |
| BASIC NOTIONS SEMINAR |
DAVID KAZHDAN (HEBREW UNIVERSITY OF JERUSALEM) |
Quivers and quantum groups. |
I will present the Ringel-Green construction of a positive part of quantum groups via Hall algebras and will try to outline recent Bridgeland s construction of full quantum group" |
November 28, 2011, 300 pm at Science Center, room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
ARTAN SHESHMANI (UNIVERSITY OF BRITISH COLUMBIA) |
Higher rank stable pairs and virtual localization over local Calabi Yau threefolds and K3 surfaces |
We introduce a higher rank analog of the Pandharipande-Thomas theory of stable pairs on a Calabi-Yau threefold X. More precisely, we develop a moduli theory for frozen triples given by the data OrX (−n) ! F where F is a sheaf of pure dimension 1. The moduli space of such objects does not naturally determine an enumerative theory that is, it does not naturally possess a perfect symmetric obstruction theory. Instead, we build a zero-dimensional virtual fundamental class by hand, by truncating a deformation-obstruction theory coming from the moduli of objects in the derived category of X. This yields the first deformationtheoretic construction of a higher-rank enumerative theory for Calabi-Yau threefolds. We calculate this enumerative theory for local P1 using the Graber-Pandharipande virtual localization technique. Moreover, if time permits we will talk about similar computations over K3 surfaces which provide us with a higher rank analog of the Kawai-Yoshioka formula" |
November 22, 2011, 300 pm at Harvard University Science Center, room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR ON GEOMETRIC REPRESENTATION THEORY |
DENNIS GAITSGORY (HARVARD UNIVERSITY) |
Finally, the Sugawara construction |
" |
November 22, 2011, 530 pm at Harvard University Science Center, room 507 |
| LOW DIMENSIONAL NOTIONS |
ETHAN STREET (HARVARD UNIVERSITY) |
Operators on Instanton Homology and Property P |
Last week, Ali defined, for each homology 3-sphere Y, a relatively Z/8 graded abelian group I*(Y). We extend this definition to any 3-manifold with odd SO(3) bundle. By defining a natural set of operators on this space coming from the homology of Y, we decompose I*(Y) into eigenspaces analogous to the Spin^c decompositions of HM* and HF*. We then discuss the application of these ideas to a solution of the Property P conjecture independent of Seiberg-Witten theory. This talk will mostly be an overview of a great many somewhat technical ideas, with the main aim to illustrate how instanton homology detects representations of the fundamental group" |
November 22, 2011, 1200 pm at Science Center, room 530 |
| BASIC NOTIONS SEMINAR |
MARK KISIN (HARVARD UNIVERSITY) |
The Tate conjecture |
For a smooth projective variety over a number field or finite field, the Tate conjecture is the Galois theoretic cousin of the Hodge conjecture. It predicts which etale cohomology classes are linear combinations of classes arising from algebraic cycles. The talk will explain the statement of the conjecture, and some of what is known and unknown. At the end, I will sketch a variant of Tate s proof of his conjecture for endomorphisms of abelian varieties over finite fields." |
November 21, 2011, 300 pm at Science Center, room 507 |
| NUMBER THEORY SEMINAR *DIFFERENT TIME &DAY* |
DINESH THAKUR (UNIVERSITY OF ARIZONA) |
Diophantine approximation in finite characteristic |
While Roth s theorem settles the exponent of Diophantine approximation for an algebraic irrational number, the function field case is not even conjecturally understood. We will describe the recent progress. (Please note the different time and day" |
November 21, 2011, 430 pm at Science Center, room 507 |
| GAUGE THEORY & TOPOLOGY |
MAX LIPYANSKIY (COLUMBIA UNIVERSITY) |
TALK POSTPONED |
Max Lipyanskiy s talk has been moved to next semester so as not to conflict with the CDM conference" |
November 18, 2011, CANCELED FOR TODAY at |
| THE THURSDAY SEMINAR |
CHRIS SCHOMMER-PRIES () |
The Free Fermion Net |
" |
November 17, 2011, 300 pm at Science Center, room 507 |
| TRIVIAL NOTIONS |
CHAO LI (HARVARD UNIVERSITY) |
Shimura Curves |
Abstract In the 60s, Shimura studied certain algebraic curves as analogues of classical modular curves in order to construct class fields of CM-fields. These curves were later coined ``Shimura curves and vastly generalized by Deligne. We will take a tour of the rich geometry and arithmetic of Shimura curves. Along the way, we may encounter tessellations of disks, quaternion algebras, abelian surfaces, elliptic curves with CM, Hurwitz curves ... and the answer to life, the universe and everything" |
November 17, 2011, 1130 am at Science Center, room 507 |
| RANDOM MATRIX SEMINAR |
SODIN, S (IAS) |
A supersymmetric transfer matrix approach to random band matrices (based on joint work with M. Disertori and Spenser) |
Abstract We shall describe several problems related to random band matrices, focusing on the density of states. Following Disertori-Pinson-Spencer ( 02), the density of states for a class of random band matrices can be represented as a functional integral. We study this integral in 1D using a transfer matrix" |
November 17, 2011, 300 pm at Science Center, room 232 |
| NUMBER THEORY SEMINAR |
AARON SILBERSTEIN (HARVARD UNIVERSITY) |
Intersection Theory in the Birational Fundamental Groups of Surfaces and Gal(Q/Q) |
We describe how the birational fundamental group of a surface encodes intersection theory on that surface and provides a model, completely within profinite group theory, for the algebraic geometry of surfaces defined over Q. We then apply these results to produce profinite groups whose outer automorphisms are exactly Gal((Q/Q)" |
November 16, 2011, 300 pm at Science Center 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
JOHANNA MANGAHAS (BROWN UNIVERSITY) |
Orbit trees in the curve complex |
Abstract There s a common idea underlying various results where one finds free groups or, more generally, right-angled Artin groups, sitting conveniently in mapping class groups. This involves using subsurface projection to understand geometrically the orbit of the group in curve complexes. I ll describe this method and the nice properties it can guarantee in the groups." |
November 16, 2011, 430 pm at Science Center, room 507 |
| INFORMAL PROBABILITY SEMINAR |
A. DEMBO (STANFORD UNIVERSITY) |
Factor models on locally tree-like graphs. |
Consider factor (graphical) models on sparse graph sequences that converge locally to a random tree T. Using a novel interpolation scheme we prove existence of limiting free energy density under uniqueness of relevant Gibbs measures for the factor model on T. We demonstrate this for Potts and independent sets models and further characterize this limit via large-deviations type minimization problem and provide an explicit formula for its solution, as the Bethe free energy for a suitable fixed point of the belief propagation recursions on T (thereby rigorously generalize heuristic calculations by statistical physicists using ``replica or ``cavity methods). This talk is based on a joint work with Andrea Montanari and Nike Sun" |
November 15, 2011, 300 pm at Science Center, room 232 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR ON GEOMETRIC REPRESENTATION THEORY |
DENNIS GAITSGORY (HARVARD UNIVERSITY) |
Structure of crystal on the category of chiral modules. |
" |
November 15, 2011, 530 pm at MIT, room 2-190 |
| LOW DIMENSIONAL NOTIONS SEMINAR |
ALIAKBAR DAEMI (HARVARD UNIVERSITY) |
Instanton Floer homology |
Abstract Donaldson theory is a relatively modern tool to develop invariants for 4-manifolds via gauge theory. Few years after Donaldson s introduction of these invariants, Floer realized one can use them to define a homology theory, nowadays known as instanton Floer homology, for a 3-manifold. In this talk after a brief review of Donaldson theory we define instanton Floer homology for homology spheres and then discuss the Floer exact triangle, which is an analogue of the long exact sequence in classical homology theories" |
November 15, 2011, 1200 pm at Science Center, room 530 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
JIE WANG (OHIO STATE) |
Generic vanishing results on certain Koszul cohomology groups |
A central problem in curve theory is to describe algebraic curves in projective spaces with fixed genus and degree. One wants to know the extrinsic geometry of the curve, i.e information on the equations defining the curve. Koszul cohomology groups in some sense carry everything one wants to know about the extrinsic geometry of curves in projective space the number of equations of each degree needed to define the curve, the relations between the equations, etc. In this talk, I will present a new method using deformation theory to study Koszul cohomology of general curves. Using this method, I will describe a way to determine number of defining equations of a general curve in some special degree range (but for any genus)" |
November 15, 2011, 300 pm at MIT (2-146) |
| BASIC NOTIONS SEMINAR |
NIR AVNI (HARVARD UNIVERSITY) |
IRS |
I ll talk about (conjugation) Invariant Random Subgroups, and their uses in ergodic theory, representation theory, and the geometry of locally symmetric spaces" |
November 14, 2011, 300 pm at Science Center, room 507 |
| RANDOM MATRIX SEMINAR |
DMITRY DOLGOPYAT (MARYLAND UNIVERSITY) |
Random perturbations of area preserving flows of surfaces. |
Abstract We show that viscosity type regularization of the small perturbations of area preserving flows of surfaces can exhibit a metastable behavior." |
November 10, 2011, 300 pm at Science Center, room 232 |
| TRIVIAL NOTIONS |
XIOHENG WANG (HARVARD UNIVERSITY) |
BCGRS II - Baby Coxeter Groups and Root Systems II |
Abstract A Coxeter group is defined as an abstract group generated by elements of order 2 by specifying the orders of pairwise products. The goal of this talk is to give a survey of finite irreducible Coxeter groups and discuss some of their combinatorial invariants, namely their characteristic degrees and the factorization of their Poincare polynomials" |
November 10, 2011, 1130 am at Science Center, room 309 |
| BRANDEIS - HARVARD-MIT-NORTHEARSTERN COLLOQUIUM AT HARVARD |
CRAIG TRACY (U C DAVIS) |
Turbulent liquid crystals, KPZ universality and the asymmetric simple exclusion process |
Abstract We review recent experimental work on stochastically growing interfaces and compare these results with the recent theoretical developments for the Kardar-Parisi-Zhang equation and the closely related asymmetric simple exclusion process. The emphasis in this talk will be on the underlying results in the asymmetric simple exclusion process" |
November 10, 2011, 430 pm at Science Center, Lecture Hall A |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
TANYA FIRSOVA (SUNY STONY BROOK) |
The critical locus for complex Henon Maps |
Abstract In one-dimensional dynamics, the behavior of the critical points governs the global dynamics of the map. Henon maps are biholomorphisms of C^2, so these maps do not have critical points in the classical sense. However, within the forward and backward escaping loci, there are dynamically defined foliations. The critical locus is the set of tangencies between these two foliations. We give a description of the critical locus for Henon maps that are small perturbations of quadratic polynomials with disconnected Julia set. We justify the picture conjectured by John Hubbard" |
November 9, 2011, 430 pm at Science Center, room 507 |
| NUMBER THEORY SEMINAR |
JEANINE VAN ORDER (ECOLE POLYTECHNIQUE FEDERALE LAUSANNE) |
Some divisibility questions for p-adic L-functions |
I will first review the construction of p-adic L-functions associated to Hilbert modular forms of parallel weight 2 in ring class towers of CM extensions of totally real fields. I will then describe some results about the divisibility of these elements coming from the associated Iwasawa main conjectures with subsequent Euler characteristic computations, as well as some open questions" |
November 9, 2011, 300 pm at Science Center, room 507 |
| LOW DIMENSIONAL NOTIONS |
ANDREW COTTON-CLAY (HARVARD UNIVERSITY) |
Geometric applications of pseudo-holomorphic curves |
Abstract We ll review Gromov compactness and give some applications of holomorphic curves in symplectic manifolds relying on the presence of the curves themselves as opposed to invariants derived from them, starting from Gromov s original paper." |
November 8, 2011, 1200 pm at Science Center, room 530 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR ON GEOMETRIC REPRESENTATION THEORY |
DENNIS GAITSGORY (HARVARD UNIVERSITY) |
Universal constructions of crystals and Sugawara, a continuation of the previous talk. |
" |
November 8, 2011, 530 pm at Science Center, room 507 |
| BASIC NOTIONS SEMINAR |
CLIFF TAUBES (HARVARD UNIVERSITY) |
'Differential equations, compactness and topology'. |
" |
November 7, 2011, 300 - 400 pm at Science Center, room 507 |
| GAUGE THEORY & TOPOLOGY |
BARNEY BRAMHAM () |
Approximating Hamiltonian systems by integrable systems using pseudo-holomorphic curves |
I will talk about an approach using finite energy foliations to a question raised by Anatole Katok In low dimensions is every conservative dynamical system with zero topological entropy a limit of integrable systems" |
November 4, 2011, 330 - 430 pm at Science Center, room 507 |
| TRIVIAL NOTIONS |
STERGIOS ANTONAKOUDIS (HARVARD UNIVERSITY) |
Dynamics on M_g |
Abstract The talk will be an introduction to Teichmuller theory. Our goal will be to understand how to play Billiards on polygons using the dynamics on the moduli space curves" |
November 3, 2011, 1130 am at Science Center, room 309 |
| RANDOM MATRIX SEMINAR |
KAROL KOZLOWSKI (INDIANA UNIVERSITY-PERDUE UNIVERSITY INDIANAPOLIS) |
Asymptotic analysis of cyclic multiple intergrals |
Quantum integrable models in one dimension provide one with a class of non-trivial many-body quantum Hamiltonians where a great number of calculations is feasible to the very end, this without any approximations. It has been shown, over the years, that it is possible to give a precise description of the spectrum of such operators. More recently, there appeared various techniques allowing one to provide representations for the two-point correlation functions (i.e. expectation values of two-local operators in some eigenstates of the Hamiltonian) in terms of series of multiple integrals. In such representations, the distance between the operators appears as an oscillatory exponent in each of the multiple integrals arizing in the series. The aforementioned series of multiple integrals can be thought of as being a new class of special functions (of the distance) that generalizes the Painleve transcendents. Among the results interesting for physical applications is the obtention, from such exact representations, of the long-distance asymptotics of two-point functions. In this talk, I shall describe several aspects of the method of large parameter asymptotic analysis of such series that we have developed recently with my collaborators. More precisely, I shall focus on describing techniques allowing to to extract the asymptotic behavior of the so-called cyclic integrals. These correspond to a class of oscillatory multiple integrals that appears as a building block of the multiple integrals arizing in the aforementioned series representations. The method I shall present opens a way towards a systematic approach to the asymptotic analysis of many types of multiple integrals. This is a joint work with Kitanine, Maillet, Slavnov and Terras." |
November 3, 2011, 300 pm at Science Center, room 232 |
| THE THURSDAY SEMINAR |
MIKE HOPKINS (HARVARD UNIVERSITY) |
Examples of conformal nets loop groups and free fermions |
" |
November 3, 2011, 300 pm at Science Center, room 507 |
| LOGIC COLLOQUIUM |
CHARLES PARSONS () |
EXploring the Frontiers of Incompleteness (Fourth Presentation) / Evidence and the hierarchy of mathematical theories |
httplogic.harvard.ed" |
November 2, 2011, 400 pm at The Fong Auditorium, Harvard University |
| NUMBER THEORY SEMINAR |
ANDREW SNOWDEN (MIT) |
Singularities of ordinary deformation rings |
ABSTRACT Given a two dimensional residual representation of a local Galois group, one can consider the quotient R of its universal deformation ring R^{univ} classifying ordinary deformations. These rings play an important role in modularity lifting theorems. In nice enough situations, R admits a moduli interpretation and is easy to study. In degenerate cases, R is defined more indirectly and is therefore more difficult to study. I will give a more direct description of this ring, and use it to show that the ring is Cohen-Macaulay. I will then explain some consequences this result has for global deformation rings. I will not assume prior knowledge of Galois deformation theory" |
November 2, 2011, 300 pm at Science Center, room 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
XAVIER BUFF (UNIVERSITY PAUL SABATIER, TOULOUSE) |
Rescaling limits of rational maps |
" |
November 2, 2011, 430 pm at Science Center, room 507 |
| LOW DIMENSIONAL NOTIONS |
TIRASAN KHANDHAWIT () |
Introduction to monopole Floer homology |
Abstract As we have seen a construction of Seiberg-Witten invariant for 4-manifolds, we will now look at how to construct Floer homology for 3-manifolds from Seiberg-Witten theory. The main idea is to associate a 3-manifold with some moduli spaces and consider Morse homology of these spaces. One important aspect is to understand how one extend Morse homology to infinite dimensional setting. We will discuss some ingredients for this construction, such as Chern-Simons-Dirac functional and spectral flow of self-adjoint elliptic operators." |
November 1, 2011, 1200 pm at Science Center, room 530 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR ON GEOMETRIC REPRESENTATION THEORY |
DENNIS GAITSGORY (HARVARD UNIVERSITY) |
Universal construction on curves, a rerun of the talk from Oct. 18th |
*Please note change of speaker and title for Geometric Representation Theory seminar." |
November 1, 2011, 530 pm at MIT, room 2-190 |
| BASIC NOTIONS SEMINAR |
JACOB LURIE (HARVARD UNIVERSITY) |
Dijkgraaf-Witten models and vanishing theorems for higher Tate cohomology |
Abstract I will begin with a description of the Dijkgraaf-Witten model, which gives a procedure for using finite groups to produce invariants of manifolds. To generalize this procedure, one needs a certain finiteness condition, which has an interpretation in terms of the vanishing of certain Tate cohomology groups. If time permits, I ll describe a general setting where this vanishing takes place automatically (joint work with Mike Hopkins)" |
October 31, 2011, 300 - 400 pm at Science Center, room 507 |
| GAUGE THEORY & TOPOLOGY |
HIROFUMI SASAHIRA (NAGOYA UNIVERSITY) |
Instanton Floer homology for lens space |
We will define instanton Floer homology for lens space. The difficulty in the construction comes from the fact that flat connections on lens space are reducible. Using Floer homology we prove a gluing formula for a variant of Donaldson invariant. Lastly we will discuss an application of the gluing formula" |
October 28, 2011, 330 - 430 pm at Science Center, room 507 |
| RANDOM MATRIX SEMINAR |
J. NOVAK (MIT) |
Monotone Hurwitz numbers and the HCIZ integral |
ABSTRACT The Harish-Chandra-Itzykson-Zuber integral is a unitary matrix integral which first arose in the context of the Hermitian two-matrix model. The need for a structured understanding of the asymptotics of the HCIZ integral is one of the principal obstructions which makes the two-matrix model difficult to analyze rigorously. In this lecture, I will discuss joint work with I. Goulden and M. Guay-Paquet which makes some progress towards a proof of Matytsin s conjectural genus expansion of the HCIZ free energy" |
October 27, 2011, 300 pm at Science Center, room 232 |
| THURSDAY SEMINAR |
JACOB LURIE (HARVARD UNIVERSITY) |
Fusion, revisited |
" |
October 27, 2011, 300 - 500 pm at Science Center, room 507 |
| TRIVIAL NOTIONS |
NATHAN PFLUEGER (HARVARD UNIVERSITY) |
Semigroups and curves |
Abstract A numerical semigroup is a subset of the positive integers which is closed under addition and has finite complement. Every point on an algebraic curve defines a numerical semigroup, given by the set of pole orders of meromorphic functions that are regular except at the chosen point. I will discuss some of the interplay between the combinatorics of semigroups and the geometry of curves, emphasizing examples in very low genus" |
October 27, 2011, 1130 am at Science Center, room 309 |
| NUMBER THEORY SEMINAR |
() |
NO SEMINAR ON THIS DATE |
" |
October 26, 2011, 300 - 400 pm at |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
ROLAND ROEDER (INDIANA UNIVERSITY-PERDUE UNIVERSITY INDIANAPOLIS) |
Intertwined Basis for a cylinder map arising from statistical physics |
http//www.math.harvard.edu/~kochs/seminar.htm" |
October 26, 2011, 430 pm at Science Center, room 507 |
| LOW DIMENSIONAL NOTIONS |
JOSHUA BATSON () |
Applications of Heegaard Floer Homology |
Abstract Now that we have a definition of Heegaard Floer homology, let s put it to use. We ll do some example computations (lens spaces, knot surgeries), and see how 3-manifolds related by surgeries have Floer groups related by an exact triangle. Specializing to knots, and Heegaard diagrams adapted to them, we ll get the groups HFK, which control the Floer homologies of large surgeries on a knot. Now some topology comes out HFK categorifies the Alexander polynomial, detects the knot genus, and provides a lower bound on the 4-ball genus. Putting all the machinery together, we ll deduce the Milnor conjecture (a computation of the 4-ball genus of torus knots) and that the only alternating knots admitting lens space surgeries are the (2,2k+1) torus knots" |
October 25, 2011, 1200 pm at Science Center, room 530 |
| GEOMETRY REPRESENTATION THEORY |
() |
NO TALK TODAY |
" |
October 25, 2011, 530 pm at |
| BASIC NOTIONS |
PETER KRONHEIMER (HARVARD UNIVERSITY) |
A recent history of the 4-dimensional Poincaré conjecture |
Abstract If a smooth 4-manifold has the homotopy type of the 4-sphere, must it be diffeomorphic to the 4-sphere? This is the 4-dimensional Poincaré conjecture in the smooth category, and it is without any doubt one of the great unsolved problems in topology. A notable feature of the question is that there is no real consensus among topologists as to whether the answer should be yes or no. Perhaps we would bet on a negative answer for the simple reason that proving the affirmative seems well out of reach of most of us. After a brief look back to 1980 to set the scene, this talk will examine some more recent events. Longstanding potential counterexamples have turned out to be the standard sphere after all, and an interesting avenue for detecting counterexamples using Khovanov homology has been closed. Perhaps we should bet on the conjecture being true after all" |
October 24, 2011, 330 - 430 pm at Science Center, room 507 |
| SPECIAL SEMINAR |
ILAN BARNEA (HEBREW UNIVERSITY OF JERUSALEM) |
How can homotopy theory be useful to number theory |
In this lecture I will present a joint work with Tomer Schlank, where we define a new model structure on the category of pro simplicial sheaves.This model structure enables to define the etale homotopy type Artin and Mazur as the result of applying a derived functor. This new definition has several advantages over the classical approach 1. It gives an actual pro space, and not just a pro object in the homotopy category of spaces. 2. It applies to any topos. and most importantly 3. It extends naturally to a relative notion, which in turn enables us to use the general machinery of model categories to define and study obstructions to the existence of rational points" |
October 24, 2011, 430 pm at Science Center, room 507 |
| PROBABILITY SEMINAR |
E. CARLEN (RUTGERS UNIVERSITY) |
Recent Progress on Kac's Probabilistic Approach to Kinetic Theory |
Abstract Kinetic theory describes the evolution of dilute gas of particles interacting through binary collisions. The equations of kinetic theory are non-linear evolution equations (various forms of the Boltzmann equation for a probability density. In 1956, Mark Kac proposed a strategy for investigating such equations via a direct analysis of a stochastic model, different from, and simpler than, the underlying physical collision model, but still leading to the same equations. There has been much recent progress on Kac s program. We shall discuss recent work on determining the rate of equilibriation in this model. Until now, this had only had been made only for Maxwellian molecules, or, in a singular result of Villani, for super-hard collisions Recent work of myself, Carvalho and Loss extends this progress to the physically significant hard-sphere case, as will be explained in this lecture. I will also discuss recent results of Mischler and Mouhot on propagation of chaos for this model that makes use of the new rate information" |
October 21, 2011, 130 pm at Science Center, room 232 |
| GAUGE THEORY & TOPOLOGY |
VIVEK SHENDE (MIT) |
Hilbert schemes of plane curve singularities and knot invariants |
Abstract To a singular point on a complex plane curve in a surface, one associates a link by intersecting the curve with a small sphere around the singularity. It has long been understood that there is a close relationship between the topology of the link and the geometry of the singularity. I will discuss here a conjectural relationship between the Khovanov-Rozansky invariants of the link and the cohomology of Hilbert schemes of points on the singular curve" |
October 21, 2011, 330 pm at Science Center, room 507 |
| THE THURSDAY SEMINAR |
GIJS HUETS () |
The 3-catagory of conformal nets, part III sectors |
" |
October 20, 2011, 300 - 500 pm at Science Center, room 507 |
| WORKING SEMINAR OF RANDOM MATRICES |
J. NOVAK () |
Discovering the free world/ LECTURE II |
Abstract Free probability is a theory of non-commutative random variables developed by Voiculescu in order to address certain longstanding problems in operators algebras, particularly the free group factors isomorphism problem. This theory is based on the observation that in a non-commutative algebra of random variables there is room for a new, non-commutative notion of stochastic independence. In the course of developing this framework, Voiculescu discovered that free independence is closely related to the arithmetic properties of large random matrices. Other surprising connections with classical topics have since emerged, e.g. with the character theory of symmetric groups and symmetric function theory, and free probability has developed into an active field of research. While certainly of interest to an audience interested in random matrices, there is a didactic problem in that the initial definition of free independence seems to come out of the blue (unless you re willing to start thinking about free group factors right away). I will attempt to give an elementary introduction to the free independence concept by discovering it in a graph counting problem." |
October 20, 2011, 3 pm at Science Center, Room 232 |
| TRIVIAL NOTIONS |
ERIC REIDL (HARVARD UNIVERSITY) |
The Syzygy |
Abstract Syzygies are relations between generators of an ideal. Aside from being useful in Scrabble, they are also useful in understanding the geometry of varieties. They are closely related to the Hilbert function, and they help characterize what varieties a particular variety lies on. In this talk, I will define syzygies and minimal resolutions, then focus on an example, talking about computing syzygies of seven points in P^3" |
October 20, 2011, 1130 - 1230 at Science Center, room 309 |
| NUMBER THEORY SEMINAR |
ANA CARAIANI (HARVARD UNIVERSITY) |
Local-global compatibility and monodromy |
Given a cuspidal automorphic representation of GL(n) over a CM field which is regular algebraic and conjugate self-dual, one can associate to it a Galois representation. This Galois representation is known in most cases to be compatible with local Langlands. When n is even, the compatibility is known up to semisimplification or when the representation satisfies an additional regularity condition. I will extend the compatibility to Frobenius semisimplification by identifying the monodromy operators" |
October 19, 2011, 300 pm at Science Center, room 507 |
| LOGIC COLLOQUIUM |
JOEL HAMKINS () |
Exploring the Frontiers of Incompleteness (Third Presentation) / The Set-theoretic Multiverse |
httplogic.harvard.ed" |
October 19, 2011, 400 pm at The Fong Auditorium, Harvard University |
| GEOMETRY REPRESENTATION THEORY |
ANDREI NEGUT (HARVARD UNIVERSITY) |
The Sugawara Construction |
" |
October 18, 2011, 530 pm at MIT, room 2-190 |
| LOW DIMENSIONAL NOTIONS |
AILSA KEATING () |
Introduction to Lagrangian Floer homology |
The first part of the talk will be an overview of Morse homology; it will be followed by an introduction to (a flavor of) Lagrangian Floer homology, focusing on definitions, and on the conditions under which these can be made. Floer homologies are often referred to as infinite dimensional Morse homologies; we shall endeavor to let this analogy guide our presentation" |
October 18, 2011, 1200 pm at Science Center 530 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
ANAND DEOPURKAR (HARVARD UNIVERSITY) |
Alternate compactifications of Hurwitz spaces |
Moduli spaces of geometrically interesting objects are usually not compact. They need to be compactified by allowing certain carefully chosen degenerations. Often, this can be done in several ways, leading to different birational models that are related in interesting ways. I will describe a range of compactifications of the Hurwitz space Hdg, which parametrizes d sheeted, simply branched, genus g covers of the projective line. These compactifications are constructed by allowing degenerations where the branch points can collide in a prescribed way, recovering as a particular case the standard compactification by admissible covers. After the general construction, I will focus on the case of d = 3. In this case, the above construction, the above construction gives a sequence of compactifications which contract the boundary divisors in the admissible cover compactification. I will construct a sequence of yet more compactifications that modify the interior, featuring the classical Maroni invariant of trigonal curves" |
October 18, 2011, 300 pm at MIT (2-146) |
| BASIC NOTIONS SEMINAR |
GERALD SACKS (HARVARD UNIVERSITY) |
Models of set theory via measure theory |
Abstract Independence results for set can theory be obtained by measure-theoretic arguments. The only delicate point is the definability of certain measures." |
October 17, 2011, 3 PM at Science Center, Room 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
JEREMY KAHN (BROWN UNIVERSITY) |
Geometric Limits and Renormalization |
" |
October 17, 2011, 430 pm at Science Center, room 507 |
| GAUGE THEORY AND TOPOLOGY |
NIKOLAI SAVELIEV (MIAMI) |
An index theorem for end-periodic operators |
Abstract We extend the Atiyah, Patodi, and Singer index theorem for Dirac type operators from the context of manifolds with cylindrical ends to that of manifolds with periodic ends. Our theorem provides a natural complement to Taubes Fredholm theory for general and-periodic operators. It expresses the index in terms of a new end-periodic eta-invariant which equals the Atiyah-Patodi-Singer eta-invariant in the cylindrical setting. This is joint project with Tom Mrowka and Daniel Ruberman" |
October 14, 2011, 330 - 430 pm at Science Center, Room 507 |
| WORKING SEMINAR OF RANDOM MATRICES |
J. NOVAK () |
Discovering the free world/ LECTURE 1 |
Abstract Free probability is a theory of non-commutative random variables developed by Vioculescu in order to address certain longstanding problems in operators algebras, particularly the free group factors isomorphism problem. This theory is based on the observation that in a non-commutative algebra of random variables there is room for a new, non-commutative notion of stochastic independence. In the course of developing this framework, Voiculescu discovered that free independence is closely related to the arithmetic properties of large random matrices. Other surprising connections with classical topics have since emerged, e.g. with the character theory of symmetric groups and symmetric function theory, and free probability has developed into an active field of research. While certainly of interest to an audience interested in random matrices, there is a didactic problem in that the initial definition of free independence seems to come out of the blue (unless you re willing to start thinking about free group factors right away). I will attempt to give an elementary introduction to the free independence concept by discovering it in a graph counting problem." |
October 14, 2011, 130 PM at Science Center, Room 530 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
A. SOSHINIKOV (UC DAVIS) |
Outliers of finite rank deformations of Wigner matrices and related things |
Abstract In a series of recent preprints written with S. O Rourke, A. Pizzo, and D. Renfrew we study two related questions. The first question concerns the limiting distribution of the outliers in the spectrum of finite rank deformations of Wigner matrices. We extend the earlier results obtained by Capitaine, Donati-Martin, and Feral. The second question deals with fluctuation of matrix entries of regular functions of Wigner and sample covariance matrices. In the GUE/GOE case, this problem was studied by A. Lytova and L. Pastur in 2009. We extend their results to the non-Gaussian case" |
October 13, 2011, 3 pm at Science Center, Room 530 |
| THE THURSDAY SEMINAR |
EMILY PETERS () |
The Connes fusion tensor product |
" |
October 13, 2011, 3 - 5 PM at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
JONATHAN POTTHARST (BOSTON UNIVERSITY) |
Selmer groups on the eigencurve |
Abstract We explain the completion of a program to p-adically interpolate the Selmer groups associated to modular forms, including progress on the parity conjecture in the nonordinary case. This is joint work with Liang Xiao" |
October 12, 2011, 300 - 400 pm at Science Center, room 507 |
| LOW DIMENSIONAL NOTIONS |
PETER KRONHEIMER (HARVARD UNIVERSITY) |
Seiberg-Written invariants of 4-manifolds (II) |
" |
October 11, 2011, 1200 pm at Science Center, room 530 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
DAWEI CHEN (BOSTON COLLEGE) |
Geometry of Teichmueller Curves II Quadratic Differentials |
Teichmueller curves are generated by quadratic differentials. A year ago in this seminar I talked about the case when the generator is a global square of an abelian differential. Now I would like to address the other case when it is not a global square. The situation is similar in the interior of the moduli space, but more intriguing at the boundary. Using 4-branced covers of the Riemann sphere as an example, I will highlight a beautiful interplay between billiard dynamics, flat geometry, Hurwitz counting problem, and the intersection theory on moduli space. A non-varying numerical property for such Teichmueller curves will be explained. This is a joint work in progress with Martin Moeller." |
October 11, 2011, 300 - 400 pm at Harvard University Science Center, room 507 |
| SPECIAL LECTURE |
JEAN-PIERRE SERRE () |
Modular forms modulo 2 of level 1 |
" |
October 11, 2011, 200 - 300 at Harvard University Science Center, room 507 |
| GAUGE THEORY AND TOPOLOGY |
PAUL SEIDEL (MIT) |
Symplectic invariants beyond Gromov-Witten theory/ Please notice the change in date. |
Abstract One can define invariants of closed symplectic manifolds by looking at families of Lagrangian submanifolds (similar in principle to the classical notion of flux group, but more abstract). These invariants can be used to distinguish simply-connected symplectic manifolds which have the same Gromov-Witten invariants." |
October 07, 2011, 330 PM at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
GIJS HEUTS () |
The 3 category of conformal nets, part II defects |
" |
October 6, 2011, 300 - 500 pm at Science Center, room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
FRANCESCO CELLAROSI (PRINCETON UNIVERSITY) |
On the M\obius Function and Statistical Mechanics |
Abstract We study a probabilistic model for square-free numbers and we prove a several limit theorems describing the properties of a typical square-free number. The limit transition we consider is analogous to a thermodynamic limit in Statistical Mechanics and one of our results can be understood as a non-standard Shannon-McMillan theorem. This work was motivated by a recent conjecture by P. Sarnak on the randomness of the M\obius function and its connection to the theory of Dynamical Systems. Joint work with Ya.G.Sinai" |
October 06, 2011, 3 pm at Science Center, Room 232 |
| TRIVIAL NOTIONS |
MATTHEW WOOLF (HARVARD UNIVERSITY) |
Amenable groups |
Every compact group admits a countably additive invariant probability measure the Haar measure. We will see that the existence of a mean on a group - a finitely additive invariant probability measure - is a much weaker condition, but still allows allows us to draw some striking conclusions about the group. In particular, we will look at the existence of a mean and of almost-invariant subsets, and of the impossibility of a Banach-Tarski-type paradox for such groups" |
October 6, 2011, 1130 - 1230 at Science Center, room 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
OLEG IVRIL (HARVARD UNIVERSITY) |
A Weil-Petersson metric on Blaschke products |
Abstract In his paper Thermodynamics, dimension and the Weil-Petersson metric, McMullen showed the Weil-Petersson metric on Teichmuller space is the double derivative of the Hausdorff dimension of families of quasi-circles arising from simultaneous uniformization. He noticed that a similar construction can be carried out on spaces of Blaschke products; and so by analogy, one can define a Weil-Petersson metric there" |
October 05, 2011, 430 pm at Science Center, room 507 |
| LOGIC COLLOQUIUM |
SOLOMON FEFERMAN () |
Exploring the Frontiers of Incompleteness/ Is the Continuum Hypothesis a definite mathematical problem? |
" |
October 5, 2011, 400 pm at The Fong Auditorium |
| NUMBER THEORY SEMINAR |
JEAN-PIERRE SERRE () |
Introduction to the Sato-Tate conjecture |
*Please note that the room may be moved to a larger hall depending on attendance" |
October 05, 2011, 300 - 400 pm at Science Center, room 507 |
| AHLFORS LECTURES |
ELLIOTT LIEB (PRINCETON UNIVERSITY) |
The Hardy-Littlewood-Sobolev inequality and its generalization to the Heisenberg group |
Elliott Lieb has made fundamental contributions to both mathematics and physics. His work on the ice problem, Lieb-Thirring inequalities, Bose gases, and the strong subadditivity of entropy has had a lasting impact on mathematical analysis, combinatorics, statistical and quantum physics, and quantum information theory. Lieb has received many honors, including the Rolf Schock prize from the Swedish Academy of Sciences, the Boltzmann medal of IUPAP, and the Birkhoff prize of the AMS and SIAM" |
October 04, 2011, 415 - 515 pm at Harvard University Science Center Lecture Hall A |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
GIORGIA FORTUNA () |
The Fusion tensor product |
" |
October 04, 2011, 530 pm at MIT, room 2-190 |
| LOW DIMENSIONAL NOTIONS |
TATYANA KOBYLYATSKAYA (HARVARD UNIVERSITY) |
Introduction to Heegaard Floer Homology |
Abstract This talk will be about Heegaard Floer homology, which was introduced by Peter Ozsvath and Zoltan Szabo around the year 2000. The theory provides very strong invariants for closed oriented 3-manifolds, and has connections to knot theory, contact structures on 3-manifolds, Seiberg Witten invariants and many others. I will talk about the basic outline of its construction." |
October 04, 2011, 1200 pm at Science Center, room 530 |
| AHLFORS LECTURES |
ELLIOTT LIEB (PRINCETON UNIVERSITY) |
Symmetry breaking, reflection positivity and phase transitions |
Elliott Lieb has made fundamental contributions to both mathematics and physics. His work on the ice problem, Lieb-Thirring inequalities, Bose gases, and the strong subadditivity of entropy has had a lasting impact on mathematical analysis, combinatorics, statistical and quantum physics, and quantum information theory. Lieb has received many honors, including the Rolf Schock prize from the Swedish Academy of Sciences, the Boltzmann medal of IUPAP, and the Birkhoff prize of the AMS and SIAM" |
October 03, 2011, 415 - 515 pm at Harvard University Science Center Lecture Hall B |
| BASIC NOTIONS |
Jean-Pierre Serre () |
Integration and Equidistribution |
*Please note that the room may be moved to a larger hall depending on attendance" |
October 03, 2011, 300 - 400 pm at Science Center, room 507 |
| GAUGE THEORY & TOPOLOGY |
THOMAS KRAGH (MIT) |
Fibration of Symplectic Homology in Contangent Bundles |
Abstract Let M be a Liouville domain exact embedded in a cotangent bundle T*N. In this talk I will describe a fiber-wise version of symplectic homology of M defined for each q in N. I will then sketch a proof of why this does not depend on q and defines a local coefficient system, and why there is a Serre type spectral sequence converging to the symplectic homology of M - Page 2 of which is isomorphic to the homology of N with coefficients in this local system. Finally I will discuss applications, and if time permits - products" |
September 30, 2011, 330 - 430 pm at Science Center, room 507 |
| THE THURSDAY SEMINAR |
Mike Hopkins (HARVARD UNIVERSITY) |
The 3-catagory of conformal nets, part I |
" |
September 29, 2011, Thursday, September 29, 2011 at Science Center, room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
P. FERRARI (BONN) |
Non-intersecting random walks in the neighborhood of a symmetric tacnode |
" |
September 29, 2011, 3 pm at Science Center, Room 232 |
| TRIVIAL NOTIONS |
JEFF KUAN () |
Interlacing particle systems |
Abstract We consider an interlacing particle system in the two-dimensional lattice, which can also be interpreted as a growing stepped surface. This model has connections to the representation theory of Lie groups and to the AKPZ equation from mathematical physics. The main results are the discovery of new kernels, and that the fluctuations of the height function converge to the Gaussian free field" |
September 29, 2011, 1130 - 1230 at Science Center, room 309 |
| NUMBER THEORY SEMINAR |
JARED WEINSTEIN (BOSTON UNIVERSITY) |
Maximal varieties over finite fields |
Abstract This is joint work with Mitya Boyarchenko. We construct a special hypersurface X over a finite field, which has the property of maximality, meaning that it has the maximum number of rational points relative to its topology. Our variety is derived from a certain unipotent algebraic group, in an analogous manner as Deligne-Lusztig varieties are derived from reductive algebraic groups. As a consequence, the cohomology of X can be shown to realize a piece of the local Langlands correspondence for certain wild Weil parameters of low conductor." |
September 28, 2011, 3 - 4 pm at Science Center, Room 507 |
| INFORMAL DYNAMICS & GEOMETRY SEMINAR |
Will Cavendish (PRINCETON UNIVERSITY) |
Solenoids over 3-manifolds |
Abstract Given a compact topological space $X$, the inverse limit of the set of all finite sheeted regular covering spaces of $X$ yields a natural compact space called a solenoid, which comes equipped with a natural $\pi_1(X)$ action.In this talk I will discuss what is known about the topology of these spaces when $X$ is a 3-manifold, and will show how these objects can be used to study questions about finite-sheeted covering spaces of 3-manifolds" |
September 28, 2011, 430 pm at Science Center, room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
SASHA TSYMBALYUK & GIORGIA FORTUNA () |
Talk 1 Structure of Category O (Continuation of the talk last week). Talk 2 The fusion tensor product. |
" |
September 27, 2011, 530 PM at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
Elham Izadi (UNIVERSITY OF GEORGIA) |
Some limits of the Scorza correspondence |
The Scorza correspondence is defined on the second Cartesian power of a smooth curve for an even theta-charactistic with no global sections (this is a special case of the Szergo Kernel). We compute some limits of this correspondence, for instance when the theta characteristic acquires two sections or for some simple degenerations of the underlying curve. These are useful for understanding the map between the moduli spaces of curves given by the Scorza correspondence. This is joint work with Gavril Farkas" |
September 27, 2011, 300 pm at Science Center 507 |
| LOW DIMENSIONAL NOTIONS |
Peter Kronheimer (HARVARD UNIVERSITY) |
Seiberg-Written invariants of 4-manifolds |
Abstract This introductory talk will start with the idea of a Fredholm map" |
September 27, 2011, 1200 pm at Science Center |
| BASIC NOTIONS SEMINAR |
NOAM ELKIES (HARVARD UNIVERSITY) |
Covers of the Riemann sphere branched at few points |
A compact Riemann surface X equpped with a rational function is a branched cover of the Riemann sphere, and may be recovered from the branch locus together with some discrete combinatorial data. This analytic and topological construction arises remarkably often in number theory and related areas, where it gives rise to diverse theoretical and computational challenges. We outline some of these connections and questions, concentrating on the cases of three and four branch points where rich structure first emerges. For example, a celebrated theorem of Belyi asserts that given X and a (possibly empty) finite set S of points on X, there s a rational map with three branch points whose preimage contains S if and only if there is a finite extension F of the rational numbers such that X can be defined by algebraic equations with coefficients in F and each point of S has coordinates in F" |
September 26, 2011, 3 PM at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
STEVEN SIVEK (HARVARD UNIVERSITY) |
Monopole Floer homology and Legendrian knots |
Abstract We will define invariants of Legendrian knots using Kronheimer and Mrowka s construction of monopole Floer homology for sutured manifolds. These invariants have several interesting properties their behavior under stabilization and contact surgery suggests that they are closely related to the Lisca-Ozsvath-Stipsicz-Szabo invariant in knot Floer homology, and they are functorial with respect to Lagrangian concordance. As an application, we will construct many examples of non-loose knots in overtwisted contact manifolds." |
September 23, 2011, 330 - 430 pm at Science Center, Room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
O. BERNARDI (MIT) |
Computing the moments of the GOE bijectively PLEASE NOTICE THE CHANGE IN ROOM |
Abstract We consider the problem of finding the nth moment of the eigenvalues of the matrices in the Gaussian Orthogonal Ensemble (GOE). This problem is closely related to a question about the different ways of gluing the edges of a 2n-gon in pairs so as to create a surface without boundary. More precisely, among the (2n)!/n! possible gluings, how many times does one get each surface (considered up to homeomorphism)? In this talk, we will recall the connection between the two questions, and present a bijective solution. Our results are analogous to the one obtained by Harer and Zagier (1986) about the gluings of a 2n-gon giving an orientable surface (or in matrix terms, about the Gaussian Unitary Ensemble). We also recover a recurence formula for the moments of the GOE recently obtained by Ledoux." |
September 22, 2011, 3 pm at Science Center, Room 530 |
| THE THURSDAY SEMINAR |
JACOB LURIE (HARVARD UNIVERSITY) |
Chern-Simons theory |
" |
September 22, 2011, 3 - 5 PM at Science Center, Room 507 |
| COLLOQUIUM |
JEAN-PIERRE SERRE () |
Variation with p of the number of solutions mod p of a system of polynomial equations |
" |
September 22, 2011, 430 pm at Science Center, Hall A |
| LOGIC COLLOQUIUM |
HUGH WOODIN () |
The realm of the infinite |
First Presentation Exploring the Frontiers of Incompleteness." |
September 21, 2011, 4 PM at The Fong Auditorium, Harvard University |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
R.E. SCHWARTZ (BROWN UNIVERSITY) |
Polygonal outer billiards, polytope exchanges, and renormalization |
Abstract Polygonal outer billiards is a 2-dimensional piecewise isometric dynamical system on the plane, based on a convex polygon. I will explain how such a system always has a higher dimensional compactification which is a polytope exchange transformation (PET) defined in terms of two incommensurable Euclidean lattices. I will give evidence, by way of pictures and examples, that such double lattice PETs have a renormalization theory associated to them." |
September 21, 2011, 430 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
SASHA TSYMBALYUK () |
Structure of Category O |
Please notice the correction in location" |
September 20, 2011, 530 pm at MIT (2-190) |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
JACK HUIZENGA (HARVARD UNIVERSITY) |
Hilbert schemes of points, vector bundles, polynomial multiplication, and the golden ratio |
Abstract The Hilbert scheme of n points in the projective plane is a smooth projective variety of dimension 2n parameterizing zero-dimensional subschemes of length n. An interesting question is to determine the various birational models of this space. A first step in this program is to determine the cone of effective divisors. It turns out that this cone is closely related to the geometry of vector bundles on the plane. For many values of n, we will construct extremal effective divisors on the Hilbert scheme by studying Steiner Bundle, which are particularly nice vector bundles generalizing the tangent bundle. In particular, we will investigate the stability and splitting properties of these vector bundles. This will lead us to consider a basic problem about multiplication of polynomials in one variable, whose answer involves a surprising occurrence of the golden ratio and its continued fraction expansion." |
September 20, 2011, 3 PM at MIT (2-146) |
| LOW DIMENTIONAL NOTIONS SEMINAR |
STEVEN SIVEK () |
Contact Geometry and Giroux Correspondence |
Abstract A contact structure on a 3-manifold is a 2-plane field which is completely nonintegrable. We will define contact structures, prove some basic properties, and then investigate their relation to 3-dimensional topology. In particular, we will discuss the Giroux correspondence, which relates contact structures on a manifold to the notion of an open book decomposition." |
September 20, 2011, 4 - 5PM at Science Center, Hall D |
| BASIC NOTIONS SEMINAR |
DENNIS GAITSGORY (HARVARD UNIVERSITY) |
Contractibility of the space of rational maps |
Abstract We will define an algebro-geometric model for the space of rational maps from an algebraic curve X to an affine algebraic variety Z, and we ll show that if Z is rational this space has trivial homology. We ll then discuss applications of this result to the cohomology of the stack of G-bundles on X." |
September 19, 2011, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
JONATHAN BLOOM (MIT) |
Floer homology with boundary |
Abstract We extend the TQFT structure of monopole Floer homology to cobordisms with multiple ends, equipped with (degenerating) families of metrics. The story is complicated by the fact that the configuration space has boundary, consisting of reducible monopoles. We show how to package the cobordism relations among the resulting moduli spaces into algebraic structure, using a notion of path DGA on a directed hypergraph. Our approach is motivated by, and applies to, the finite-dimensional model Morse homology on a manifold with boundary. We discuss some applications." |
September 16, 2011, 330 PM at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
DAVID KAZHDAN (HARVARD UNIVERSITY) |
Background on quantum field theory |
" |
September 15, 2011, 3 - 5 PM at Science Center, Room 507 |
| DYNAMICS AND GEOMETRY SEMINAR |
CLIFFORD EARLE (CORNELL UNIVERSITY) |
Holomorphic coordinates on Teichmueller space and compactified moduli space |
" |
September 14, 2011, 430 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
KEERTHI MADAPUSI (HARVARD UNIVERSITY) |
The p-adic comparison isomorphism for abelian varieties via Dieudonne theory for log 1-motifs |
Abstract We will give a construction of a Dieudonne theory for degenerating abelian varieties and sketch how it can be used to construct a p-adic comparison isomorphism for semi-stable abelian varieties over a p-adic field." |
September 14, 2011, 3 - 4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
VIVEK SHENDE (MIT) |
On Severi degrees |
Abstract I will explain how Euler characteristics of Hilbert schemes of points encode the number of nodal curves present in a family. This allows results on the smoothness of relative Hilbert schemes to be translated into enumerative information. In particular, the multiplicities of the Severi varieties in the versal deformation of an integral planar curve are encoded by the Euler characteristics of the Hilbert schemes of the central fibre alone. In the global setting, the number of nodal curves in a general slice of a sufficiently ample linear system on a surface can be determined from the Euler characteristics of the relative Hilbert schemes. These in turn may be computed by a tautological integral over the Hilbert scheme of points; as a consequence we learn that these Severi degrees are given by universal polynomials in the Chern classes of surface and bundle." |
September 13, 2011, 3 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR ON GEOMETRIC REPRESENTATION THEORY |
DAVID KAZHDAN (HARVARD UNIVERSITY) |
Representations of Kac-Moody algebras and modules over quantum groups overview of the theory |
" |
September 13, 2011, 530 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
JOE HARRIS (HARVARD UNIVERSITY) |
Brill-Noether theory |
Abstract Brill-Noether theory deals with a basic question given an abstract curve $C$, how can we realize $C$ as a projective variety? The answer provides a critical link between the classical view of curves as subsets of projective space defined by polynomial equations, and the more modern view of curves as abstract schemes. In this talk I ll describe what s known about the answer, and survey some of the open problems in the area." |
September 12, 2011, 3 - 430 PM at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
MIKE HOPKINS (HARVARD UNIVERSITY) |
The 3-category of conformal nets background and topological motivation |
" |
September 08, 2011, 3-5pm at Science Center, Room 507 |
| GEOMETRY AND DYNAMICS SEMINAR |
SARAH KOCH (HARVARD UNIVERSITY) |
Twisted Matings of Polynomials |
" |
September 07, 2011, 430 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
DANIEL MATHEWS () |
Sutured Floer homology and TQFT |
Abstract We consider TQFT properties of sutured Floer homology, following from the work of Honda--Kazez--Matic. In certain simple cases, SFH has elementary algebraic and graphical descriptions, with curious connections to physics and representation theory, and can be considered as a Sutured Quantum Field Theory defined independently of holomorphic curves or Heegaard decompositions." |
May 13, 2011, 330 pm at Science Center, Room 507 |
| DYNAMICS AND GEOMETRY SEMINAR |
CURT MCMULLEN (HARVARD UNIVERSITY) |
Manifolds, topology and dynamics |
Subtitle Milnor s work and subsequent development" |
May 11, 2011, 4 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
VERA VERTESI () |
Transverse invariants in Heegaard Floer homology |
Abstract Using the language of Heegaard Floer knot homology recently two invariants were defined for Legendrian knots. One in the standard contact 3-sphere defined by Ozsvath, Szabo and Thurston in the combinatorial settings of knot Floer homology, on by Lisca, Ozsvath, Stipsicz and Szabo in knot floer homology for a general contact 3--manifold. Both of them naturally generalized to transverse knots. In this talk I will give an characterization of the transverse invariant, similar to the one given by Ozsvath and Szabo for the contact invariant. Namely for transverse braids both transverse invariants are given as the bottommost elements with respect to the filtration of knot Floer homology given by the axis. The above characterization allows us to prove that the two invariants are the same in the standard contact 3--sphere. This is joint work with J. Baldwin and D.S. Vela-Vick" |
May 06, 2011, 330 PM at Science Center, Room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
IVAN CORWIN (COURANT INSTITUTE NYU) |
Harmonic analysis of the geometric (tropical) RSK correspondence via Whittaker functions |
Abstract Consider a matrix of real, positive weights distributed independently as inverse-gamma random variables. We prove that the push-forward of this product measure under Kirillov s geometric (or as he called it tropical) Robinson-Schensted-Knuth correspondence has a particularly nice structure which hallows for many exact calculations. Underlying this structure is an algebraic identity in the form of an intertwining relationship between two Markov kernels, and underlying the exact calculations is the fact that Whittaker functions diagonalize the resulting Markov chain. As an application we compute the Laplace transform for the partition function of a positive temperature, discrete directed polymer model with inverse-gamma weight,s generalizing some of Johansson s work on last passage percolation. We present this within the wider context of the Kardar-Parisi-Zhang equation and universality class. This is based on joint work in progress with Neil O Connell, Timo Seppalainen and Nikos Zygouras." |
May 05, 2011, 3 pm at Science Center, Room 232 |
| COLLOQUIUM |
FLORIAN POP (UNIVERSITY OF PENNSYLVANIA) |
On the Ihara/Oda-Matsumoto Conjecture |
Abstract One of the exciting questions from Grothendieck s Esquisse d un Programme is to go give a geometric-combinatorial description of the absolute Galois group of the rationals by using its action on geometric fundamental groups. My talk will be about that question, in particular discussing a solution of the so called Ihara/Oda-Matsumoto Conjecture." |
May 05, 2011, 430 pm at Science Center, Hall D |
| NUMBER THEORY SEMINAR |
TASHO KALETHA (IAS) |
Simple wild L-packets |
Abstract In a recent paper, Gross and Reeder have described an interesting class of smooth representations of reductive p-adic groups, which they call simple supercuspidal representations. They also describe a set of Langlands parameters which have minimal wild ramification, and conjecture that these simple wild parameters are the ones assigned to the simple supercuspidal representations under the local Langlands correspondence. In this talk we will report on a construction which explicitly associates to each simple wild parameter a finite set of simple supercuspidal representations. This finite set satisfies many properties expected from an L-packet-it provides as stable character, contains a unique generic representation for a fixed Whittaker datum, and admits as description in terms of the Langlands dual group" |
May 04, 2011, 3 - 4 PM at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
VLADIMIR LAZIC (IMPERIAL COLLEGE, LONDON) |
The MMP revisited |
Abstract I will show how finite generation of the canonical ring implies all the known foundational theorems of Mori theory. This is joint work with A. Corti" |
May 03, 2011, 4 pm at MIT (2-142) |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
MARTIN OLSON (UC BERKELEY) |
Borel-Moore homology, cycle maps, and local terms in etale cohomology |
Abstract For singular schemes, the natural target for cycle class maps is Borel-Moore homology. In this talk I will discuss ongoing work aimed at understanding the relationship between this cycle class map and the calculation of local terms for correspondences acting on etale cohomology, as defined in SGA 5. In particular I will discuss compatibility with Fulton s refined intersection products, as well as a variant cohomology theory which is the target for localized chern class maps" |
May 03, 2011, 3 pm at MIT (2-142) |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
JEREMY QUASTEL (UNIVERSITY OF TORONTO) |
Exact formulas in random growth and directed polymers |
Abstract About 30 years ago it was observed by physicists that a large class of one dimensional random systems (the KPZ universality class) have highly anomalous, but universal, fluctuation behavior. We will describe some of the models, and survey recent progress in proving some of the conjectured scalings and limiting distributions for the Kardar-Parisi-Zhang equation itself, and the associated continuum random polymer" |
May 02, 2011, 1030 am at Science Center, Room 232 |
| GAUGE THEORY AND TOPOLOGY |
JACOB RASMUSSEN (UNIVERSITY OF CAMBRIDGE, AND SIMONS CENTER FOR GEOMETRY AND PHYSICS) |
Khovanov homology of torus knots |
Abstract I will describe some conjectures about the structure of Khovanov homology for torus knots. They are motivated by work of Oblomkov and Shende in algebraic geometry, but can be stated purely in terms of the representation theory of the rational Cherednik algebra (a.k.a. rational DAHA). This is joint work with E. Gorsky, A. Oblomkov, and V. Shende." |
April 29, 2011, 11 am at Science Center, Room 507 |
| SPECIAL NUMBER THEORY SEMINAR |
JEAN-MARC FONTAINE (UNIVERSITE' DE PARIS-SUD) |
p-adic Galois representations and vector bundles on curves |
Abstract Joint work with Laurent Fargues These three talks will be a continuation of my previous talk. Let F be a perfect field of characteristic p>0 and E be a non archimedean local field whose residue field is a subfield of F. To these data, we associate a complete curve X=X_{F,E} and study vector bundles over X. 1- Construction of the ring B of rigid analytic functions on the punctured unit disk of F with values in extensions of E. Factorization in B and description of the curve X_{F,E} when F is algebraically closed. 2- Galois descent, description of X_{F,E} in general and study of vector bundles. 3- Applications to p-adic Hodge theory" |
April 28, 2011, 3 - 4 pm at Science Center, Room 309A |
| THE THURSDAY SEMINAR |
JACOB LURIE (HARVARD UNIVERSITY) |
The Chain Rule (Continued) |
" |
April 28, 2011, 3 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
ZHIWEI YUN (MIT) |
Simple Lie groups as motivic Galois groups |
Abstract More than two decades ago, J.P. Serre asked the following question can every simple Lie group be realized as the motivic Galois group of some motive over Q? Concretely, this means whether there are Galois representations (for Q), with Zariski dense image in a given simple Lie group, which come from geometry. The question has been open for all exceptional groups other than G_2. In this talk, I will give a *uniform* construction of motives over Q, which give an affirmative answer to Serre s question for most simple Lie groups including E_7, E_8, F_4 and G_2. The construction starts with certain automorphic representations and uses techniques from geometric Langlands theory." |
April 27, 2011, 3 PM at Science Center, Room 507 |
| SPECIAL SEMINAR |
PAUL HORN (EMORY UNIVERSITY) |
Random Processes on Graphs |
Abstract In this talk, we discuss two processes on graphs. First, we study a model of taking a random subgraph of a graph where each edge of the original graph is taken independently with some probability $p$. Here, we establish the critical threshold for the emergence of a giant component for a wide class of underlying graphs. Second, we study the evolution of the contact process, a stochastic model of disease, on arbitrary finite graphs. In both cases, we will use the tools of spectral graph theory to understand the geometry of the underlying network. We then combine this understanding with tools from probabilistic combinatorics to understand the high probability result of the processes. Organized by Professor Shing-Tung Yau." |
April 27, 2011, 3 - 4 pm at Science Center, Room 530 |
| GEOMETRY AND DYNAMICS SEMINAR |
MOON DUCHIN () |
Flat structures as currents |
" |
April 27, 2011, 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
LONGZHI LIN (JOHN HOPKINS UNIVERSITY) |
Modified mean curvature flow of star-shaped hypersurfaces in hyperbolic space |
Abstract I will talk about my recent joint work with Ling Xiao on the long time existence of modied mean curvature flow (MMCF) of star-shaped hypersurfaces in hyperbolic space with prescribed asymptotic boundary at infinity. As an application, this recovers the existence and uniqueness of smooth complete hypersurfaces of constant mean curvature in hyperbolic space with prescribed asymptotic boundary at infinity, which was first shown by Guan and Spruck. Organized by Professor Shing-Tung Yau" |
April 26, 2011, 130-300 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
QILE CHEN (BROWN UNIVERSITY) |
Stable logarithmic maps to Deligne-Faltings pairs |
Abstract For the purpose of computing Gromov-Witten invariants, the compactification of the space of relative stable maps with respect to a smooth divisor were introduced and studied using expanded degeneration during the past decade. I will introduce a new way of compactification using logarithmic structures in the sense of Kato-Fontaine-Illusie. In particular, this covers many interesting cases, such as the target variety with a simple normal crossings divisor, or a simple normal crossings degeneration of a variety with simple normal crossings singularities. This is joint work with Dan Abramovich" |
April 26, 2011, 3 pm at MIT (2-142) |
| BASIC NOTIONS SEMINAR |
() |
There is no Basic Notions Seminar this week. |
" |
April 25, 2011, at |
| GAUGE THEORY AND TOPOLOGY |
CHRIS WOODWARD (RUTGERS UNIVERSITY) |
Quilted Floer theory and fibered Dehn twists |
Abstract I will talk about a generalization of the exact triangle for Dehn twists, due to Seidel, to the fibered (i.e. Morse-Bott) case. The resulting triangle relates a fibered Dehn twist with a push-pull functor associated to the vanishing cycle, constructed using quilted Floer theory. Applied to moduli spaces of SU(r) bundles with singularities around graphs it gives an exact triangle similar to Khovanov-Rozansky.This is joint with K. Wehrheim." |
April 22, 2011, 330 pm at Science Center, Room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
A. AUFFINGER (NYU) |
Landscape of random function on many variables via Random Matrix Theory |
" |
April 21, 2011, 4 pm at Science Center, Room 232 |
| THE THURSDAY SEMINAR |
JACOB LURIE (HARVARD UNIVERSITY) |
The Chain Rule in the Calculus of Functors |
" |
April 21, 2011, 3 pm at Science Center, Room 507 |
| SPECIAL NUMBER THEORY SEMINAR |
JEAN-MARC FONTAINE (UNIVERSITE' DE PARIS-SUD) |
p-adic Galois representations and vector bundles on curves |
Abstract Joint work with Laurent Fargues These three talks will be a continuation of my previous talk. Let F be a perfect field of characteristic p>0 and E be a non archimedean local field whose residue field is a subfield of F. To these data, we associate a complete curve X=X_{F,E} and study vector bundles over X. 1- Construction of the ring B of rigid analytic functions on the punctured unit disk of F with values in extensions of E. Factorization in B and description of the curve X_{F,E} when F is algebraically closed. 2- Galois descent, description of X_{F,E} in general and study of vector bundles. 3- Applications to p-adic Hodge theory." |
April 21, 2011, 3 - 4 pm at Science Center, Room 309A |
| GEOMETRY AND DYNAMICS SEMINAR |
NATHAN DUNFIELD (UNIVERSITY OF ILLINOIS, URBANA-CHAMPAIGN) |
The least spanning area of a knot and the Optimal Bounding Chain Problem |
" |
April 20, 2011, 4 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
ALEXANDER A BEILINSON (UNIVERSITY OF CHICAGO) |
i p-adic periods and derived de Rham cohomology |
Abstract The classical period isomorphism (integration of algebraic differential forms on topological cycles) identifies algebraic de Rham cohomology of a complex algebraic variety with its singular cohomology. The existence of a similar isomorphism for varieties over Q_p was conjectured in the beginning of 80s by Fontaine, and was later established by several authors (Faltings, Niziol, Tsuji). In the talks I will explain another simple construction of the p-adic periods isomorphism. No preliminary acquaintance with the subject is needed" |
April 20, 2011, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
FREDERICK DENEF (HARVARD PHYSICS DEPARTMENT) |
Black hole bound states |
Abstract N=2 supergravity theories in our four dimensions admit a zoo of exact, stable, stationary multi black hole bound state solutions, of arbitrary complexity. I will review their construction and some of the remarkable results they have led to, including in particular general wall crossing formulae, and will formulate and motivate a number of existence conjectures. Differential Geometry Seminars are organized by Professor Shing-Tung Yau" |
April 19, 2011, 130 - 300 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
ALEXANDER A BEILINSON (UNIVERSITY OF CHICAGO) |
p-adic Periods and Derived de Rham Cohomology |
Abstract The classical period isomorphism (integration of algebraic differential forms on topological cycles) identifies algebraic de Rham cohomology of a complex algebraic variety with its singular cohomology. The existence of a similar isomorphism for varieties over Qp was conjectured in the beginning of 80s by Fontaine, and was later established by several authors (Faltings, Niziol, Tsuji). In the talks I will explain another simple construction of the p-adic periods isomorphism. No preliminary acquaintance with the subject is needed" |
April 19, 2011, 3 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
MIRANDA CHENG (HARVARD UNIVERSITY) |
The sporadic group M24 and (Mock) Automorphic forms |
Organized by Professor Shing Tung Yau" |
April 18, 2011, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
() |
There is no Gauge Theory Seminar this week. |
" |
April 15, 2011, at |
| SPECIAL NUMBER THEORY SEMINAR |
TOMER SCHLANK (HEBREW UNIVERSITY OF JERUSALEM) |
Relative Homotopy type and Diophantine Equations/PLEASE NOTICE THE CHANGE IN PLACE AND TIME |
Abstract In 1969 Artin and Mazur defined the étale homotopy type Et(X) of scheme X, as a way to homotopically realizing the étale topos of X. In the talk I shall present for a map of schemes X→S a relative version of this notion. We denote this construction by Et(X/S) and call it the homotopy type of X over S. It turns out that the relative homotopy type can be especially useful in studying the sections of the map X→S. In the special case where S = Spec K is the spectrum of a field, the set of sections is just the set of rational points X(K) and then the relative homotopy type Et(X/Spec K) can be used to define obstructions to the existence of a rational point on X. When K in a number field it turns out that most known obstructions for the existence of rational points (such as Grothendieck s section obstruction, the regular and étale Brauer-Manin obstructions, etc.) can be obtained in this way and this point of view can be used to show new properties of these obstructions. In the case where K is a general field or ring this method allows one to get new obstructions that generalize the obstructions above. This is joint work in progress with Y. Harpaz. Many of the results appear in our joint paper http//arxiv.org/abs/1002.1423" |
April 15, 2011, 1 pm at Science Center, Room 309 |
| BRANDIES-HARVARD-MIT-NORTHEASTERN JOINT MATHEMATICS COLLOQUIUM |
THOMAS HAINES (MARYLAND/IAS) |
Endoscopic transfer of the Bernstein center |
Abstract The Langlands-Shelstad theory of endoscopy plays a central role in the study of Shimura varieties and the Arthur-Selberg trace formula. The fundamental lemma and a deep consequence, endoscopic transfer, have now been established in works of Ngo, Waldspurger, and Hales. Both of these statements are identities involving orbital integrals of a function $f$ on a $p$-adic group $G$ and those of a certain transfer function $f^H$ on a related group $H$, called endoscopic. This talk will give background on the fundamental lemma, some of its variants, and the roles they played. Then I will describe a conjectural construction of a large class of matching functions in the Bernstein centers of $G$ and $H$. This conjecture has been verified in some encouraging cases. The functions being transferred arise in connection with Shimura varieties with bad reduction, and some applications to that subject will also be briefly discussed" |
April 14, 2011, 430 pm at Science Center, Hall D |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
() |
There is no Random Matrix Seminar this week. |
" |
April 14, 2011, at |
| SPECIAL NUMBER THEORY SEMINAR |
JEAN-MARC FONTAINE (UNIVERSITE' DE PARIS-SUD) |
p-adic Galois representations and vector bundles on curves |
AbstractJoint work with Laurent Fargues These three talks will be a continuation of my previous talk. Let F be a perfect field of characteristic p>0 and E be a non archimedean local field whose residue field is a subfield of F. To these data, we associate a complete curve X=X_{F,E} and study vector bundles over X. 1- Construction of the ring B of rigid analytic functions on the punctured unit disk of F with values in extensions of E. Factorization in B and description of the curve X_{F,E} when F is algebraically closed. 2- Galois descent, description of X_{F,E} in general and study of vector bundles. 3- Applications to p-adic Hodge theory." |
April 14, 2011, 3 - 4 PM at Science Center, Room 309A |
| THE THURSDAY SEMINAR |
MIKE HOPKINS (HARVARD UNIVERSITY) |
The Tits building and the partition complex, after Arone-Dwyer, II |
" |
April 14, 2011, 3 - 5 PM at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
THOMAS J. HAINES (UNIVERSITY OF MARYLAND AT COLLEGE PARK) |
Test functions for Shimura varieties with arbitrary level |
Abstract The Langlands-Kottwitz expression of the Lefschetz formula for a Shimura variety with good reduction at p involves twisted orbital integrals at p evaluated on a certain test function in a suitable spherical Hecke algebra. To extend this to bad reduction cases, one needs to find the correct test functions in Hecke algebras with deeper level. I will explain a conjecture (joint with Kottwitz) which predicts the correct test function for arbitrary level. I will then discuss joint work with Rapoport which verifies a stronger version of this conjecture for certain unitary Shimura varieties (the Drinfeld case) with Γ1(p)-level at p" |
April 13, 2011, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
GABOR LIPPNER (HARVARD UNIVERSITY) |
Quantum Tunneling on Graphs |
Abstract We investigate the evolution of a quantum particle moving on a graph, in the presence of a potential. In the case of a double-well potential we show that whether Klein s paradox can be observed depends only on the local geometry. In contrast, when there are three wells, we can exhibit a rather surprising instability phenomenon the local evolution of the particle can be very sensitive to arbitrarily distant, small perturbations of the graph. (Joint work with Yong-Lin and Shing-Tung Yau). Differential Geometry Seminars are organized by Professor Shing-Tung Yau" |
April 12, 2011, 130 pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
HEPING HE (UNIVERSITY OF KANSAS) |
Asymptotic properties of maximum likelihood estimators in models with multiple change points |
Abstract Models with multiple change points are used in many fields; however, the theoretical properties of such models have received relatively little attention. The goal of this paper is to establish the asymptotic properties of maximum likelihood estimators of the parameters of a multiple-change-point model for a general class of models in which the form of the distribution can change from segment to segment and in which, possibly, there are parameters that are common to all segments. Consistency of the maximum likelihood estimators of change points is established and the rate of convergence is determined; the asymptotic distribution of the maximum likelihood estimators of the parameters of the within-segment distributions is also derived. Since the approach used in single change-point models is not easily extended to multiple change-point models, these results require the development of new tools for analyzing the likelihood function in a multiple change-point model. This seminar is organized by Professor Shing-Tung Yau" |
April 11, 2011, 2 pm at Science Center, Room 530 |
| BASIC NOTIONS SEMINAR |
JOE RABINOFF (HARVARD UNIVERSITY) |
Implicitization via harmonic analysis on graphs, non-Archimedean analytic curves, and tropicalization |
Organized by Professor Shing Tung Yau" |
April 11, 2011, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
BASAK GUREL (VANDERBILT) |
Conley conjecture for negative monotone symplectic manifolds |
Abstract The Conley conjecture, formulated by Coney in 1984, asserts the existence of infinitely many periodic orbits for Hamiltonian diffeomorphisms of tori and was established by Hingston in 2004. Of course, one can expect the conjecture to hold for a much broader class of closed manifolds and this is indeed the case. For instance, by now, it has been proved for all closed, symplectically aspherical manifolds and Calabi-Yau manifolds using symplectic topological methods. Most recently, jointly with Ginzburg, we establish the conjecture for negative monotone, closed symplectic manifolds. In this talk, based on joint works with Ginzburg, we wil examine the question of existence of infinitely many periodic orbits for Hamiltonian diffeomorphisms and outline a proof of the Conley conjecture in the negative monotone case." |
April 08, 2011, 330 pm at Science Center, Room 507 |
| LOGIC COLLOQUIUM |
BJORN POONEN (MIT) |
Diophantine subsets of rational numbers |
Abstract I will discuss recent work of Koenigsmann,building on work of the speaker, showing that the complement of Z in Q is diophantine (or equivalently, defined by an existential formula). If Z itself were shown to be diophantine in Q, it would follow that there is no algorithm to decide whether a multivariable polynomial equation has a solution in rational numbers. For information about background material to be read, visit logic.harvard.ed" |
April 08, 2011, 4 pm at Science Center, Room 309 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
R. KENYON (BROWN UNIVERSITY) |
Dimers and integrability |
Abstract This is joint work with A. Goncharov. The dimer model is a probability measure on the set of perfect matchings of a graph. Natural parameters are edge weights. We show that the parameter space of dimer models (equivalently, the space of line bundles) on a bipartite graph on a torus has the structure of a cluster variety, and is equipped with a Poisson structure defining a (quantizable) integrable Hamiltonian system. A complete set of commuting Hamiltonians can give explicitly in terms of dimers" |
April 07, 2011, 3 pm at Science Center, Room 232 |
| THE THURSDAY SEMINAR |
ROBIN KOYTCHEFF () |
Orthogonal Calculus (part 2) |
" |
April 07, 2011, 3 - 5 PM at Science Center, Room 507 |
| SPECIAL NUMBER THEORY SEMINAR |
JEAN-MARC FONTAINE (UNIVERSITE' PARIS-SUD) |
$p$-adic Galois representations and vector bundles on curves |
Abstract I shall describe a part of a joint work with Laurent Fargues. Let $F$ be a perfect field of characteristic $p>0$and $E$ be a non archimedean local field whose residue field is a subfield of $F$. To these datas, we associate a \og complete regular curve\fg $X=X_{F,E}$ defined over $E$. One can define the degree of a vector bundle over $X$ and Harder-Narasimhan theorem holds. If $\overline F$ is an algebraic closure of $F$, we have an equivalence of categories between semi-stable of slope $0$ vector bundles over $X$ and continuous finite dimensional $E$-linear representations of ${\rm Gal}(\overline F/F)$. If $\overline K$ is the algebraic closure of a $p$-adic field $K$, there is a field $F$as above, which is algebraically closed, naturally associated to $\overline K$. The group $G_K={\rm Gal}(overline K/K)$ acts on $X=X_{F,\mathbb Q_p}$. We ll define what it means for a $G_K$-equivariant vector bundle over $X$ to be {\it de Rham} and describe an equivalence between the category of de Rham $G_K$-equivalent vector bundles over $X$ and the category of {\it filtered $(\varphi,N,G_K)$-modules over $K$}. The two main theorems of the arithmetic part of $p$-adic Hodge theory are recovered by applying this equivalence to semistable vector bundles of slope $0" |
April 07, 2011, 3 - 4 pm at Science Center, Room 221 |
| NUMBER THEORY SEMINAR |
DANIEL KANE (HARVARD UNIVERSITY) |
Presentations for Deligne-Lusztig Curves |
Abstract Deligne-Lusztig varieties are an important construction for studying the representation theory of Chevalley groups G. For four of these groups, A1, 2A2,2B2, and 2G2, the associated variety is a curve with symmetry group G and a large number of rational points for its genus. We discuss the definitions of the latter three of these groups and come up with canonical constructions for these groups and their curves." |
April 06, 2011, 3 PM at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
STEFAN ROSEMANN (INSTITUTE OF MATHEMATICS OF THE UNIVERSITY OF JENA (GERMANY)) |
Yano-Obata conjecture for holomorph-projective transformations |
Abstract In this talk, I want to present a joint work with A. Fedorova, V. Kiosak and V. Matveev. Given a kaehler manifold, one associates a class of distinguished curves to the Kaehler metric which are called (holomorphically)-planar curves. Such curves can be seen as some kind of generalization of geodesics on Kahler manifolds. On problem of interest is to understand whether the group of holomorph-projective transformations (i.e., the group of all bi-holomorphic mappings which preserve the set of all h-planar curves) is really bigger than the group of holomorphic isometries of the Kaehler manifold. We have proven a classical conjecture attributed to Yano and Obata stating that on a compact, connected Riemannian Kaehler manifold, the connected components of both groups coincide unless the metric has constant positive holomorphic sectional curvature. Differential Geometry Seminars are organized by Professor Shing-Tung Yau" |
April 05, 2011, 130 - 300 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
DANIEL GREB (ALBERT-LUDWIGS-UNIVERSITAT FREIBURG) |
Lagrangian fibrations on hyperkahler manifolds |
Hyperkahler (also called irreducible holomorphic symplectic) manifolds form an important class of manifolds wit trivial canonical bundle. One fundamental aspect of their structure theory is the question whether a given hyperkaehler manifold admits a Lagrangian fibration. I will report on a joint project with Christian Lehn and Soenke Rollenske investigating the following question of Beauville if a hyperkaehler manifold contains a complex torus T as a Lagrangian submanifold, does it admit a (meromorphic) Lagrangian fibration with fibre T" |
April 05, 2011, 3 pm at MIT (2-142) |
| BASIC NOTIONS SEMINAR |
LI-SHENG TSENG (HARVARD UNIVERSITY) |
Similarities between complex and symplectic analysis |
Organized by Professor Shing Tung Yau" |
April 04, 2011, 3 PM at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
MICHAEL USHER (UNIVERSITY OF GEORGIA) |
Boundary depth and the Hofer norm |
Abstract In 1990, Hofer introduced a remarkable conjugation-invariant norm on the group of Hamiltonian diffeormorphisms of a symplectic manifold. Many properties of this norm remain little-understood; in particular it is still not known whether the group always has infinite diameter with respect to the norm. I will discuss a proof that the group has infinite diameter whenever the manifold satisfies a certain dimple dynamical condition--indeed, under this condition, the group even contains subgroups quasi-isometric to infinite-dimensional normed vector spaces. The proof is based on Hamiltonian Floer theory, and in particular on the behavior of a Floer-theoretic quantity called the boundary depth of a hamiltonian diffeomorphism" |
April 01, 2011, 330 - 430 PM at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
ROBIN KOYTCHEFF () |
Orthogonal Calculus/PLEASE NOTE THE CHANGE OF LOCATION |
Abstract I will talk about Michael Weiss paper Orthogonal Calculus, which studies functors from vector spaces with an inner product to spaces. As one might expect, this flavor of calculus bears some resemblance to the homotopy calculus and the manifold calculus. One outcome of this theory is that the derivatives reproduce and generalize characteristic classes" |
March 31, 2011, 3 - 5 pm at Science Center, Room 309 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
NICK PATTERSON (BROAD INSTITUTE) |
Large Matrices and Genetic. PLEASE NOTICE THE CHANGE IN TIME AND PLACE. |
Abstract We describe how large matrices arise in Genetics and give some illustrations of the application of modern statistical methods to the analysis." |
March 31, 2011, 4 pm at Science Center, Room 309 a |
| DIFFERENTIAL GEOMETRY SEMINAR |
HONGNIAN HUANG (CIRGET UNIVERSITY OF QUEBEC AT MONTREAL) |
Symmetries of extremal metrics on projective bundles and stability. PLEASE NOTICE THE CHANGE IN TIME. |
Abstract In this talk, we will discuss some partial results in a project initiated by Vestislav Apostolov aiming to solve a conjecture about the specific form of an extremal Kahler metric on a projective bundle over a curve. The conjecture, on one hand, connects to the Donaldson-Uhlenbeck-Yau Theorem and, on the other hand relates the existence of extremal metrics to the stability of the vector bundle, which is a natural extension of Yau s conjecture in the case of Kaehler Einstein metric when the first Chern class of the Kaehler manifold is positive. Differential Geometry Seminars are organized by Professor Shing-Tung Yau" |
March 29, 2011, 1 - 2 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
JESSE KASS (UNIVERSITY OF MICHIGAN) |
The local structure of the compactified Jacobian |
Abstract The Jacobian variety of a non-singular curve in a basic tool in algebraic geometry, and a fundamental question is how to extend this construction to singular curves. Starting with work of Igusa in the 1950 s, a great deal of effort has gone into answering this question. Today we have a detailed understanding of how to assign a degenerate Jacobian to a singular curve, but our knowledge of the geometry of the resulting object is less extensive. In my talk, I discuss work on the local geometry of the Caporaso-Pandharipande degenerate Jacobian. This work is joint with Sebastian Casalaina-Martin and Filippo Viviani" |
March 29, 2011, 3 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
JACOB LURIE (HARVARD UNIVERSITY) |
Tamagawa Numbers Via Nonabelian Poincare Duality |
Organized by Professor Shing Tung Yau" |
March 28, 2011, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
PETER ALBERS (PURDUE UNIVERSITY) |
A variational approach to Givental's nonlinear Maslov index |
" |
March 25, 2011, 330 - 430 pm at Science Center, Room 507 |
| LOGIC COLLOQUIUM |
HARVEY M. FRIEDMAN () |
Algorithmic Unsolvability in Euclidean Geometry |
Abstract We show the algorithmic unsolvability of a number of decision procedures in ordinary two dimensional Euclidean geometry, involving lines and integer points. We also consider formulations involving integral domains of characteristic 0, and ordered rings. The main tool is the solution to Hilbert s Tenth Problem. The limited number of facts used from recursion theory and isolated at the beginning." |
March 25, 2011, 4 - 530 PM at Science Center, Room 309 |
| JOINT BRANDEIS-HARVARD-MIT NORTHEASTERN MATHEMATICS COLLOQUIUM |
MATILDE MARCOLLI (CALTECH UNIVERSITY) |
Quantum statistical mechanics and anabelian geometry |
Abstract I will review constructions of quantum statistical mechanical systems (from the original Bost-Connes system to generalizations to arbitrary number fields) that exhibit interesting arithmetic properties. Following ongoing work with Gunther Cornelissen, I will show how these quantum statistical mechanical systems an be used to reconstruct a number field from a family of L-series" |
March 24, 2011, 430 pm at Science Center, Hall D |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
M. ADLER (BRANDEIS UNIVERSITY) |
Dyson's Brownian motions and critical diffusions |
Abstract We will discuss the zoo of universal processes that come from various limiting cases of Dyson s Brownian motion, as the number of diffusions becomes infinite, and how they connect with each other. In particular we will discuss a new process, namely the tacnode process and the hard tacnode process. These processes are realized also from discrete models, like joining 2 Aztec Diamonds or 2 multi-layer PNG s meeting, the latter process coming only from a special case of the first model" |
March 24, 2011, 3 pm at Science Center, Room 232 |
| THE THURSDAY SEMINAR |
ALEXANDER BERGLUND (UNIVERSITY OF COPENHAGEN) |
Minimal Koszul Models |
Abstract I will briefly review Koszul duality for algebras over operads and some of its uses in algebraic topology, in particular the role of the recently established Koszul self-duality of chains on the little n-cubes operad. Then I will introduce what I call Koszul models for spaces and describe how these can be used for calculations of in particular the homology of free and based loop spaces and rational homotopy groups of spaces of self-homotopy equivalences" |
March 24, 2011, 3 - 5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
DANIEL KANE (HARVARD UNIVERSITY) |
Ranks of 2-Selmer Groups of Twists of an Elliptic Curve |
Abstract Let E/Q be an elliptic curve with full 2-torsion over Q. We wish to study the distribution of the ranks of the 2-Selmer groups of twists of E as we vary the twist parameter. A recent result of Swinnerton-Dyer shows that if E has no cyclic 4- isogeny defined over Q, then the density of twists with given rank approaches a particular distribution. Unfortunately Swinnerton-Dyer proved this result for an unusual notion of density. His notion of density can be thought of as letting the number of primes dividing the twist parameter go to infinity. We extend this result to cover density in the natural sense." |
March 23, 2011, 3 - 4 pm at Science Center, Room 507 |
| DYNAMICS AND GEOMETRY SEMINAR |
JOHN HUBBARD (CORNELL UNIVERSITY) |
On the density of Strebel differentials |
" |
March 23, 2011, 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
WENXUAN LU (MIT) |
Instanton Correction, Wall Crossing and Mirror Symmetry of Hitchin's Moduli Spaces |
Abstract We study two instanton correction problems of Hitchin s moduli spaces along with their wall crossing formulas. The hyperkahler metric of a Hitchin s moduli space can be put into an instanton-corrected form according to physicists Gaiotto, Moore and Neitzke. The problem boils down to the construction of a set of special coordinate which can be constructed as Fock-Goncharov coordinates associated with foliations of quadratic differentials on a Riemann surface. A wall crossing formula of Kontsevich and Soibelman arises both as a crucial consistency condition and an effective computational tool. On the other hand Gross and Siebert have succeeded in determining instanton corrections of complex structures of Calabi-Yau varieties in the context of mirror symmetry from a singular affine structure with additional date. We will show that the two instanton correction problems are equivalent in an appropriate sense. This is a nontrivial statement of mirror symmetry of Hitchin s moduli spaces which till now has been mostly studied in the framework of geometric Langlands duality. This result provides examples of Calabi-Yau varieties where the instanton correction(in the sense of mirror symmetry) of metrics and complex structures can be determined. Differential Geometry Seminars are organized by Professor Shing-Tung Yau" |
March 22, 2011, 130 - 300 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
LASZLO ERDOS (UNIVERSITY OF MUNICH) |
Large atoms and molecules in a self-generated magnetic field |
Abstract We consider a large neutral molecule with total nuclear charge $Z$ in non-relativistic quantum mechanics with a self-generated classical electromagnetic field. To ensure stability, we assume that $\kappa=Z\alpha^2$ is sufficiently small, where $\alpha$is the fine structure constant. We show that, in the simultaneous limit $Z\to\infty$, $\al\to 0$ such that $\kappa=Z\al^2$ is fixed, the ground state energy of the system is given by a two term expansion $c_1Z^{7/3} + c_2(\kappa) Z^2 + 0(Z^2)$. The leading term is given by the non-magnetic Thomas-Fermi theory. Our result shows that the magnetic field affects only the second (so-called Scott) term in the expansion. In this talk I will summarize related results about stability of matter and large $Z$ expansion. Some connections to semiclassical analysis with rough data will also be explained. Basic Notions Seminars are organized by Professor Shing-Tung Yau" |
March 21, 2011, 3 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
MARK BEHRENS () |
Derivatives of the identity, ctd |
" |
March 10, 2011, 3 - 5 pm at Science Center, Room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
T. AUSTIN (BROWN UNIVERSITY) |
Some recent advances in Multiple Recurrence |
Abstract In 1975 Szemeredi proved the remarkable combinatorial fact that any subset of the integers having positive upper density contains arbitrarily long arithmetic progressions. Shortly afterwards Furstenberg gave a new proof of Szemeredi s Theorem using a conversion to an assertion of multiple recurrence for probability-preserving systems, which he then proved using newly-developed machinery in ergodic theory. Furstenberg s work gave rise to a new subdiscipline called Ergodic Ramsey Theory, which then found several further combinatorial applications. More recent work has provided a much more detailed picture of the structures that underlie this area of ergodic theory, and offered a clearer insight into the connections between this field and purely combinatorial approaches to the same results. I will describe a purely structural question within ergodic theory that has recently emerged from these efforts, and whose solution in some special cases gives a new approach to the multidimensional generalizations of multiple recurrence and Szemeredi s Theorem" |
March 10, 2011, 3 pm at Science Center, Room 232 |
| NUMBER THEORY SEMINAR |
ABHINAV KUMAR (MIT) |
K3 surfaces and Hilbert modular surfaces |
Abstract There is an explicit birational map between the moduli space of principally polarized abelian surfaces, and a certain 3-dimensional family of elliptic K3 surfaces, which uses a Shioda-Inose structure on the K3 family. We will recall this map, and describe joint work with Noam Elkies which exploits it to obtain parametrizations and explicit equations for Hilbert modular surfaces Y−(D), which are moduli spaces for abelian surfaces with real multiplication by the full ring of integers in Q(D1/2). We use these explicit equations to find previously inaccesible examples (or families) of genus 2 curves with real multiplication, or modular forms with q-expansion coefficients in a real quadratic field" |
March 09, 2011, 3 - 4 pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
GREGG ZUCKERMAN (YALE UNIVERSITY) |
Modeling the mind with non-well founded set theory. Please note the change in time. |
Abstract In joint work with Willard Miranker, we describe a mathematical model of consciousness that incorporates a mapping from neural states in the brain to non-well founded sets in a Platonic universe. Specifically, this universe is the standard model of Aczel s set-theoretic axiom of anti-foundation. We define the notion of a consciousness operator on this universe and then we characterize mental activity as the application of consciousness operators to those sets which arise from neural states. Geometrically, the Aczel universe bears a formal resemblance to a bounded domain; proper classes provide an ideal boundary for the is domain. The collection of all consciousness operators is a very large commutative semigroup. The identity element of the semigroup of consciousness operators is the Russell operator, which corresponds to the proper class of all sets that are not elements of themselves. An informal introduction to our theory was presented a year ago at the Brandeis-Harvard-MIT- Northeastern colloquium with the title From Russell s Paradox to a Theory of Consciousness. A video of this lecture can be found online. Differential Geometry Seminars are organized by Professor Shing-Tung Yau" |
March 08, 2011, 415 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
STEFFEN MARCUS (BROWN UNIVERSITY) |
Polynomial Families of Tautological Classes on the Moduli Space of Curves |
Abstract The Tautological ring is a heavily studied subring of the Chow ring of the moduli space of curves. Simply stated, it is just large enough to contain all the known Chow classes admitting some geometric construction. In this talk, I will describe natural families of tautological classes which arise by pushing forward the virtual fundamental classes of spaces of relative stable maps to an unparameterized projective line. Relative in this case means our maps have prescribed ramification over zero and infinity given by partitions of the degree. Using an argument of Ravi Vakil, we show the families are polynomial in the parts of the partitions. I will discuss our approach to computing these polynomials explicitly using localization techniques. This is joint work with Renzo Cavalieri" |
March 08, 2011, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
VAIBHAV SURESH GADRE (HARVARD UNIVERSITY) |
Bounds for minimal pseudo-Anosov translation lengths in the complex of curves |
Abstract The work of Masur and Minsky with later refinements from Bowditch shows that the asymptotic translation lengths for the action of pseudo-Anosov maps on the complex of curves, are rational with bounded denominators. We will discuss new bounds for minimal translation lengths improving on the bounds given by Farb-Leininger-Margalit. This is joint work with Chia-yen Tsai" |
March 04, 2011, 330 - 430 PM at Science Center, Room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
J. DING (BERKELEY) |
Cover times, blanket times, and the Gaussian free field |
Abstract The cover time of a finite graph, (the expected time for the simple random walk to visit all the vertices) has been extensively studied, yet a number of fundamental questions concerning cover times have remained open. Aldous and Fill (1994) asked whether there is a deterministic polynomial-time algorithm that computes the cover time up to an O(1) factor. Winkler and Zuckerman (1996) defined the blanket time (when the empirical distribution is within a factor of 2, say, of the stationary distribution) and conjectured that the blanker time is always within O(1) of the cover time. The best approximation factor found so far for both these problems was (log log n)^2 for n-vertex graphs, due to Kahn, Kim, Lovasz, and Vu (2000). We show that the cover time of a graph, appropriately normalized, is proportional to the expected maximum of the (discrete) Gaussian free field on G. We use this connection and Talagrand s majorizing measures theory to deduce a positive answer to the question of Aldous and Fill and to establish the conjecture of Winkler and Zuckerman. These results extend to arbitrary reversible finite Markov chains. No prior knowledge of Talagrand s theory or of cover times will be assumed. This is joint work with James Lee and Tuval Peres" |
March 03, 2011, 3 pm at Science Center, Room 232 |
| THE THURSDAY SEMINAR |
MIKE HOPKINS (HARVARD UNIVERSITY) |
Symmetric powers and the Steinberg module (after Mitchell-Priddy and Arone-Dwyer) |
" |
March 03, 2011, 3 - 5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
WEI ZHANG (HARVARD UNIVERSITY) |
Fourier transform, period and L-function |
Abstract Existence of transfer in comparison of trace formulae (including the relative case) can usually be reduced to whether Fourier transform commutes with transfer (for example, in the endoscopic case). We show such commutativity in some relative cases. A first application is on the global conjecture of Gan-Gross-Prasad for unitary group about period and central L-values (under some local restriction and we assume Flicker-Rallis s description of quadratic base change). A second application is on a conjecture of Guo-Jacquet generalizing an early work of Waldspurger." |
March 02, 2011, 3 - 4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
MIRCEA MUSTATA (UNIVERSITY OF MICHIGAN) |
Invariants of singularities in zero and positive characteristic |
Invariants of singularities are defined in birational geometry via divisorial valuations, and are computed by resolution of singularities. In positive characteristic, one defines similar invariants via the action of the Frobenius morphism. The talk will give an overview of the known results and conjectures relating the two sets of invariants." |
March 01, 2011, 3 pm at MIT (2-142) |
| DIFFERENTIAL GEOMETRY SEMINAR |
CHRISTINA SORMANI (CUNY GC AND LEHMAN COLLEGE) |
Applications of Intrinsic Flat Convergence |
Abstract The intrinsic flat distance between oriented compact Riemannian manifolds with boundary was introduced in work with S. Wenger (UIC) applying methods of Ambrosio-Kirchheim. After reviewing this new concept, we will discuss potential applications to the stability of Euclidean space in the Positive Mass Theorem of Schoen-Yau and the stability of Schwarzschild space in the Penrose Inequality. Preliminary work with D. Lee (CUNY) covering the rotationally symmetric case leading to appropriate conjectures in the general case will be presented. The presentation is constructive and Riemannian and does not require knowledge of Geometric Measure Theory. Doctoral students are welcome to attend. Differential Geometry Seminars are organized by Professor Shing-Tung Yau" |
March 01, 2011, 130 - 300 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
RACHEL LOUISE EPSTEIN (HARVARD UNIVERSITY) |
The Structure of the Computably Enumerable Sets |
Organized by Professor Shing Tung Yau" |
February 28, 2011, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
EDWARD WITTEN () |
Khovanov Homology and Gauge Theory |
Please notice the special location for this talk." |
February 25, 2011, 330 - 430 PM at Science Center, Hall C |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
() |
|
There is no Random Matrix Seminar this week." |
February 24, 2011, at |
| THE THURSDAY SEMINAR |
MARK BEHRENS () |
Derivatives of the identity |
" |
February 24, 2011, 3 - 5 PM at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
WUSHI GOLDRING (HARVARD UNIVERSITY) |
Galois representations associated to holomorphic limits of discrete series |
Abstract We attach Galois representations to automorphic representations on unitary groups whose weight (=component at infinity) is a holomorphic limit of discrete series. The main innovation is a new construction of congruences, using the Hasse Invariant, which avoids q-expansion and so is applicable in much greater generality than previous methods. Our result is a natural generalization of the classical Deligne-Serre Theorem on weight one modular forms and work of Taylor on GSp(4)" |
February 23, 2011, 3 - 4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
CHENYANG XU (MIT) |
Boundaries of Algebraic Varieties |
" |
February 22, 2011, 3 - 4 PM at MIT (2-142) |
| DIFFERENTIAL GEOMETRY SEMINAR |
SI LI (HARVARD UNIVERSITY) |
Higher genus B-model on the elliptic curve and almost holomorphic modular forms |
Abstract I ll discuss the joint work with Kevin Costello on the geometric framework of constructing higher genus B-model from perturbative renormalization of BCOV theory on Calabi-Yau manifolds. This is conjectured to be the mirror of higher genus Gromov-Witten theory in the A-model. We carry out the construction in the one-dim cases, i.e. , elliptic curves, and show that such constructed B-model correlation functions on the elliptic curve is given by almost holomorphic modular forms, and can be identified under the mirror map with the A-model descendant Gromov-Witten invariants. This is the first compact example where mirror symmetry can be established at all genera. Differential Geometry Seminars are organized by Professor Shing-Tung Yau" |
February 22, 2011, 130 - 300 PM at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
() |
There will be no seminar due to President's Day |
" |
February 21, 2011, at |
| GAUGE THEORY AND TOPOLOGY |
STEVEN SIVEK () |
A bordered Chekanov-Eliashberg algebra |
" |
February 18, 2011, 330 - 430 PM at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
DAVID AYALA (HARVARD UNIVERSITY) |
Embedding calculus again |
" |
February 17, 2011, 3 - 5 pm at Science Center, Room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
LIONEL LEVINE (MIT) |
Logarithmic fluctuations from circularity |
Abstract Start with n particles at the origin in Z^d, and let each particle in turn perform simple random walk until reaching an unoccupied site. Lawler, Bramson and Griffeath proved that with high probability the resulting random set of n occupied sites formed is close to a ball. We show that its fluctuations from circularity are, with high probability, at most logarithmic in the radius of the ball, answering a question posed by Lawler in 1995. These logarithmic fluctuations were predicted numerically be chemical physicists in the 1980 s. Joint work with David Jerison and Scott Sheffield" |
February 17, 2011, 3 pm at Science Center, Room 232 |
| NUMBER THEORY SEMINAR |
NOAM ELKIES (HARVARD UNIVERSITY) |
Refined 3-adic approximations to j(nζ3) |
For some positive integer n, let E be an elliptic curve n-isogenous with a curve of j-invariant zero. It is “easy” to show that j(E) is 27 times an algebraic integer. We prove that in fact j(E) is congruent to 54 mod 35 for n=3k−1, and to 0 or ±39/2 mod 36 for n=3k+1" |
February 16, 2011, 3 - 4pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
YAKAR KANNAI (WEIZMANN INSTITUTE OF SCIENCE) |
Kernels associated with second order operators, Sub-Riemannian geometry, and special functions |
Abstract The geodesic flow on a Riemannian manifold plays an important role in the analysis of non-degenerate second order linear partial differential operators, e.g. for writing down explicit representations for the associated heat and wave kernels. For several degenerate operators (such as the Heisenberg Laplacian) Sub-Riemannian geodesics play an analogous role, but the structure is much more involved. Both real and complex approaches are considered and compared. In some cases one may apply transform methods to get explicit fundamental solutions for higher step cases. Certain special functions appear. Differential Geometry Seminars are organized by Professor Shing-Tung Yau" |
February 15, 2011, 130 - 300 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
GABOR LIPPNER (HARVARD UNIVERSITY) |
Eigenvalue multiplicity and the genus of graphs |
Organized by Professor Shing Tung Yau" |
February 14, 2011, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
JAMES PASCALEFF () |
Floer cohomology in the mirror of CP^2 relative to a conic and a line |
Abstract In the Strominger-Yau-Zaslow description of mirror symmetry, singularities of the torus fibration lead to difficulties in the construction of mirror spaces and the computation of algebraic structures associated to these spaces. We will discuss one such algebraic structure, the Floer cohomology of Lagrangian sections of the torus fibration, in a space with a simple type of singularity, the Landau-Ginzburg mirror of CP^2 relative to a conic and a line, along with some natural generalizations. Of particular interest will be the canonical basis for the Floer cohomology groups (and construction gives rise to" |
February 11, 2011, 330 - 430 PM at Science Center, Room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
ALEXEI BORODIN (MIT) |
Growth of random surfaces |
Abstract We describe a class of exactly solvable random growth models of one and two-dimensional interfaces. The growth is local (distant parts of the interface grow independently), it has a smoothing mechanism (fractal boundaries do not appear), and the speed of growth depends on the local slope of the interface. The models enjoy a rich algebraic structure that is reflected through closed determinantal formulas for the correlation functions. Large time asymptotic analysis of such formulas reveals asymptotic featured of the emerging interface in different scales. Macroscopically, a deterministic limit shape phenomenon can be observed. Fluctuations around the limit shape range from universal laws of Random Matrix Theory to conformally invariant Gaussian processes in the plane. On the microscopic (lattice) scale, certain universal determinantal random point processes arise." |
February 10, 2011, 3 pm at Science Center, Room 232 |
| THE THURSDAY SEMINAR |
TOM GOODWILLIE () |
Tangent Bundle Analogy (continued) |
" |
February 10, 2011, 3 - 5 PM at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
DAVID ROE (HARVARD UNIVERSITY) |
The Local Langlands Correspondence for Tamely Ramified Groups |
Abstract The Langlands correspondence relates global Galois representations with automorphic representations; the local correspondence works at each prime. For any reductive group G over a local field K we construct a complex reductive group LG. For any homomorphism from the Galois group of K to LG (called a Langlands parameter) we then construct a set of representations of G(K) (called an L-packet). I will make these constructions explicit in the case that the Langlands parameter is discrete, tamely ramified and regular and that G is the unitary group associated to a tame extension of K" |
February 09, 2011, 3 - 4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
AMNON YEKUTIELI (BEN GURION UNIVERSITY) |
Central Extensions of Gerbes |
Abstract The talk will begin with an explanation of the concept of extension of groupoids. This is a mild generalization of the familiar concept of extension of groups. Oddly this concept appears to be new; perhaps because it is not very interesting... Next I will explain what is a gerbe. This is a very complicated concept. My point of view is that a gerbe G, on a topological space X, is the geometric version of a nonempty connected groupoid- much in the same way that a sheaf of groups on X is the geometric version of a group. I will try to avoid the horrid technicalities of 2-categories and stacks. The structure of nonabelian gerbes is known to be very complicated. Mainly one wants to know if a given gerbe G is trivial. The theory of nonabelian cohomology (Giraud, 1960 s) was invented for this purpose. However this theory is too abstract to be useful. An extension of gerbes is gotten by geometrizing the concept of extension of groupoids. Now this is a very interesting concept. A special case is that of central extension of gerbes, and I will give some examples. Next I will state a couple of results about obstruction theory for central extensions of gerbes. This theory gives concrete criteria to determine if a given gerbe is trivial. A more elaborate result is about the structure of pronilpotent gerbes. If time permits I will explain how the last result is used in my work on twisted deformation quantization of algebraic varieties. The paper (same title as lecture) appeared in Advances Math" |
February 08, 2011, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
YU-JONG TZENG (HARVARD UNIVERSITY) |
Counting singular curves on surfaces |
Abstract I will talk about recent development on counting nodal curves on surfaces, including a new proof of Goettsche s conjecture by Kool-Shende-Thomas and Ardila-Block s results using tropical geometry. Moreover, I will discuss the possibility to generalize Goettsche s conjecture for curves with higher singularities. Differential Geometry Seminars are organized by Professor Shing-Tung Yau" |
February 08, 2011, 130 - 300 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
CHEN-YU CHI (HARVARD UNIVERSITY) |
Singularities of hypersurfaces and the image of pluricanonical maps -- a metrical approach |
Organized by Professor Shing Tung Yau" |
February 07, 2011, 3 pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
MARIA ALESSANDRA RAGUSA (UNIVERSITA DI CATANIA) |
Current regularity problems of Partial Differential Equations |
Abstract Current results related to Morrey regularity of the maximum order derivatives of the solutions to some class of linear and nonlinear elliptic equations and systems both in divergence and in nondivergence form, are showed. At first is treated the study made for linear elliptic equations in nondivergence form, then are considered parabolic and ultraparabolic equations and finally the case of elliptic systems. The highest order coefficients belong to the subclass of the John-Nirenberg space of Vanishing Means Oscillation functions, at first considered by Donald Sarason. We point out that because of C is contained in the VMO class the coefficients can be discontinuous. Organized by Professor Shing-Tung Yau." |
February 04, 2011, 430 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
SERGEY CHERKIS () |
Yang-Mills Instantons on Asymptotically Locally Flat Spaces and their Moduli Spaces |
Abstract Kronheimer and Nakajima constructed Yang-Mills instantons on orbifolds of flat Euclidean four-space (and on their hyperkaehler resolutions). Their construction is formulated in terms of quivers. We generalize this construction to obtain Yang-Mills instantons on Asymptotically Locally Flat hyperkaehler spaces. To organize the data needed for our construction we introduce the notion of a bow, which generalizes that of a quiver. We compute the moduli spaces of instantons and comment on their relation to the representation theory" |
February 04, 2011, 330 - 430 pm at Science Center, Room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
SCOTT SHEFFIELD (MIT) |
How do you divide your (two dimensional) time? Zippers, necklaces, and quantum gravity |
Abstract Liouville quantum gravity and the Schramm-Loewner evolution (SLE) rank among the great mathematical physics discoveries of the last few decades. Liouville quantum gravity is a canonical model of a random two dimensional Riemannian manifold. It was introduced by Polyakov in 1981 as a model for the intrinsic geometry on the space-time trajectory of a string. The Schramm-Loewner evolution, introduced by Schramm in 1999, is a canonical model of a random path in the plane that doesn t cross itself. Each of these models is the subject of a large and active literature spanning physics and mathematics. We will connect these two objects to each other in the simplest possible way. Roughly speaking, we will show that if one glues together two independent Liouville quantum gravity random surfaces along boundary segments (in a boundary-length-preserving way)---and then conformally maps the resulting surface to a planar domain---then the interface between the two surfaces is an SLE. In a sense, the welding/subdivision of random surfaces (which parameterize string trajectories) is analogous to the concatenation/subdivision of one-dimensional time intervals( which parameterize point-particle trajectories)" |
February 03, 2011, 3 PM at Science Center, Room 232 |
| THE THURSDAY SEMINAR |
TOM GOODWILLIE () |
More on the calculus of functors |
" |
February 03, 2011, 3 - 5pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
NOAM ELKIES (HARVARD UNIVERSITY) |
Refined 3-adic approximations to j(nζ3) |
For some positive integer n, let E be an elliptic curve n-isogenous with a curve of j-invariant zero. It is “easy” to show that j(E) is 27 times an algebraic integer. We prove that in fact j(E) is congruent to 54 mod 35 for n=3k−1, and to 0 or ±39/2 mod 36 for n=3k+1." |
February 02, 2011, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
ANDREW STROMINGER (HARVARD UNIVERSITY) |
From Navier-Stokes to Einstein |
Abstract We show by explicit construction that for every solution of the incompressible Navier-Strokes equation in p+1 dimensions, there is a uniquely associated dual solution of the vacuum Einstein equations in p+2 dimensions. The near-horizon expansion in gravity is shown to be mathematically equivalent to the hydrodynamic expansion in fluid dynamics, and the Einstein equation reduces at leading order to the incompressible Navier-Stokes equation. The construction is a mathematically precise realization of suggestions of a holographic duality relating fluids and horizons which began with the study of black hole thermodynamics in the 70 s and resurfaced recently in the context of the AdS/CFT correspondence" |
February 01, 2011, 130 - 300 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
LARS ANDERSSON (ALBERT EINSTEIN INSTITUTE) |
The black hole stability problem |
Abstract The problem of nonlinear stability for the Kerr model of a rotating black hole is one of the central problems in general relativity. The analysis of linear fields on the Kerr spacetime is an important model problem for full nonlinear stability. In this talk, I will present recent work with Pieter Blue which makes use of the hidden symmetry related to the Carter constant to circumvent these difficulties and give physical space approach to estimates for the wave equation, including energy bounds, trapping, and dispersive estimates. I will also discuss the field equations for higher spin fields including linearized gravity. Basic Notions Seminars are organized by Professor Shing -Tung Yau" |
January 31, 2011, 3 pm at Science Center, Room 507 |
| SPECIAL ALGEBRAIC GEOMETRY SEMINAR |
JASON STARR (S.U.N.Y.) |
Rational points and rational simple connectedness for hypersurfaces in Grassmannians. |
Abstract Just as a fiber bundle with 2-dimensional base and simply connected fiber has a continuous section, so also an algebraic fibration over an algebraic surface has a rational section of the fibers are rationally simply connected in a suitable and if the elementary obstruction of Colliot-Th\el\ene and Sansuc vanishes. Two motivation cases are the Tsen-Lang theorem and de Jong s Period-Index theorem the cases when a general fiber is a (low degree) hypersurface in projective space, respectively a general fiber is a Grassmannian (Joe Harris and I proved rational simple connectedness in approximately the same degree range as occurs in the Tsen-Lang theorem, and the case of a Grassmannian is even easier). A synthesis of these two cases is when a general fiber is a hypersurface in a Grassmannian. In his recent thesis, Robert Findley proved that degree $d$ hypersurfaces in the Grassmannian $G(k,n)$ of $K$-planes in a (linear) $n$-space are rationally simply connected if $d$, $k$ and $n$ satisfy an inequality which is approximately $d^2
| January 28, 2011, 3 PM at Science Center, Room 507 | |
| NUMBER THEORY SEMINAR |
PAUL BAUM (PENN STATE UNIVERSITY) |
Geometric structure in the representation theory of reductive p-adic groups |
Abstract Let G be a reductive p-adic group. Examples are GL(n,F), SL(n,F) where n can be any positive integer and F can be any finite extension of the field Q_p of p-adic numbers. The smooth (or admissible) dual of G is the set of (equivalence classes of) smooth irreducible representations of G. The representations are on vector spaces over the complex numbers. This talk will explain a conjecture formulated by Aubert-Baum-Plymen which asserts that there is a very simple geometric structure in the smooth dual of any reductive p-adic group G. According to ABP, the smooth dual of G is a disjoint union of complex affine varieties each of which is explicitly identified as an extended quotient. ABP interacts with the Baum-Connes conjecture and with the Local Langlands conjecture. In particular, validity of ABP give information on L-packets. Due to recent results by a number of mathematicians, a substantial part of ABP is now known to be true for many examples" |
January 26, 2011, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
SERGEI GUKOV (UNIVERSITY OF CALIFORNIA, SANTA BARABARA) |
The Verlinde formula via mirror symmetry |
Organized by Professor Shing Tung Yau" |
January 25, 2011, 130 - 300 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
YANKI LEKILI (MIT) |
Fukaya categories of the torus and Dehn surgery on 3-manifolds |
Abstract In joint work with Tim Perutz, we extend Heegard Floer theory of Ozsvath and Szabo to compact 3--manifolds with two boundary components. This extension uses the machinery of holomorphic quilts and Fukaya categories of Sym^g(Sigma_g). After giving an overview of this extension, I will focus on the first interesting case the invariants of 3--manifolds bounding S2 union T2. In particular, I will discuss an explicit model for the Fukaya category of the once punctured torus" |
December 03, 2010, 330 - 430 pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
JOHN LOFTIN (RUTGERS UNIVERSITY) |
Minimal Lagrangian Surfaces in $\mathbb{CH}^2$ |
Abstract For $\Sigma$ a closed Riemann surface equipped with a hyperbolic metric and a small cubic differential $U$, we produce a minimal Lagrangian immersion of the universal cover $\tilde\Sigma$ into $\mathbb{CH}^2$ by solving the integrability condition $$\Delta u - 4\|U\|^2 e^{-2u} - 4e^u + 2 = 0$$ on $\Sigma$. The development of a natural frame provides a representation of $\pi_1\Sigmas$ into $SU(2,1)$. If $U$ is small enough, then the minimal Lagrangian surface is embedded, and the induced representation is complex-hyperbolic quasi-Fuchsian. We also discuss similar integrability conditions for such geometric surfaces as (1) minimal surfaces in real hyperbolic 3-space, (2) affine spheres in $\mathbb R^3$, (3) minimal Lagrangian surfaces in $\mathbb{CP}^2$. This is joint work with Ian Mclntosh. This seminar is organized by Professor Shing-Tung Yau" |
December 03, 2010, 430 - 530 pm at Science Center, Room 530 |
| SPECIAL SEMINAR |
LYDIA BIERI (UNIVERSITY OF MICHIGAN) |
Geometry of Spacetimes Solving the Einstein-Maxwell Equations in general Relativity and Gravitational Radiation |
Abstract A major goal of mathematical General Relativity (GR) and astrophysics is to precisely describe and finally observe gravitational radiation, one of the predictions of GR. In order to do so, one has to study the null asymptotical limits of the spacetimes for typical sources. Among the latter we find binary neutron stars and binary black hole mergers. In these processes typically mass and momenta are radiated away in form of gravitational waves. D. Christodoulou showed that every gravitational-wave burst has a nonlinear memory. In this talk, we discuss the null asymptotics or spacetimes solving the Einstein-Maxwell (EM) equations, compute the radiated energy and derive limits at null infinity and compare them with the Einstein vacuum (EV) case. The physical insights are based on geometric-analytic investigations of the solution spacetimes. Organized by Professor Shing-Tung Yau" |
December 02, 2010, 3 - 4 pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
EUGEN HELLMANN (BONN UNIVERSITY) |
On families of filtered phi-modules and crystalline representations |
Abstract We study families of filtered phi-modules associated to families of p-adic Galois representations as considered by Berger and Colmez. We show that the weakly admissible locus in a family of filtered phi-modules is open and that the groupoid of weakly admissible modules is in fact an Artin stack. Working in the category of adic spaces instead of the category of rigid analytic spaces one can show that there is an open substack of the weakly admissible locus over which the filtered phi-modules is induced from a family of crystalline representations." |
December 01, 2010, 3 - 4 pm at Science Center, Room 507 |
| DYNAMICS AND GEOMETRY SEMINAR |
D. MEYER () |
Invariant Peano curves of expanding Thurston maps. |
" |
December 01, 2010, 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
MING-TAO CHUAN (HARVARD UNIVERSITY) |
Existence of Hermitian-Yang-Mills connections under conifold transitions |
Organized by Professor Shing Tung Yau" |
November 30, 2010, 130 - 300 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
HORNG-TZER YAU (HARVARD UNIVERSITY) |
Random matrices a review of its history and the conjectures by Wigner and Dyson |
Abstract Random matrices were introduced by E. Wigner to model the excitation spectra of large nuclei. The central idea is based on the hypothesis that the local statistics of the excitation spectrum for a large complicated system is universal in the sense that it depends only on the symmetry class of the physical system but not on other detailed structures. Dyson Brownian motion is the flow of eigenvalues of random matrices when each matrix element performs independent Brownian motions. In this lecture, we will give a short review of the history of random matrices and its recent applications. We will also explain the connection between the universality of random matrices and the approach to local equilibrium of Dyson Brownian motion, which has led to a complete solution of the universality conjecture by Wigner, Dyson, Gaudin and Mehta. Basic Notions Seminars are organized by Professor Shing-Tung Yau" |
November 29, 2010, 3 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
XINWEN ZHU (HARVARD UNIVERSITY) |
Determinants, commutators, and the reciprocity laws |
Organized by Professor Shing Tung Yau" |
November 22, 2010, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
CHRIS WOODWARD (RUTGERS UNIVERSITY) |
Quilted Floer theory and fibered Dehn twists |
Cancelled due to CDM conference. Moved to Spring Semester" |
November 19, 2010, 330 pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
QILE CHEN (BROWN UNIVERSITY) |
Logarithmic stable maps to Deligne-Faltings pairs |
Abstract For the purpose of computing Gromov-Witten invariants, the compactification of the space of relative stable maps with respect to a smooth divisor were introduced and studied using expanded degeneration during the past decade. Starting from the backgrounds and basic definitions, I will introduce a new way of compactification using logarithmic structures in the sense of Kato-Fontaine-Illusie. In particular, this covers many interesting cases., such as the target variety with a simple normal crossings divisor, or a simple normal crossings degeneration of a variety with simple normal crossings singularities. This is in part joint work with Dan Abramovich. Organized by Professor Shing-Tung Yau" |
November 18, 2010, 530 pm at Science Center, Room 530 |
| COLLOQUIUM |
EYAL GOREN (MCGILL UNIVERSITY) |
Recent developments in the theory of complex multiplication |
Abstract Our story begins more than a century ago with Kronecker s Jugendtraum and Hilbert s 12th problem, where complex multiplication appears as a way to understand Galois extensions of number fields - a problem still at the heart of number theory. Our lecture will have a strong historical flavour; we shall attempt to survey the development of the theory of complex multiplication and the philosophy behind it. On this background, we will present some exciting recent results, some of which build in an essential way on Borcherds theory. Finally, we shall sketch some of the key challenges of the theory of complex multiplication today and future directions." |
November 18, 2010, 430 pm at Science Center, Hall E |
| THE THURSDAY SEMINAR |
KIRSTEN WICKELGREN (HARVARD UNIVERSITY) |
Homotopy Nilpotent Groups |
" |
November 18, 2010, 4 - 6 PM at Science Center, Room 507 |
| LOGIC COLLOQUIUM |
HUGH WOODIN (UC BERKELEY) |
The Search for Mathematical Truth |
Abstract The evident ubiquity of (formally) unsolvable problems in Set Theory argues for a re-examination of the conception of truth at least for Set Theory. The mathematical investigation of this apparently non-mathematical problem has led to a surprising series of mathematical conjectures, problems and successes. The stage is now set for either 1-The validation of a single additional axiom which if added to the traditional ZFC axioms would entirely eliminate the phenomena of unsolvability based on Cohen s method of forcing while preserving the fundamental strong axioms of infinity; or 2- The refutation from the same strong axioms of infinity of any such possibility based on anything like that currently imagined. In other words, Set Theory is facing a critical dichotomy in possible futures." |
November 17, 2010, 4 - 530 PM at Fong Auditorium, Boylston Hall 110 |
| NUMBER THEORY SEMINAR |
EYAL GOREN (MCGILL UNIVERSITY) |
Curves of genus 2 with complex multiplication |
Abstract Curves of genus 2 with complex multiplication are a natural analogue of elliptic curves with complex multiplication, parameterized by CM points of modular curves. The theory concerning values of modular functions at CM points of modular curves is well developed. Some applications include the construction of elliptic units, and construction of elliptic curves suitable for cryptography. In comparison, little is known about analogous questions for modular functions of genus 2. The study of such questions can be motivated by constructing units in abelian extensions of quartic CM fields (related to Stark s conjecture) and applications to cryptography. K. Lauter (Microsoft Research) and myself have investigated such questions and obtained several results, allowing in particular the applications to cryptography, and construction of S-units, where S is effectively controlled in terms of the CM data. We were also able to prove an analogue of the Gross-Zagier theorem in this setting. In this talk I will attempt to give an overview of the subject and indicated the main ideas going into the proofs" |
November 17, 2010, 3 - 4 pm at Science Center, Room 507 |
| DYNAMICS AND GEOMETRY SEMINAR |
GIULIO TIOZZO (HARVARD UNIVERSITY) |
Continued fractions and kneading sequences of unimodal maps |
" |
November 17, 2010, 4 pm at Science Center, Room 507 |
| ADDITIONAL DIFFERENTIAL GEOMETRY SEMINAR |
MICHAEL EICHMAIR (MIT) |
Large isoperimetric surfaces in initial data sets |
Abstract This is joint work with Jan Metzger. We consider initial data sets $(M,g)$ that are $C^0$-asymptotic to the Schwarzschild metric with mass $m>0$. We show that isoperimetric surfaces of every large volume exist in $(M,g)$, and that any such isoperimetric surface must be close to a large, centered coordinate ball. This implies that the stable constant mean curvature surfaces constructed by G. Huisken and S.T. Yau (and others) are isoperimetric surfaces and confirms a conjecture of H. Bray s. We will discuss the relevance of this in the context of G. Huisken s recent development of isoperimetric mass. Time permitting we will discuss further results for more general asymptotics. Differential Geometry Seminars are organized by Professor Shing-Tung Yau" |
November 16, 2010, 430 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
MIRANDA CHENG (HARVARD UNIVERSITY) |
K3 surfaces and a Moonshine for Mathieu 24 |
Abstract Recently a relation between K3 surfaces and the sporadic group Mathieu 24 has been discovered in the context of string theory. First, the conformal field theory on K3 contains modular objects given by the representations of the group M24. This fact points to a novel theory of moonshine relating M24 and weak Jacobi forms. Second, this implies an M24 symmetry of a generalized Kac-Moody algebra, whose denominator is an automorphic form. This automorphic form turns out to encode both the above mentioned weak Jacobi forms and a set of eta-products which are the key objects in an earlier version of moonshine relating M24 and cusp forms. In this talk I will summarize my work on the relationship between back holes, K3 surfaces, M24, modular objects and generalized Kac-Moody algebras. Organized by Professor Shing-Tung Yau" |
November 16, 2010, 130 - 300 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
HELENE ESNAULT () |
Lifting of cycle class in crystalline cohomology |
Abstract We show that the infinitesimal lifting of the crystalline cycle of an algebraic cycle as a Milnor $K$-class is entirely controlled by a Kodaira-Spencer type cohomology class. In the proof appears a p-adic dilogarithm function. Work in progress, joint with Spencer Bloch and Moritz Kerz" |
November 16, 2010, 3 pm at MIT (26-310) |
| BASIC NOTIONS SEMINAR |
VAIBHAV SURESH GADRE (HARVARD UNIVERSITY) |
Length spectra for pseudo-Anosov maps bounds for low dilatation examples |
Organized by Professor Shing Tung Yau" |
November 15, 2010, 3 pm at Science Center, Room 507 |
| LOGIC COLLOQUIUM |
GERALD SACKS (HARVARD UNIVERSITY) |
Models of Long Sentences II |
Abstract The construction of uncountable models of certain infinitary theories via intransitive countable hulls" |
November 12, 2010, 4 - 530 pm at Science Center, Room 309 |
| GAUGE THEORY AND TOPOLOGY |
SEN HU (USTC) |
On a generalization of the Ricci flow |
Abstract By using supergravity action we propose a generalization of the Ricci flow. In the generalized Ricci flow we also have gauge fields and B fields. It is found that the generalized Ricci flow shares many properties of the Ricci flow such as being parabolic systems after modulo gauge symmetries, monotonicity of entropy along an orbit, Harnack inequality etc. Critical points of this flow are also very interesting. In the three dimensional cases it gives Thurston s eight geometries. In the four dimensional case there are interesting connections between the critical points and the newly introduced generalized complex geometries" |
November 12, 2010, 330 - 430 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
DAVID AYALA (HARVARD UNIVERSITY) |
The Embedding Calculus |
" |
November 11, 2010, 4 - 6 PM at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
ANDREW OBUS (COLUMBIA UNIVERSITY) |
Lifting Cyclic Extensions |
Abstract The local lifting problem asks given a finite group G and an embedding i G--> (continuous k-automorphisms of k[[t]]), where k is algebraically closed of characteristic p, does there exist a finite extension R/W(k) and an embedding j G--> (continuous R-automorphisms of R[[t]]) such that j lifts i? The Oort conjecture states that the local lifting problem should always have a solution for G cyclic. This is basic Kummer theory when p does not divide G, and has been proven when v_p(lGl)=1 (Oort, Sekiguchi, Suwa) and when v_p(G)=2 (Green, Matignon). We will first motivate the local lifting problem from geometry, and then we will show that it has a solution for a large family of cyclic extensions. This family includes all extensions where v_p(lGl) =3 and many extensions where v_p(lGl) is arbitrarily high. This is joint work with Stefan Wewers." |
November 10, 2010, 3 - 4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
RAGNI PIENE (UNIVERSITY OF OSLO) |
Inflection loci of projective varieties |
Rational normal curves are the only smooth projective curves that have no inflection points (of any order). In fact this property characterizes Veronese embeddings of projective spaces of any dimension. For a given class of varieties, e.g. toric varieties or scrolls, one can ask to characterize those that are uninflected. In some cases it is possible to compute the degree of the inflection locus, and hence give criteria for it to be empty. The talk will survey some old and new results, and focus on recent joint work with A. Lanteri and R. Mallavibarrena concerning scrolls." |
November 09, 2010, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
HELENE ESNAULT (UNIVERSITAT DUISBERG-ESSEN) |
Fundamental groups and connections |
Abstract Over a smooth projective complex variety X, if the étale fundamental group is trivial, then there are no non-trivial no non-trivial O-coherent D-modules (Malcev, Grothendieck). Gieseker (1975) conjectured the same result in char p>0. We showed this, using in particular a theorem of Hrushovsly stemming form model theory. (Joint work with V. Mehta). We ll discuss this and questions around" |
November 09, 2010, 130 - 300 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
HELENE ESNAULT (UNIVERSITAT DUISBERG-ESSEN) |
Rational points and motivic integration |
Abstract Serre observed that if a finite L-group acts on the affice space An over a field K of characteristic different from L, then the fixed scheme is non-empty. He asked whether, as he shows over finite fields, they are always rational fixed points. We discuss this question over strictly henselian fields and give a positive answer when the residue characteristic is not L. (Joint work with Johannes Nicaise)." |
November 08, 2010, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
TIM NGUYEN (MIT) |
The Seiberg-Witten Equations on Manifolds with Boundary |
Abstract The analysis of the Seiberg-Witten equations have led to many important results in low-dimensional topology. These include the invariants defined by Witten for 4-manifolds and the monopole Floer invariants for 3-manifolds defined by Kronheimer-Mrowka and others. In both these situations, the equations and their moduli space of solutions are studied on closed manifolds. In this talk, we study the analysis of the Seiberg-Witten equations on manifolds with boundary. First, we discuss the space of solutions to the Seiberg-Witten equations on 3-manifolds with boundary. This solution space is infinite dimensional (even modulo gauge) since no boundary conditions are imposed on the equations. Second, we discuss how this solution space yields natural boundary conditions for the Seiberg-Witten equations on a cylindrical 4-manifold R x Y, where Y is a 3-manifold with boundary. We explain how the resulting nonlinear boundary value problem has well-posedness and compactness properties, and how these results therefore serve as foundational analysis for an eventual construction of a monopole Floer theory on manifolds with boundary" |
November 05, 2010, 330 - 430 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
SOREN GALATIUS () |
Homology of moduli spaces of manifolds |
" |
November 04, 2010, 4 - 530 pm at Science Center, Room 507 |
| DYNAMICS AND GEOMETRY SEMINAR |
EVA UHRE () |
The Mandelbrot set and its deformations |
" |
November 03, 2010, 4 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
NIR AVNI (HARVARD UNIVERSITY) |
Representations Zeta Functions of Arithmetic Groups |
Abstract I will talk about the d-dimensional representations of an arithmetic lattice. For higher rank lattices, this sequence grows polynomially, with some mysterious exponent. I will talk about some known values of this exponent, and the relations between the representation growths of different lattices" |
November 03, 2010, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
DEMETRIOS CHRISTODOULOU (ETH ZURICH) |
The formation of black holes in vacuum |
Organized by Professor Shing Tung Yau" |
November 02, 2010, 130 - 300 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
PAUL BOURGADE (HARVARD UNIVERSITY) |
Extreme spacings in random spectra |
Basic Notions Seminars are organized by Professor Shing Tung Yau" |
November 01, 2010, 3 pm at Science Center, Room 507 |
| LOGIC COLLOQUIUM |
RACHEL LOUISE EPSTEIN (HARVARD UNIVERSITY) |
Definability in the Computably Enumerable Sets |
Abstract Definability is one of the fundamental themes of computability theory. We examine the structure of the computably enumerable (c.e.) sets under set inclusion. The problem of which classes of degrees are definable in this structure has been an important topic of study in computability theory. In particular, it has been shown that all upward-closed jump classes (such as high, nonlow2, etc.) are definable except for the nonlow degrees, which are not definable. To show that the nonlow degrees are not definable, we use automorphisms, which we build on trees of strategies. We will discuss the history of the problem and some of the ideas of the proof" |
October 29, 2010, 4 - 6 pm at Science Center, Room 309 |
| GAUGE THEORY AND TOPOLOGY |
PETER OZSVATH (MIT) |
Bordered Floer homology and the spectral sequence of a branched double-cover |
Abstract In earlier work with Zoltan Szabo, we constructed a spectral sequence whose E_2 term is Khovanov s homology (reduced, with Z/2 coefficients). I will explain how bordered Floer homology can be used to calculate this spectral sequence explicitly. This is joint work with Robert Lipshitz and Dylan Thurston." |
October 29, 2010, 330 - 430 pm at Science Center, Room 507 |
| BRANDIES-HARVARD-MIT-NORTHEASTERN JOINT MATHEMATICS COLLOQUIUM |
SIMON BRENDLE (STANFORD UNIVERSITY) |
Curvature, sphere theorems, and the Ricci flow |
Abstract In 1926, Hopf proved that any compact, simply connected Riemannian manifold with constant curvature 1 is isometric to the standard sphere. Motivated by this result, Hopf posed the question of whether a compact, simply connected manifold with suitably pinched curvature is topologically a sphere. This question has been studied by many authors over the past six decades, a milestone being the Topological Sphere Theorem proved by Berger and Klingenberg in 1960. In this lecture, I will discuss the history of this problem, and describe the proof of the Differentiable Sphere Theorem. This thorem classified all manifolds with 1/4-pinched curvature up to diffeomorphism. The distinction between homeomorphism and diffeomorphism is significant in light of the exotic spheres constructed by Milnor; the proof uses the Ricci flow technique introduced y Hamilton." |
October 28, 2010, 430 PM at Science Center, Hall A |
| DYNAMICS AND GEOMETRY SEMINAR |
XAVIER BUFF () |
Transversality for Herman rings |
" |
October 27, 2010, 4 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
HUI JUNE ZHU (SUNY BUFFALO/HARVARD) |
Construction of crystalline representations in families and generalized Serre weights |
Abstract The goal of this talk is to give a complete classification of crystalline representations of Gal(K) where K is unramified over Qp with given Hodge-Tate weight, and show how to make them into an analytic family (in the same sense as via Mazur s deformation theory) when the weights lie in the interval [0,p]. As an application in 2-dimensional case, our result gives a proof to one direction of Buzzard-Diamond-Jarvis conjecture regarding generalized Serre weight and conjecture." |
October 27, 2010, 3 - 4 pm at Science Center, Room 507 |
| LOGIC COLLOQUIUM |
CAMERON FREER (UNIVERSITY OF HAWAII) |
Invariant measures on countable models |
Abstract The Erdos-Renyi random graph construction can be seen as inducing a probability measure concentrated on the Rado graph (sometimes known as the countable random graph) that is invariant under arbitrary permutations of the underlying set of vertices. The following question arises naturally On which countable combinatorial structures is there such an invariant measure Up until recent work of Petrov and Vershik (2010), it was not even known if Henson s universal countable triangle-free graph admitted an invariant measure. We provide a complete characterization of countable structures admitting invariant measures, in terms of the model-theoretic notion of definable closure. This leads to a characterization for ultrahomogeneous structures, as well as new examples of invariant measures on graphs and other combinatorial structures. Joint work with Nate Acherman and Rehana Patel" |
October 27, 2010, 400 pm at Science Center, Room 113 |
| DIFFERENTIAL GEOMETRY SEMINAR |
VINCENT MONCRIEF (YALE UNIVERSITY) |
Einstein spaces as attractors for the Einstein flow |
Abstract In recent joint work with Lars Anderson (AEI, Potsdam) we studied the stability, in the direction of cosmological expansion, of a family n + 1 dimensional Lorentz cones over negative Einstein spaces of dimension n>3. We used a variant of the constant mean curvature spatially harmonic (CMCSH) gauge condition introduced earlier. An important difference from the 3+1 dimensional case treated previously is that now one may have a nontrivial moduli space of negative Einstein geometries. This makes it necessary to introduce a time-dependent reference metric which is used to define the spatially harmonic coordinate system that goes into the gauge. By introducing scale factors defined in terms of the mean curvature and rewriting Einstein s equations in terms of scale invariant geometric quantities we use suitable higher order energy estimates to prove that the scale invariant spatial metric decays asymptotically to an Einstein metric in the associated moduli space provided that the initial energy is sufficiently small. The argument assumes a certain stability property for the background Einstein metric of which no counterexample are currently known. Differential Geometry Seminars are organized by Professor Shing-Tung Yau" |
October 26, 2010, 500 pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
ERIC VERLINDE (UNIVERSITY OF AMSTERDAM) |
Counting Dyons, Wall Crossing, and Borcherds Algebra |
Abstract The counting of supersymmetric charged black hole states in string theory leads to a fruitful interaction with mathematics. The first known counting formula for 4d black holes with electric and magnetic charge is expressed in terms of the product formula of a Borcherds algebra, and is closely related to the elliptic genus of a symmetric product (Hilbert scheme) of K3 surfaces. The dependence on the moduli of thr K3 surfaces is incorporated in the contour prescription of the counting formula. Due to the presence of double poles, the counting formula exhibits a wall crossing phenomena which is beautifully described by the Weyl reflections of the underlying Borcherds algbera. The interpretation of these result in the physics context will be briefly mentioned." |
October 26, 2010, 130 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
MICHAEL RAPOPORT (HARVARD UNIVERSITY) |
Occult period maps |
Abstract We give a reinterpretation of the (hidden) period maps for cubic surfaces (Allcock, Carlson, Toledo), for cubic threefolds (ACT and Looijenga, Swierstra), and for curves of genus 3 and 4 (Kondo), in terms of my work with Kudla on Picard moduli spaces of abelian varieties and special divisors on then. We also discuss some problems that this reinterpretation raises." |
October 26, 2010, 3 - 4 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
PETER KRONHEIMER (HARVARD UNIVERSITY) |
Knots, links and Khovanov homology |
Organized by Professor Shing Tung Yau" |
October 25, 2010, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
STAVROS GAROUFALIDIS (GEORGIA TECH) |
The Slope Conjecture |
Abstract The Slope Conjecture relates the quadratic growth rate of the degree of the Jones polynomial of a knot and its parallels to slopes of incompressible surfaces in the knot complement. The conjecture is known for alternating knots, and 2-parameter classes of 2-fusion knots (the latter, joint with Nathan Dunfield)" |
October 22, 2010, 330 - 430 pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
ALEXANDER GRIGORYAN (UNIVERSITAET BIELEFELD) |
Exterior differentiations on graphs (work in progress) |
" |
October 21, 2010, 3 - 4 pm at Science Center, Room 530 |
| THE THURSDAY SEMINAR |
DUSTIN CLAUSEN () |
The Taylor tower of the stabilization of mapping spaces (after Greg Arone) |
" |
October 21, 2010, 4 - 6 pm at Science Center, Room 507 |
| DYNAMICS AND GEOMETRY SEMINAR |
R. ROEDER () |
Blaschke products ad renormalization on the diamond hierarchical lattice. |
" |
October 20, 2010, 4PM at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
JOEL BELLAICHE (BRANDEIS UNIVERSITY) |
Critical -p-adic L-functions |
Abstract In this talk, I will explain two works concerning p-adic L-functions of the eigencurve. The first work, which is mine, is an analytic construction of p-adic L-functions of modular forms n the missing, critical, cases, and of a two-variable p-adic L-function on the eigencurve including the critical points. The second work is essentially Walter Kims s thesis (2007, unfortunately unpublished) it is the construction of a one variable p-adic L-function on the eithencurve interpolating the values at 1 of the adjoint complex L-functions of modular forms. In both cases, there are relations between the vanishing properties of the p-adic L-functions and the geometry of the eigencurve. Both works rely heavily on ideas and results of Stevens, which I will recall" |
October 20, 2010, 3 - 4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
DUILIU DIACONESCU (RUTGERS UNIVERSITY) |
Wallcrossing and Cohomology of The Hitchin System |
A conjectural recursive formula for the Poincare polynomial of the Hitchin system will be derived from wallcrossing in the local Donaldson-Thomas theory of curves. This formula establishes a connection between previous work of Hausel and Rodrigues-Villegas and refined local Donaldson-Thomas invariants" |
October 19, 2010, 3 pm at MIT (26-310) |
| DIFFERENTIAL GEOMETRY SEMINAR |
WILLIAM MEEKS (UNIVERSITY OF MASSACHUSETTS, AMHERST) |
Constant mean curvature sphere in homogeneou 3-manifolds |
Abstract I will talk about the existence, uniqueness and embeddedness of constant mean curvature spheres in a simply connected homogeneous 3-manifold. The results generalize the classical theorem of Hopf that a constant mean curvature H sphere in R^3 is round of radius l/H. Organized by Professor Shing-Tung Yau" |
October 19, 2010, 130 - 300 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
BENEDICT GROSS (HARVARD UNIVERSITY) |
Automorphisms of root lattices |
Organized by Professor Shing Tung Yau" |
October 18, 2010, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
MOHAMMED ABOUZAID (MIT) |
A plethora of exotic Stein manifolds |
Abstract In real dimensions greater than 4, I will explain how a smooth manifold underlying an affine variety admits uncountably many distinct (Wein) stein structures, of which countably many have finite type, and which are distinguished by their symplectic cohomology groups. Starting with a Lefschetz fibration on such a variety, I shall perform an explicit sequence of appropriate surgeries, keeping track of the changes to the Fukaya category and hence, by understanding open-closed maps, obtain descriptions of symplectic cohomology after surgery. (Joint work with P. Seidel" |
October 15, 2010, 330 - 430 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
JACOB LURIE (HARVARD UNIVERSITY) |
More on the Goodwillie derivative of the identity |
" |
October 14, 2010, 4 - 6 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
DICK GROSS (HARVARD UNIVERSITY) |
Parahorics and supercuspidal representations |
" |
October 13, 2010, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
LI-SHENG TSENG (HARVARD UNIVERSITY) |
Primitive elliptic operators on symplectic manifolds |
" |
October 12, 2010, 130 - 300 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
KEVIN TUCKER (UNIVERSITY OF UTAH) |
On the behavior of multiplier ideals and test ideals under finite morphisms in positive characteristic |
The multiplier ideal of a Q-divisor on a complex algebraic variety is a fundamental object in the study of higher dimensional birational geometry. However, the behavior of multiplier ideals in positive characteristic can be quite enigmatic. In many cases, a related invariant called the test ideal displays preferable behavior. In this talk, we will review the relationship between the multiplier ideal and test ideal in positive characteristic. Furthermore, we will describe (and contrast transformation rules for each of these invariants under an arbitrary (i.e. not necessarily separable) finite morphism" |
October 12, 2010, 3 pm at Science Center, Room 507 |
| LOGIC COLLOQUIUM |
THEODORE A. SLAMAN () |
Randomness and Mathematical Logic |
Abstract There has been considerable progress in the recursion theoretic study of randomness in the past several years. I will give a conceptual overview of the area and a more focused discussion of my joint work with Jan Reimann, in which we study the question, For which infinite binary sequences X is there a (continuous) probability measure relative to which X is effectively random? The investigation has a surprisingly meta-mathematical character, and necessarily so" |
October 08, 2010, 4 - 6 pm at Science Center, Room 309 |
| GAUGE THEORY AND TOPOLOGY |
GENEVIEVE WALSH (TUFTS) |
Knot commensurability and the Berge conjecture |
Abstract This talk addresses commensurability of knot complements in S3 in the generic case of knots without hidden symmetries. In particular such knots which are commensurable are cyclically commensurable, and there are at most three knot complements in such a commensurable, and there are at most three knot complements in such a commensurability class. Moreover if two hyperbolic knots without hidden symmetries have commensurable complements then they are fibred with the same genus and are chiral. I will also discuss close connections between commensurability of knot complements are the Berge conjecture, and give a partial classification of commensurable knot complements in S3. This is joint work with M. Boileau, S. Boyer, and R. Cebanu" |
October 08, 2010, 330 - 430 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
MARK BEHRENS () |
The Goodwillie tower of the Identity |
Abstract I will begin to survey what is known about the Goodwillie tower of the identity functor from pointed spaces to pointed spaces. Topics I would like to cover include identification of the derivatives, mod p stable homology of the layers evaluated on spheres, chromatic ramifications." |
October 07, 2010, 4 - 545 pm at Science Center, Room 507 |
| DYNAMICS AND GEOMETRY SEMINAR |
VAIBHAV GADRE (HARVARD UNIVERSITY) |
Singularity of harmonic measures for random walks on the mapping class group. |
" |
October 06, 2010, 4 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
BJORN POONEN (MIT) |
Random maximal isotropic subspaces and Selmer groups |
" |
October 06, 2010, 3 - 4 PM at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
XIAOTAO SUN (INSTITUTE OF MATHEMATICS, CHINESE ACADEMY OF SCIENCES) |
Minimal rational curves on moduli spaces of stable bundles |
Abstract The moduli space of stable bundles of rank r with a fixed determinant over a smooth projective curve is a Fano manifold with cyclic Picard group. In this talk, we will determine all rational curves of minimal degree on the moduli space and minimal rational curves through generic point. Then we will give some applications of the main theorem. Some recent results about minimal elliptic curves on moduli spaces will be given if time permits. Organized by Professor Shing-Tung Yau" |
October 05, 2010, 130 - 300 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
JACOB LURIE (HARVARD UNIVERSITY) |
Tamagawa Numbers via Nonabelian Poincare Duality |
A conjecture of Weil asserts that if G is a simply connected semisimple algebraic group defined over a global field k, then the Tamagawa number of G is equal to 1. This result was proven by Kottwitz in the case where k is a number field, building on earlier work of Langlands and Lai. In this talk, I will explain some of the motivations for Weil s conjecture. I will then describe some joint work with Dennis Gaitsgory, sketching a proof in the case where k is a function field" |
October 05, 2010, 3 - 4 pm at MIT (26-310) |
| BASIC NOTIONS SEMINAR |
MICHAEL RAPOPORT (MATHEMATICAL INSTITUTE, UNIVERSITY OF BONN) |
Period domains over finite and p-adic fields |
Organized by Professor Shing Tung Yau" |
October 04, 2010, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
MARK McLEAN () |
The growth rate of symplectic homology and algebraic Stein fillings |
Abstract The unit cotangent bundle of any manifold is Stein fillable. I will show that if I have an rationally hyperbolic manifold then its unit cotangent bundle cannot be filled by a Stein domain whose completion is symplectomorphic a smooth affine variety. This also shows in particular that its cotangent bundle is not symplectomorphic to any smooth affine variety. To do this I show that any Stein manifold symplectomorphic to a smooth affine variety outside a compact set has polynomial growth rate. Then I use the fact that the growth rate of T^*M is greater than the growth rate of the sum of its Betti numbers" |
October 01, 2010, 330 - 430 PM at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
TOM GOODWILLIE () |
Overview of the calculus of functors, continued |
" |
September 30, 2010, 4 - 6 pm at Science Center, Room 507 |
| DYNAMICS AND GEOMETRY SEMINAR |
THOMAS KOBERDA (HARVARD UNIVERSITY) |
A ping-pong theorem for the mapping-class group. |
" |
September 29, 2010, 4 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
CHARLES SAMUELS (UNIVERSITY OF BRITISH COLUMBIA) |
Polynomials whose reducibility is connected to the Goldbach conjecture |
Abstract We introduce a collection of polynomials GN in Z[z] having the following property the N th cyclotomic polynomial divides GN if and only if N cannot be represented as a sum of two odd primes. Numerical evidence suggests that, in fact, GN is irreducible and has no roots on the unit circle, providing two generalizations of the Goldbach conjecture. We proceed to discuss some basic properties of GN, including producing asymptotic estimates on the size of their coefficients. At various stages, this work is joint with P. Borwein, K.K. Choi and G. Martin" |
September 29, 2010, 3 - 4 PM at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
DAWEI CHEN (UNIVERSITY OF ILLINOIS AT CHICAGO) |
Geometry of Teichmuller curves |
Teichmuller curves are central objects in dynamics and geometry. They have provided fertile connections between billiards in polygons, flat surfaces and moduli spaces. In this talk, we introduce algebro-geometric techniques to solve problems regarding Teichmuller curves. As applications in algebraic geometry, we construct rigid curves on moduli space of pointed rational curves and bound the effective cone of moduli space of curves, which yield new approaches to Fulton s conjecture and the Schottky problem. As applications in dynamics, we verify Kontsevich-Zorich s conjecture on the invariance of Siegel-Veech constants (joint with Martin Moller) and calculate the sum of Lyapunov exponents of Hodge bundle." |
September 28, 2010, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
SI LI (HARVARD UNIVERSITY) |
BCOV theory on elliptic curve and higher genus mirror symmetry |
Organized by Professor Shing Tung Yau" |
September 28, 2010, 130 - 300 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
JOE HARRIS (HARVARD UNIVERSITY) |
Galois Groups in Geometry |
" |
September 27, 2010, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
VLADIMIR CHERNOV () |
Causality, Low conjecture and the partial order on the space of Legendrian spheres |
Abstract Let (Xm+1, g) be a globally hyperbolic spacetime with Cauchy surface diffeomorphic to an open subset of Rm. The Legendrian Low conjecture formulated by Natario and Tod says that two events x,y in X are causally related if and only if the Legendrian link of spheres Sx, Sy whose points are light geodesics passing through x and y is non-trivial in the contact manifold of all light geodesics in X. The Low conjecture says that for m=2 the events x,y and causally related if and only is Sx, Sy is non-trivial as a topological link. We prove that Low and the Legendrain Low conjectures. We also show that similar statements hold for any globally hyperbolic (X,g) such that the universal cover of its Cauchy surface is an open manifold. The conjecture follows from the existence of the natural partial order on the space of Legendrian spheres in the spherical cotangent bundle of such Cauchy surfaces. We also discuss related joint works with Yuli Rudyak." |
September 24, 2010, 330 - 430 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
() |
|
THE THURSDAY SEMINAR FOR TODAY IS CANCELLE" |
September 23, 2010, 4 9 6 PM at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
YIFENG LIU (COLUMBIA UNIVERSITY) |
Monge-Ampère equation in non-Archimedean geometry |
Abstract Recently, a question about the non-archimedean analogue of the famous Calabi-Yau theorem was proposed by X. Yuan and S. Zhang. In their new paper, they prove the uniqueness of the non-archimedean analogue and deduce from that a very strong result in complex algebraic dynamics, via Arkelov geometry! A natural question is about the non-archimedean analogue of the existence part of the Calabi-Yau theorem. It seems that this half is much more mysterious and quite different from the archimedean case. In this talk, I will show an example of totally degenerate Abelian varieties where the existence part does hod in some sense. Interestingly, a Monge-Ampère equation shows up at the end in the non-archimedean case as well" |
September 22, 2010, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
MARK HASKINS (IMPERIAL COLLEGE, LONDON) |
Exceptional holonomy and calibrated submanifolds |
Abstract We give an introduction to recent developments in the geometry of compact manifolds with exceptional holonomy, focusing on recent work with Corti, Nordstrom and Pacini; we prove the existence of many compact 7-manifolds with holonomy G2 that contain rigid associative submanifolds. The main ingredients in the proof are an appropriate noncompact version of the Calabi conjecture, gluing methods and a certain class of complex projective 3-folds (weak Fano 3-folds). Organized by Professor Shing-Tung Yau" |
September 21, 2010, 1230 - 200 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
STEFAN KEBEKUS (MIT) |
Positivity properties of differentials, the minimal model program, and hyperbolicity of moduli stacks |
" |
September 21, 2010, 3 - 4 PM at MIT (26-310) |
| BASIC NOTIONS SEMINAR |
CURT MCMULLEN (HARVARD UNIVERSITY) |
The Evolution of Geometric Structures on 3- Manifolds |
" |
September 20, 2010, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
ELISENDA GRIGSBY (BOSTON COLLEGE) |
On Khovanov homology, Heegaard Floer homology, and Gluing |
Abstract Ozsvath-Szabo s spectral sequence from Khovanov homology to Heegaard Floer homology has generated a number of interesting applications to questions in low-dimensional topology. By combining the constructions of Ozsvath-Szabo with sutured manifold theory, we now have an enhanced understanding of the algebraic structure of the connection. In particular, a generalization of of Juhasz s surface decomposition theorem implies that the algebra of the spectral sequence behaves as expected under natural geometric operations like cutting and stacking. In this talk, I will discuss joint work in progress with Denis Auroux and Stephen Wehrli aimed at understanding how the connection between Khovanov and Heegaard-Floer homology behaves under gluing. More precisely, we will see how to recover (a portion of) the sutured version of Khovanov homology as the Hochschild homology of certain bimodules over quiver algebras defined by Khovanov-Seidel. Along the way, we will discuss an intriguing relationship between these Khovanov-Seidel bimodules and certain bimodules appearing in the bordered Floer package of Lipshitz-Ozsvath-Thurston" |
September 17, 2010, 330 - 430 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
TOM GOODWILLIE () |
Overview of the calculus of functors, ctd |
" |
September 16, 2010, 4 - 6 pm at Science Center, Room 507 |
| INFORMAL SEMINAR |
MORITZ GROTH (BONN) |
Introduction to Grothendieck's Derivators II |
Abstract In this last talk we stick to the stable situation, namely, triangulated derivators. These can be considered as a further enhancement of triangulated categories. We will outline a proof that every triangulated derivator takes canonically values in triangulated categories and that these triangulated structures are respected by the induced functors." |
September 16, 2010, 2 - 4 pm at Science Center, Room 232 |
| DYNAMICS AND GEOMETRY SEMINAR |
LAURA DE MARCO (UIC) |
Dynamics of cubic polynomials and enumeration of cusps |
" |
September 15, 2010, 4 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
PETER SCHOLZE (BONN) |
A new approach to the Local Langlands Correspondence for GL_n over p-adic fields |
Abstract We give a new local characterization of the Local Langlands Correspondence, using deformation spaces of p-divisible groups, and show its existence by a comparison with the cohomology of some Shimura varieties. This reproves results of Harris-Taylor on the compatibility of local and global correspondences, but completely avoids the use of lgusa varieties and instead relies on the classical method of counting points a la Langlands and Kottwitz. Further, we have a new proof of bijectivity of this correspondence, relying on a description of the inertia-invariant nearby cycles in certain situations." |
September 15, 2010, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
BAOSEN WU () |
Disk-counting of toric Calabi-Yau and mirror symmetry |
Abstract For the toric Calabi-Yau manifolds, I ll discuss a mirror construction based on $T$-duality and Fourier transform. The periods of the mirror are expressed in terms of FOOO s disk-counting invariants, and the construction of the mirror via SYZ gives an enumerative meaning to the periods. (Joint work with K-W. Chan, S-C. Lau, N.C. Leung" |
September 14, 2010, 130 - 300 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
ABHINAV KUMAR () |
All the elliptic fibrations on a generic Jacobian Kummer surface |
Abstract By a theorem of Sterk, there are only finitely many elliptic fibrations on a K3 surface over the complex numbers, up to automorphism. However, explicitly computing all the elliptic fibrations is often a non-trivial problem. I will talk about the solution for Kummer surfaces of Jacobians of genus 2 curves without extra endomorphisms, where the automorphism group is understood by work of Keum and Kondo" |
September 14, 2010, 3- 4 pm at Science Center, Room 507 |
| INFORMAL SEMINAR |
MORITZ GROTH (BONN) |
Introduction to Grothendieck's Derivators I |
Abstract Motivated by the defect of the non-functoriality of the cone construction in triangulated categories we give the definition of a derivator. Some elementary properties are deduced from the axioms indicating that the derivator encodes some higher structure on the underlying category. As a main source of examples we will see that every model category $\mathcal{M}$ has an associated derivator $\mathbb{D}_{\mathcal{M}}$.\\ If one restricts attention to combinatorial model categories on the one side and to derivators of small presentation on the other side, one can show that both theories do essentially the same job. More precisely, after a localization at the class of Quillen equivalences between combinatorial model categories, the association$\mathcal{M}\mapsto\mathbb{D}_{\mathcal{M}}$ becomes an equivalence of these two approaches. We will sketch some of the arguments leading to a proof of this result due to Renaudin" |
September 14, 2010, 2 - 4 pm at Science Center, Room 232 |
| BASIC NOTIONS SEMINAR |
VARIOUS FACULTY (HARVARD UNIVERSITY) |
Job Search Seminar |
" |
September 13, 2010, 3 PM at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
TOM GOODWILLIE () |
Overview of the calculus of functors |
" |
September 09, 2010, 4 - 6 pm at Science Center, Room 507 |
| INFORMAL SEMINAR |
ROBION KIRBY (UC BERKELEY) |
A new calculus for 4-manifolds |
" |
September 08, 2010, 4-5pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
MICHAEL RAPOPORT (BONN) |
Algebraic cycles on Picard moduli spaces of abelian varieties |
Abstract Picard moduli spaces parametrize principally polarized abelian varieties with complex multiplication by the ring of integers in an imaginary-quadratic field. The loci where the abelian varieties split off an elliptic curve in a controlled way are divisors on this moduli space. We study the intersection behavior of these divisors and prove in the non-degenerate case a relation between their intersection numbers and Fourier coefficients of the derivative at s=0 of a certain incoherent Eisenstein series for the unitary group. This is joint work with Kudla" |
September 08, 2010, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
JUERGEN JOST (MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES) |
The Bernstein problem for minimal hypersurfaces |
Abstract I shall report on new conditions that ensure that a complete minimal hypersurface in Euclidean space is affine linear. These results use the fact that the Gauss map of a minimal hypersurface is a harmonic map into a sphere. The proofs depend on convexity properties of subsets of spheres and on regularity schemes for harmonic mappings. I shall also discuss some extensions to the case of higher codimension." |
September 07, 2010, 130 - 300 pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
RYUSHI GOTO (OSAKA UNIVERSITY) |
Generalized Kahler and Calabi-Yau structures on crepant resolutions of Sasaki-Einstein cones |
Abstract At first we will survey our results on deformations of generalized complex and Kahler structures and give applications to complex geometry. Next we will construct Ricci-Flat Kahler metrics (Calabi-Yau structures) in every Kahler class on a crepant resolution of a Sasaki-Einstein cone and discuss deformations of generalized Calabi-Yau structures on the crepant resolution. Organized by Professor Shing-Tung Yau" |
May 25, 2010, 2-330 PM at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
BJORN POONEN (MIT) |
Neron-Severi groups under specialization |
This is a joint work with Davesh Maulik and Claire Voisi" |
May 12, 2010, 3 - 4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
BJORN POONEN (MIT) |
Neron-Severi groups under specialization |
" |
May 11, 2010, 3 pm at MIT (26-142) |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
GIORGIA FORTUNA () |
Conformal blocks and D-modules on Bun(G) |
" |
May 11, 2010, 530 PM at MIT (2-190) |
| THE THURSDAY SEMINAR |
MIKE HOPKINS (HARVARD UNIVERSITY) |
Reduction of the rigidity theorem to Gm |
Please note the change of usual time" |
May 06, 2010, 330 - 5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
PASCAL BOYER (INSTITUTE DE MATHEMATIQUES DE JUSSIEU ) |
Cohomology of some local and global Shimura varieties |
The cohomology groups of Lubin-Tate spaces and some unitary Shimura varieties are related by the Serre-Tate theorem; their alternated sums were calculated by Harris and Taylor. In this talk I ll explain how one can calculate each of these groups using the theory of perverse sheaves" |
May 05, 2010, 3 - 4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
MAX LIEBLICH (UNIVERSITY OF WASHINGTON) |
Moduli spaces of sheaves and an effective version of Merkurjev's theorem |
I will describe some asymptotic geometry of the moduli space of twisted vector bundles with parabolic structure and use it to prove a general result on division algebras over function fields of surfaces over finite fields. In a special case, it gives an effective form of Merkurjev s theorem on the 2-torsion in the Brauer group. This talk is not intended for experts; I will explain everything I m talking about" |
May 04, 2010, 3 pm at MIT (26-142) |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
NICK ROZENBLYUM & GIORGIA FORTUNA () |
Title 1- Chiral Algebras-III. Title 2- Coinvariants, and how chiral module give rise to D-modules on Bun (G) |
Note 15 minutes time change" |
May 04, 2010, 545 PM at MIT (2-190) |
| NUMBER THEORY SEMINAR |
PHAM TIEP (UNIVERSITY OF ARIZONA) |
Representations of finite simple groups and applications |
Abstract In the first part of the talk we will survey recent results on representations of finite (quasi) simple groups. In the second part we will describe some applications of these results in group theory and algebraic geometry. In particular, we will discuss recent proofs by the speaker and his collaborators of some conjectures of Katz, Kollar, Larsen, and Ore" |
April 28, 2010, 3 - 4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
PAUL HACKING (UNIVERSITY OF MASSACHUSETTS, AMHERST) |
Mirror Symmetry and deformations of surface singularities |
We use the Strominger-Yau-Zaslow interpretation of mirror symmetry to describe deformations of surface singularities in terms of counts of holomorphic curves and discs on a mirror surface. In particular we prove Looijenga s conjecture on smoothability of cusp singularities. This is joint work with Mark Gross and Sean Keel" |
April 27, 2010, 330 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
NICK ROZENBLYUM () |
Chiral algebras-II |
" |
April 27, 2010, 530 - 800 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
YAKOV ELIASHBERG (STANFORD UNIVERSITY) |
Symplectic geometry of Stein manifolds |
" |
April 23, 2010, 330 - 430 pm at Science Center, Room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
DONG WANG (MICHIGAN) |
Hermitian matrix model with spiked external source |
Abstract The Hermitian matrix model with spiked (i.e., finite rank) external source has been extensively studied when the potential is Gaussian or Laguerre, and an interesting phase transition phenomenon has been observed. We utilize an integrable structure to obtain the asymptotic distribution of the largest eigenvalue of Hermitian random matrices with spiked external source for general potential. As a result, we find a new universal pattern of phase transition for a large class of non-convex potentials. This is joint work with Jinho Baik" |
April 22, 2010, 310 pm at Science Center, Room 232 |
| THE THURSDAY SEMINAR |
ANATOLY PREYGEL (MIT) |
More on motivic cobordism and HZ |
" |
April 22, 2010, 3 - 5 PM at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
GLENN STEVENS (HARVARD UNIVERSITY) |
Eigenvarieties and a Conjecture of Urban |
" |
April 21, 2010, 3 - 4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
RAGNI PIENE (UNIVERSITY OF OSLO) |
Inflection loci of projective varieties |
Rational normal curves are the only smooth projective curves that have no inflection points (of any order). In fact this property characterizes Veronese embeddings of projective spaces of any dimension. Some varieties that are everywhere inflected, such as scrolls and certain toric varieties, still have well defined generalized inflection loci. One wants to describe these loci and to characterize those for which these loci are empty. The talk will survey some old and new results, and focus on recent joint work with A. Lanteri and R. Mallavibarrena concerning scrolls" |
April 20, 2010, 330 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
ANDREI NEGUT AND NICK ROZENBLYUM () |
I- Proof of the Hecke eigenproperty. II- Introduction to chiral algebras |
" |
April 20, 2010, 530 - 800 pm at MIT (2-190) |
| BASIC NOTIONS SEMINAR |
KRISTEN WICKELGREN (HARVARD UNIVERSITY) |
Grothendieck's Anabelian Conjectures |
Organized by Professor Shing Tung Yau" |
April 19, 2010, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
DAN FREED (UT AUSTIN) |
A differential index theorem |
" |
April 16, 2010, 3;30 - 430 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
EREZ LIEBERMAN-AIDEN (HARVARD & MIT) |
Physical Analogues of Peano Curves the folding principles of the human genome |
Abstract I will discuss our recent work mapping the three-dimensional architecture of the human genome, highlighting both geometric and topological feature, and emphasizing he role of the fractal globule, a physical analogue of the Peano curve. Motivated by our experimental findings, we identify a new symmetry property possessed by finite approximations of Peano curves, and construct several new Peano curves with interesting properties. I will point out knot-theoretic questions that arise. Based on joint work with Maxim Imakaev, Nynke van Berkum, Louise Williams, Andreas Gnirke, Jian Li, Najeeb Tarazi, Diana Hubbard, Eric S. Lander and Leonid A. Mirny. Organized by Professor Shing-Tung Yau" |
April 16, 2010, 230 - 330 pm at Science Center, Room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
OFER ZEITOUNI (MINNESOTA) |
Non-normal random matrices and convergence to a ring |
Abstract We study the empirical measure $L_{A_n}$ of the eigenvalues of non-normal square matrices of the form $A_n=U_nD_nV_n$ with $U_n,V_n$ independent Haar distributed on the unitary group and $D_n$ real diagonal. We show that when the empirical measure of the eigenvalues of $D_n$ converges, and $D_n$ satisfies some technical conditions, $L_{A_n}$ converges towards a rotationally invariant measure on the complex plan whose support is a single ring, even if the support of $D_n$ consists of several disjoint intervals. In particular, we provide a completer proof of Feinberg-Zee single ring theorem. Joint work with Alice Guionnet and Manjunath Krishnapur" |
April 15, 2010, 310 pm at Science Center, Room 232 |
| THE THURSDAY SEMINAR |
MIKE HOPKINS (HARVARD UNIVERISTY) |
Back to the Friedlander-Milnor conjecture |
" |
April 15, 2010, 3 - 5 PM at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
KIRAN S. KEDLAYA (MIT) |
The universal crystalline representation |
" |
April 14, 2010, 3 - 4 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
ANDREI NEGUT (HARVARD UNIVERSITY) |
Action of groups on categories-II |
" |
April 13, 2010, 530 - 800 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
KARL SCHWEDE (UNIVERSITY OF MICHIGAN) |
On the behavior of test ideals for finite separable morphisms |
" |
April 13, 2010, 3 pm at MIT (26-142) |
| BASIC NOTIONS SEMINAR |
SARAH KOCH (HARVARD UNIVERSITY) |
Thurston's topological characterization of rational functions |
Organized by Professor Shing Tung Yau" |
April 12, 2010, 3 - 4 pm at Science Center, Room 507 |
| WORKSHOP ON GEOMETRIC STRUCTURES IN STRNG THEORY |
JOEL SMOLLER (UNIVERSITY OF MICHIGAN) |
Decay of Solutions to the Cauchy Problem for Various Physical Systems Stability of Black Holes |
Organized by Professor Shing Tung Yau" |
April 09, 2010, 440 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
CIPRIAN MANOLESCU (UCLA) |
A combinatorial approach to four-manifold invariants |
" |
April 09, 2010, 330 - 430 pm at Science Center, Room 507 |
| COLLOQUIUM |
ASSAF NAOR (NYU) |
L_1 embeddings of the Heisenberg group and fast estimation of graph isoperimetery |
Abstract We will show that any L_1-valued mapping of an epsilon net in the unit ball of the Heisenberg group incurs bi-Lipschitz distortion (log(1/epsilon))^c, where c is a universal constant. We will also explain how this result implies an exponential improvement to the best known integrality gap for the Goemans-Linial semidefinite relaxation of the Sparsest Cut problem. Joint work with Jeff Cheeger and Bruce Kleiner" |
April 08, 2010, 430 PM at Science Center, Hall D |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
JEFFREY SCHENKER (MICHIGAN) |
Eigenvector Localization for Random Band Matrices With Power Law Band Width |
" |
April 08, 2010, 310 pm at Science Center, Room 232 |
| SPECIAL TALK |
HARRY NUSSBAUMER (INSTITUTE OF ASTRONOMY, ETH ZURICH) |
Discovering the Expanding Universe |
Abstract Twice Einstein refused theoretical evidence for an expanding universe. We shall look at some of the historical key events that led to the discovery of the expanding universe and why Einstein was finally converted. The observational support for expansion cam from nebulae. We briefly follow the story from their first observation by Simon Marius (1614) to the 20th century, when modern giant telescopes allowed Shapley 1918 to allocate the Sun its place within the Milky Way, and Hubble to finally prove in 1925 that spiral nebulae were outside the Milky Way. While the battle of the nebulae was still on, Einstein inaugurated in 1917 modern cosmology with his static universe. In the same year de Sitter published another static universe, it contained no matter. Test particles showed redshifted spectra, which seemed to agree with the large redshifts in spiral nebulae, found by Slipher since 1912. Yet no one succeeded in making sense of de Sitter s model. In 1927 Lemaitre combined general relativity with observations. He concluded that the universe was expanding. He found the linear velocity-redshift relationship, and he gave the first numerical value for the Hubble constant. How did the luminaries of cosmology, such as Einstein, de Sitter and Eddington take to Lemaitre s findings? And where does Hubbe s paper of 1929 fit in" |
April 07, 2010, 130 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
ULRICH TERSTIEGE (HARVARD UNIVERSITY) |
Local theory for special cycles on the Shimura variety of $GU(1,2)$ |
Abstract We investigate intersections of special cycles on a moduli space of $p$-divisible groups which is associated to an arithmetic model of the Shimura variety of $GU(1,2)$. The main result expresses intersection multiplicities of special cycles in terms of certain representation densities confirming a conjecture of Kudla and Rapoport. This result can be used to relate intersection multiplicities of special cycles on the arithmetic model of the Shimura variety of Fourier coefficients of derivatives of certain Eisenstein series." |
April 07, 2010, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
ALEKSANDER SUBOTIC (HARVARD UNIVERSITY) |
A monoidal structure for Fukaya categories |
Abstract Mirror symmetry can be thought of as a relation between the symplectic geometry of a space X and the algebraic geometry of a mirror dual space Y. In this talk I will discuss a definition of a monoidal structure on a Donaldson-Fukaya category of X that should mirror the one given by the tensor product of sheaves on Y, and the importance of such a structure. I will then discuss how this can be confirmed in the case of mirror symmetry of elliptic curves" |
April 06, 2010, 130 - 300 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
ANDREW SNOWDEN (PRINCETON UNIVERSITY) |
Syzygies of Segre embeddings |
" |
April 06, 2010, 330 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
WEI ZHANG (HARVARD UNIVERSITY) |
Absolutely Hodge Cycle |
Organized by Professor Shing Tung Yau" |
April 05, 2010, 3 pm at Science Center, Room 507 |
| SPECIAL NUMBER THEORY SEMINAR |
MANJUL BHARGAVA (PRINCETON UNIVERSITY) |
The average rank of elliptic curves |
Abstract A rational elliptic curve may be viewed as the set of solutions to an equation of the form $y^2=x^3+Ax+B$, where $A$ and $B$ are rational numbers. It is known that the rational points on this curve possess a natural abelian group structure, and the Mordell-Weil theorem states that this group is always finitely generated. The rank of a rational elliptic curve measures how many rational points are needed to generate all the rational points on the curve. There is a standard conjecture originating in work of Goldfeld and Katz-Sarnak that states that the average rank of all elliptic curves should be 1/2; however, it has not previously been known that the average rank is even finite! In this lecture, we describe recent work that shows that the average rank is finite (in fact, we show that the average rank is bounded by 1.5)." |
April 02, 2010, 230 - 330 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
JOHN BALDWIN (PRINCETON UNIVERSITY) |
Contact monoids and Stein cobordisms |
Abstract I will describe certain monoids in the mapping class groups of compact surfaces with boundary which are significant in 3-dimensional contact geometry" |
April 02, 2010, 330 - 430 pm at Science Center, Room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
M. HASTINGS (MICROSOFT STATION Q) |
Quasi-adiabatic continuation and the Topology of Many-body Quantum Systems |
Abstract Topological arguments play a ket role in understanding quantum systems. Recently, it has been shown that K-theory provides a tool for classifying different phases of non-interacting, or single-particle, systems. However, topological arguments have also been applied to interacting systems. I will explain the techniques of quasi-adiabatic continuation, which provides a way to rigorously formulate many of the topological arguments made by physicists for these systems. In particular, I will discuss its application to a higher dimensional Lieb-Schultz-Mattis theorem (a statement about degeneracy of ground states, which can arise for topological reasons), where this techniques was introduced in 2004, and its more recent application to proving quantum Hall conductance quantization for interacting systems" |
April 01, 2010, 310 pm at Science Center, Room 232 |
| NUMBER THEORY SEMINAR |
ROBERT POLLACK (BU) |
Fitting ideals of Selmer groups of modular forms |
" |
March 31, 2010, 3 - 4 pm at Science Center, Room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
ANATOLY VERSHIK (ST. PETERSBRUG BRACH OF STEKLOV INSTITUTE AND NORTHEASTERN UNIVERSITY) |
Random matrices with the group of symmetries and classification of Gromov's triples |
Abstract We will consider the measures on the space of matirces which are invariant with respect to a group of Inear transformations of the martices like infinite symmetric group or infinite unitary group. Such measures appeared in the problem of the classification of the measurable functions of two variables, and in particularly in the problem, posed by Gromov, about classification of metric spaces with probability measure" |
March 31, 2010, 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
KEIJI OGUISO (OSAKA UNIVERSITY) |
Some remarks on flat projective families with Calabi-Yau fibers |
Abstract Starting with a toy example in elliptic curves, which actually the starting point in this work, I would like to point out two kinds of seemingly irrational phenomena occurring in projective flat families with (at least one) Calabi-Yau fibers. Some part is a joint work with Nam-Hoon Lee. Organized by Professor Shing-Tung Yau" |
March 30, 2010, 130 - 300 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
SAM RASKIN (HARVARD UNIVERSITY) |
The birth of Opers II |
" |
March 30, 2010, 530 - 800 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
MAKSYM FEDORCHUK (COLUMBIA UNIVERSITY) |
Spaces of hyperelliptic curves with AD singularities |
The space of n-pointed smooth rational curves can be compactified to Hassett s space of weighted pointed stable curves. Different choices of weights lead to different compactifications related by well-understood birational morphisms. We study an analogous picture for a certain space and (pointed) smooth hyperelliptic curves" |
March 30, 2010, 3 pm at MIT (26-142) |
| BASIC NOTIONS SEMINAR |
ARTHUR OGUS () |
Logarithmic Geometry |
Logarithmic geometry was invented, or at least assembled, in the eighties, with the goal of extending a important set of theorems in arithmetic algebraic geometry to the case of bad reduction. Since then it has grown into a broad and powerful framework for the systematic study of compactification and degeneration in a wide range of settings. I will concentrate on the complex analytic case, in which it is possible to give a revealing topological picture of how log geometry works and what a log structure does. In particular, I will explain how one can use log structures to formulate and prove an implicit function theorem for a certain class of singular mappings. Basic Notions Seminars are organized by Professor Shing-Tung Yau" |
March 29, 2010, 3 pm at Science Center, Room 507 |
| COLLOQUIUM |
BRIAN CONRAD (STANFORD UNIVERSITY) |
Finiteness for Tamagawa numbers |
Abstract The Tamagawa number of a linear algebraic group (over a number field or over the function field of a curve over a finite field) is a certain canonical volume that arises in settings as varied as the arithmetic of quadratic forms and counting connected components of certain moduli spaces of bundles over curves over finite fields. The finiteness of such volumes for all reductive groups was proved by Borel and Harder. The finiteness in general can then be easily deduced in characteristic zero, but the case of positive characteristic needs completely different ideas and was settled only very recently. We discuss some of the highlights of this story" |
March 25, 2010, 430 pm at Science Center, Hall D |
| THE THURSDAY SEMINAR |
JACOB LURIE (HARVARD UNIVERSITY) |
Motivic Cohomology and Chow Groups |
" |
March 25, 2010, 3 - 5 PM at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
JIU-KANG YU (HARVARD UNIVERSITY) |
Moy-Prasad theory and Vinberg theory |
Abstract Moy-Prasad theory associates to a rational point on the Bruhat-Tits building of a p-adic group, a finite reductive group together with a finite sequence of rational representations. Vinberg theory associate the same kind of data to a finite reductive group with an automorphism. We show that these two theories are essentially the same, and the identification of the two allows us to solve long standing problems on both sides, regarding depth of representations, or existence if Weiestrass sections, for example" |
March 24, 2010, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
HAO XU (HARVARD UNIVERSITY) |
Intersection numbers from ADE singularities |
Abstract Motivated by Calabi-Yau/Landau-Ginzburg correspondence, Witten, Fan-Jarvis-Ruan defined quantum type Gromov-Witten invariants for quasihomogeneous singularities. We will discuss how to compute them in the case of ADE type singularities" |
March 23, 2010, 130 - 3pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
C. NEWMAN (COURANT INSTITUTE NYU) |
Ising (Conformal) Fields and Cluster Area Measures |
Abstract I will discuss a representation for the magnetization field of the critical two-dimensional Ising model in the scaling limit as a random field using renormalized area measures associated with SLE clusters. The renormalized areas come from the scaling limit of critical FK (Fortuin-Kasteleyn) clusters and the random field is a convergent sum of the area measured with random signs. The representation is based on the interpretation of the lattice magnetization as the sum of the signed areas of clusters. If time permits, potential extensions including to three dimensions, will also be discussed. The talk will be based on joint work with F.Camia (PNAS 106 (2009) 5457-5463) and on work in progress with F. Camia and C. Garban" |
March 23, 2010, 3 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
SAM RASKIN () |
Hecke eigen property-I the birth of opers |
" |
March 23, 2010, 530 - 800 pm at MIT (2-190) |
| BASIC NOTIONS SEMINAR |
XINWEN ZHU (HARVARD UNIVERSITY) |
Integral homology of loop groups via Langlands dual groups |
Organized by Professor Shing Tung Yau" |
March 22, 2010, 3 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
ERIC RAINS (CALIFORNIA INSTITUTE OF TECHNOLOGY) |
Moduli spaces of differential and difference equations |
" |
March 16, 2010, 3 pm at MIT (26-142) |
| DIFFERENTIAL GEOMETRY SEMINAR |
MU-TAO WANG (COLUMBIA UNIVERSITY) |
Lagrangian mean curvature flows and isotopy problems |
" |
March 16, 2010, 130 - 300 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
BERND AMMANN (UNIVERSITAT REGNESBURG) |
A surgery formula for the smooth Yamabe invariant |
" |
March 12, 2010, 330 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
DUSTIN CLAUSEN () |
The Conjectural Relation between HQ-modules and Grothendieck's Motives |
" |
March 11, 2010, 3 - 5 pm at Science Center, Room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
EYAL LUBETZKY (MICROSOFT) |
Critical slowdown for the Ising model on the two-dimensional lattice |
Abstract Intensive study throughout the last three decades has yielded a rigorous understanding of the spectral-gap of the Glauber dynamics for the Ising model on Z^2 everywhere except at criticality. While the critical behavior of the Ising model has long been the focus for physicists, mathematicians have only recently developed an understanding of its critical geometry with the advent of SLE, CLE and new tools to study conformally invariant systems. A rich interplay exists between the static and dynamic models. At the static phase-transition for Ising, the dynamics is conjectured to undergo a critical slowdown At high temperature the inverse-gap is O(1), at the critical beta_c it is polynomial in the side-length and at low temperature it is exponential in it. A long series of papers verified this on Z^2 except at beta=beta_c where the behavior remained unknown. In this work we establish the first rigorous polynomial upper bound for the critical mixing, thus confirming the critical slowdown for the Ising model in Z^2. Namely, we show that on a finite box with arbitrary (e.g. fixed, free, periodic) boundary conditions, the inverse-gap at beta=beta_c is polynomial in the side-length. The proof harnesses recent understanding of the Ising model together with classical tools from the analysis of Markov chains. Based on joint work with Allan Sly" |
March 11, 2010, 310 pm at Science Center, Room 232 |
| NUMBER THEORY SEMINAR |
A. GONCHAROV (BROWN UNIVERSITY) |
Hodge correlators and Rankin-Selberg integrals |
" |
March 10, 2010, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
GABOR LIPPNER (HARVARD UNIVERSITY) |
Borel Oracles and parameter testing |
Abstract I will introduce the notion of a measurable graph, and explain how it naturally arises as a limit of a graph sequence. Borel constructions in the limit can be pulled back to obtain certain sub-structures in the graph sequence. This interplay between combinatorics and measure theory enables us to prove various results on parameter testing and regularity properties of graphs. Joint work with Gabor Elek. Organized by Professor Shing-Tung Yau" |
March 09, 2010, 130 - 300 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
JONATHAN BARLEV (HARVARD UNIVERSITY) |
Opers-II |
" |
March 09, 2010, 530 - 800 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
DIMA ARINKIN (UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL) |
Autoduality of Jacobians for singular curves |
" |
March 09, 2010, 430 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
KIRAN KEDLAYA (MIT) |
Resolution of turning points for flat meromorphic connections |
" |
March 09, 2010, 3 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
XINYI YUAN (HARVARD UNIVERSITY) |
Preperiodic points and p-adic Calabi theorem |
" |
March 08, 2010, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
EDUARDO GONZALEZ (UNIVERSITY OF MASSACHUSETTS BOSTON) |
Area dependence for gauge Gromov-Witten invariants |
" |
March 05, 2010, 330 - 430 pm at Science Center, Room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
GERARD BEN AROUS (COURANT INSTITUTE) |
Random Matrices and Complexity of Random Morse functions of many variables |
Abstract We relate the computation of the complexity of general Gaussian functions on the Sphere in large dimensions with Random Matrix Theory. Using this link we compute their complexity, i.e their number of critical points, of given index on any level sets. We relate this question to the description of the low energy states of spherical spin glasses. This is joint work with A. Auffinger and J. Cerny" |
March 04, 2010, 310 pm at Science Center, Room 232 |
| THE THURSDAY SEMINAR |
MIKE HOPKINS (HARVARD UNIVERSITY) |
The slice filtration for algebraic bordism |
" |
March 04, 2010, 3 - 5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
BENOIT STROH () |
Compactification of Siegel varieties at some places of bad reduction |
" |
March 03, 2010, 3 - 4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
GAVRIL FARKAS (HUMBOLDT UNIVERSITAT) |
The birational geometry of the moduli space of spin curves |
Moduli spaces of spin curves parametrize roots of canonical bundles of curves (theta-characteristics), and are highly interesting covers of the moduli space of curves. I will discuss a complete description of the birational type of the even spin moduli space, which is a variety of general type for g>8, unirational for g<8. and a very mysterious variety of Calabi-Yau type for g=8. The is joint work with A. Verra" |
March 02, 2010, 430 pm at MIT (26-142) |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
JONATHAN BARLEV (HARVARD UNIVERSITY) |
Opers-I |
" |
March 02, 2010, 530-800 pm at MIT (2-190) |
| DIFFERENTIAL GEOMETRY SEMINAR |
ANDREW STROMINGER (HARVARD UNIVERSITY) |
The Kerr/CFT Correspondence |
Differential Geometry Seminars are organized by Professor Shing-Tung Yau" |
March 02, 2010, 130 - 300 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
CHRISTIAN SCHNELL (UNIVERSITY OF ILLINOIS AT CHICAGO) |
Complex-analytic Neron models for families of intermediate Jacobians |
I will describe a global construction of a complex-analytic Neron model for degenerating families of intermediate Jacobians (a classical and special case are families of abelian varieties ). One consequence is a new proof for the theorem of Brosnan-Pearlstein that, on an algebraic variety, the zero locus of an admissible normal function is an algebraic subvariety. Another consequence is a generalization of the theorem of Cattani-Deligne-Kaplan to admissible variations of mixed Hodge structure (joint work with Brosnan and Pearlstein)" |
March 02, 2010, 3 pm at MIT (26-142) |
| BASIC NOTIONS SEMINAR |
YAKOV SINAI (PRINCETON) |
Smoothness of solutions of the Navier-Stokes System inside the square |
Abstract I shall explain the results of the recent joint paper with E. Dinaburg and Dong Li in which we show that the solutions of the NSS inside the square are not so smooth as expected. The main difficulty is the analysis of the inverse Laplacians in special subspaces. Basic Notions Seminars are organized by Professor Shing-Tung Yau" |
March 01, 2010, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
JEREMY KAHN (STONY BROOK UNIVERSITY) |
Essential Immersed Surfaces in Closed Hyperbolic 3-Manifolds |
Abstract Given any closed hyperbolic 3-manifold M and epsilon >0, we find a closed hyperbolic surface S and a map f S to M such that f lifts to a 1+epsilon-quasi-isometry from the universal cover of S to the universal cover of M. It follows that, for epsilon small, the map f induces an injection on the fundamental group of S; thus the fundamental group of every closed hyperbolic 3-manifold has as surface subgroup. This is joint work with Vladimir Markovic of Warwich University. I will explain why the mixing of the frame flow on M implies the existence of a highly symmetric collection of pairs of pants, which can then be assembled to form the desired surface S" |
February 26, 2010, 330 - 430 pm at Science Center, Room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
ANTTI KEMPPAINEN (UNIVERSITE' PARIS-SUD AND UNIVERSITY OF HELSINKI) |
Random curves, scaling limits and Loewner evolutions |
Abstract In the 2D statistical physics and its lattice models, interfaces and random curves. A general method to prove the convergence of a random discrete curve, as the lattice mesh goes to zero, is to first show the existence of subsequent scaling limits and then to prove the uniqueness. In this talk, I introduce a sufficient condition, and some equivalent formulations, that guarantee the precompactness (existence) and also that the limits are Loewner evolutions, i.e. they correspond to continuous Loewner driving processes. The second result is needed for the uniques characterization of the limits. This framework of estimates can be used for almost all of the already existing proofs of an interface converging to a Schramm-Loewner evolution (SLE), and for at least one new result. In principle, it can be applied beyond SLE. Joint work with Stanislav Smirnov, Universite de Geneve" |
February 26, 2010, 1 pm at Science Center, Room 232 |
| THE THURSDAY SEMINAR |
CLARK BARWICK (HARVARD UNIVERSITY) |
The Atiyah-Hirzebruch spectral sequence for algebraic K-theory |
Abstract I ll describe a weight filtration on the algebraic K-theory of a regular scheme, due to Grayson. I ll describe it again using the slice filtration of Voevodsky. Finally, I ll sketch a proof that the graded pieces of this filtration are given by motivic cohomology, in the sense described in Jacob Lurie s lecture." |
February 25, 2010, 3 - 5 pm at Science Center, Room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
J. YIN (HARVARD UNIVERSITY) |
Universality for generalized Wigner matrices |
Abstract Consider NxN Hermitian or symmetric random matrices H with sigma_{ij}^2 denoting the variance the (i,j) matrix element. In this talk, we will describe the recent results stating that, under certain boundedness condition on sigma_{ij}, the eigenvalue spacing statistics of H in the bulk of the spectrum coincide with those of the Gaussian unitary or orthogonal ensemble (GUE or GOE). There are essentially no other conditions on the probability law of the matrix elements. Related results on the sample covariance ensembles and band matrices will also be discussed" |
February 25, 2010, 310 pm at Science Center, Room 232 |
| NUMBER THEORY SEMINAR |
MATT BAKER (GEORGIA INSTITUTE OF TECHNOLOGY) |
Complex dynamics and adelic potential theory |
Abstract Using tools from number theory and complex analysis, Laura DeMarco and I have recently proved the following theorem for any fixed complex numbers a and b, and any integer d at least 2, the set of complex numbers c for which both a and b are preperiodic for z^d+c is infinite if and only if a^d=b^d. This provides an affirmative answer to a question of Zannier. The main arithmetic ingredient in the proof is an adelic equidisrtibution theorem for preperiodic points over number fields and function fields, with non-archimedean Berkovich spaces playing an essential role." |
February 24, 2010, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
VICTOR GUILLEMIN (MIT) |
Rethinking the role of heat invariants in inverse spectral problems |
Abstract Given a Riemannian manifold, M, one can recapture from the heat trace of the Laplace operator such global invariants of M as its Riemannian volume. However it s long been thought that heat trace techniques are not particularly useful for computing more localized invariants. Recent developments in semi-classical analysis show, however, that this isn t entirely true. Differential Geometry Seminars are organized by Professor Shing-Tung Yau" |
February 23, 2010, 130 - 300 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
CURT MCMULLEN (HARVARD UNIVERSITY) |
K3 surfaces , entropy and glue |
Please note the change in time" |
February 23, 2010, 330 - 430 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
RYAN REICH (HARVARD UNIVERSITY) |
Affine Grassmannian-II geometric Satake equivalence |
" |
February 23, 2010, 530 - 800 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
ANTTI KNOWLES (HARVARD UNIVERSITY) |
Controlling quantum fluctuations in the mean-field limit |
Abstract I will begin by reviewing the basics of many-body quantum mechanics, the mean-field limit of a quantum Bose gas, and the nonlinear Hartree equation. I will then report on a recent joint work with P. Pickl, in which we derive explicit bounds on the magnitude of the quantum fluctuations in the mean-field limit. Our approach applies to a large class of one-body Hamiltonians and interaction potentials. In particular, we control the quantum fluctuations in the mean-field approximation of a boson star, and provide a microscopic derivation of the nonrelativistic Hartree equation with an L^2-critical nonlinearity. We also show that in a scattering regime the quantum fluctuations are bounded uniformly in time. Basic Notions Seminars are organized by Professor Shing-Tung Yau" |
February 22, 2010, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
ZHONGTAO WU (PRINCETON) |
Cosmetic Surgery Conjecture for S^3 |
" |
February 19, 2010, 330 - 430 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
JACOB LURIE (HARVARD UNIVERSITY) |
The Motivic Eilenberg-MacLane Spectrum |
" |
February 18, 2010, 3-5 pm at Science Center, Room 232 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
C. BORGS (MICROSOFT) |
Polya Urns and Convergence of Preferential Attachment Graphs |
Abstract After discussing general notions of graph sequences, including the Benjamini-Schramm limit of a sequence of graphs, I introduce a new representation for preferential attachments graphs related to an old concept from probability, the notion of Polya urns. Using this new representation, we then construct the Benjamini-Schramm limit of a sequence of preferential attachment graphs. The work presented in this talk is joint work with N. Berger, J.T. Chayes and A. Saberi" |
February 18, 2010, 310 pm at Science Center, Room 232 |
| JOINT BRANDEIS-HARVARD-MIT NORTHEASTERN MATHEMATICS COLLOQUIUM |
ZHOUPING XIN (THE CHINESE UNIVERSITY OF HONG KONG) |
Mixed Type Equations and Compressible Transonic Flows |
Abstract The mathematical theory of systems of multi-dimensional huperbolic conservations remains a great challenge to the field of nonlinear partial differential equations. Some of the main difficulties in dealing with such a system are the system is mixed type and may change types so that the classical approaches fail to yield the global well-posedness theory. This is so even for the important compressible Euler systems in gas dynamics. In this talk, I will illustrate these by the example of the transonic steady compressible flows in multi-dimensional ducts with variable sections. In particular, I will discuss some recent progress on the transonic shock problem in a class de Laval nozzles due to Courant-Friedrichs and existence of smooth subsonic-sonic and transonic flows in such nozzles" |
February 18, 2010, 430 pm at Science Center, Hall D |
| NUMBER THEORY SEMINAR |
MARK REEDER () |
Supercuspidal representations and invariant theory |
" |
February 17, 2010, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
MBOYO ESOLE (HARVARD UNIVERSITY) |
F-theory and new types of singular fibers for elliptic fibrations |
Abstract F-theory was invented by Vafa to describe the strong coupling limit of type IIB string theory. Mathematically, it is an elegant physical formulation of the geometric structure of elliptic fibrations. Singular fibers play an essential role in F-theory. Singular fibers of an elliptic surface have been classified by Kodaira and Neron. This classification have been generalized to elliptically threefolds by Miranda and more recently to elliptic n-fold by Szydlo. Miranda and Szydlo classifications rely on conditions of normal crossing and require a well defined j-invariant all over the base of the elliptic fibration. However, for physically interested cases, one has to go above these conditions. This transgression opens the door to new types of fibers. F-theory provides a setting to discuss these new singular fibers. I will present the derivation of some of these new types of singular fibers not present in previous classifications. They have an interesting link with generalization of Neron models to base with non-perfect residue field and characteristic different from zero. The new fibers often also have a simple description in terms of folding of extended Dynkin diagram by certain automorphisms. As a reward, I will present a systematic resolution of the singular Weierstrass model describing the SU(5) Grand Unified Theory. Differential Geometry Seminars are organized by Professor Shing-Tung Yau." |
February 16, 2010, 130 - 300 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
RYAN REICH (HARVARD UNIVERSITY) |
Affine Grassmannian-I factorization, convolution and fusion |
" |
February 16, 2010, 530 - 800 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
ALEX SUBOTIC (HARVARD UNIVERSITY) |
A monoidal structure for Fukaya categories |
" |
February 12, 2010, 330 - 430 pm at Science Center, Room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
HOI H. NGUYEN (RUTGERS UNIVERSITY) |
On the inverse Littlewood-Offord problem |
" |
February 11, 2010, 310 pm at Science Center, Room 232 |
| NUMBER THEORY SEMINAR |
ZHIWEI YUN () |
From automorphic forms to Klooserman sheaves |
" |
February 10, 2010, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
LOK MING (RONALD) LUI (HARVARD UNIVERSITY) |
Computational Differential Geometry and its application to Human Brain Mapping |
Abstract In Human Brain Mapping, neuroscientists commonly aim to identify structural differences between healthy and unhealthy brains, in order to detect systematic patterns of alterations in brain diseases. Surface-based cortical analysis is an important strategy and has found useful applications in disease analysis. The main obstacle is that the human brain cortical surface is a very complicated manifold with difficult geometry. In this talk, I will describe how conformal and quasiconformal geometry can be used to analyze brain structures accurately and systematically. I will firstly describe how conformal and quasiconformal maps can be computed. These maps give the best global parameterizations of cortical surfaces which align landmarks and ca n be used for various applications such as surface registration, feature detection, computation on surfaces, etc. Secondly, different surfaces with landmarks correspondence have different conformal structures. This gives a signature for different brain surfaces for shape analysis. In the second part of my talk, I will describe how conformal structure of the brain surface can be used for shape analysis. Specifically, I will describe how different conformal modules can be computed and used for abnormality detection in brain surfaces. This seminar is organized by Professor Shing-Tung Yau" |
February 09, 2010, 130 - 300 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
DENNIS GAITSGORY (HARVARD UNIVERSITY) |
Overview and recap of Dustin's talk on quantization |
" |
February 09, 2010, 530 - 800 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
MANISH PATNAIK (HARVARD UNIVERSITY) |
Geometry of arithmetic quotients of loop groups |
The moduli of G-bundles on a curve over a field of finite characteristic admits a description in terms of an arithmetic quotient of the adelic points of the group G. Replacing G by its loop group and considering an analogous arithmetic quotient, we will explain how the resulting set parametrizes G-bundles on certain algebraic surfaces together with information about the second Chern class of such bundles. The main ingredient will be an adelic Riemann-Roch type formula relating the central extension of loop groups and the K-theoretic second Chern class. We will also try to explain the connection with Eisenstein series on loop groups. This is joint work with Howard Garland" |
February 09, 2010, 3 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
THOMAS SPENCER (PRINCETON) |
Random band matrices, statistical mechanics and hyperbolic symmetry |
Abstract Random band matrices are large symmetric matrices whose random matrix elements are concentrated in a band about the diagonal. Spectral properties of these matrices can be reformulated in terms of certain statistical mechanics models with hyperbolic supersymmetry. This talk will discuss a simplified version of one of these models. The simpler model is closely related to a random walk in a correlated random environment and to an edge reinforced random walk. In 3 dimensions, a transition from a diffusive phase to a localized phase is proved. This reflects a spectral transition for certain band matrix ensembles. This is joint work with M. Disertori and M. Zirnbauer. Basic Notions Seminars are organized by Professor Shing-Tung Yau" |
February 08, 2010, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
JACOB LURIE (HARVARD UNIVERSITY) |
Nonabelian Poincare Duality |
" |
February 05, 2010, 330 - 430 pm at Science Center, Room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS |
SIJUE WU (UNIVERSITY OF MICHIGAN) |
Wellposedness of the two and three dimensional full water wave problem |
Abstract We consider the question of the global in time existence and uniqueness of solutions of the infinite depth full water wave problem. We show that the nature of the nonlinearity of the water wave equation is essentially of cubic and higher orders. For suitable small initial data, we show that the 2-D full water wave equation is uniquely solvable almost globally in time, and the 3-D full water wave equation is uniquely solvable globally in time" |
February 04, 2010, 310 pm at Science Center, Room 232 |
| THE THURSDAY SEMINAR |
MIKE HOPKINS (HARVARD UNIVERSITY) |
Applications of the Connectivity Theorem |
" |
February 04, 2010, 3 - 5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
BARRY MAZUR (HARVARD UNIVERSITY) |
Ranks of twists of elliptic curves and Hilbert's Tenth Problem |
" |
February 03, 2010, 3 - 4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
MARAT ROVINSKY (INSTITUTE FOR ADVANCED STUDY) |
Stable birational invariants with the Galois descent property |
Given a field k, an invariant in the title is understood as a rule associating a vector space to each smooth k-variety in a way, contravariant with respect to the dominant morphisms. There are basically two types of examples of invariants in the title one is related to the 0-cycles modulo rational equivalence, another is related to differentials. The goal of the talk is to discuss relations between these examples and to explain some basic properties of (and conjectures on) the category of stable birational invariants with the Galois descent property. There are several equivalent ways to look at such invariants. One of them uses representations of automorphism groups of a universal domain over K. Another one considers them as sheaves in some topology. This will be also discussed." |
February 02, 2010, 430 pm at MIT (26-142) |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
EKATERINA AMERIK (UNIVERSITE' DE PARIS-SUD) |
Self-maps and rational points |
" |
February 02, 2010, 3 pm at MIT (26-142) |
| DIFFERENTIAL GEOMETRY SEMINAR |
FRANS PRETORIUS (PRINCETON) |
Black Hole Mergers |
Abstract The class of spacetimes describing the merger of two black holes contain some of the most fascinating solutions to the equations of general relativity. In this talk I will review what has been learned about the binary black hole problem over the past several years from numerical simulations of the Einstein field equations. This included regions of parameter space describing astrophysical mergers, of relevance of gravitational wave astronomy, and the high speed regime, of possible relevance to LHC and cosmic ray physics in certain proposed large extra dimension scenarios. Some f the interesting results include events where the gravitational wave luminosity approaches a decent fraction of the Planck Luminosity, recoil velocities of up to several thousand kilometers per second, zoom-whirl orbits for comparable mass binaries, and that many aspects of the physics unfolding in this highly non-linear, dynamical regime of the theory are nevertheless well described by existing analytic and perturbative techniques." |
February 02, 2010, 130 - 300 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
BARRY MAZUR (HARVARD UNIVERSITY) |
Hilbert's 10th Problem and Elliptic Curves |
Organized by Professor Shing Tung Yau" |
February 01, 2010, 3 pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
C. HONGLER (GENEVA) |
The energy density in the 2D Ising model |
We consider the critical planar Ising model from a conformal invariance point of view, using discrete complex analysis techniques. We are interested in the scaling limit of the model in a simply connected domain with pure (+or free) boundary conditions. More precisely, we will be interested in the behavior of the energy density field in the scaling limit, proving an improved version of conjectures coming from Conformal Field Theory, exhibiting a nice connection with hyperbolic geometry. The derivation is made by using a fermionic observable, which is a discrete holomorphic deformation of a partition function, and then by passing to the limit, obtaining a continuous holomorphic function, which solves a certain boundary value problem. This seminar is organized by Professor Shing-Tung Yau" |
January 29, 2010, 130 pm at Science Center, Room 232 |
| SPECIAL SEMINAR |
DAN MANGOUBI (HEBREW UNIVERSITY) |
Properties of Eigenfunctions and Harmonic Junctions |
This seminar is organized by Professor Shing Tung Yau" |
January 28, 2010, 5 pm at Science Center, Room 507 |
| RANDOM MATRIX SEMINARS |
DAN STROOCK (MIT) |
An old theorem of I.M Segal's in a probabilistic setting |
Abstract In connection with his attempt to construct quantum fields via Euclidean fields, Segal proved an interesting result which, in spite of the absence of any measure, he called an ergodic theorem. In this lecture, I will explain Segal s theorem, show how it can be proved in a measure-theoretic setting, and apply it to several examples" |
January 28, 2010, 310 pm at Science Center, Room 232 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
YU-JONG TZENG (STANFORD UNIVERSITY) |
Universal Formulas for Counting Nodal Curves on Surfaces |
" |
January 26, 2010, 3 pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
XIAOFENG SUN (LEHIGH UNIVERSITY) |
Global Torelli theorem of the Teichmuller space of Calabi-Yau and Hyperkahler manifold |
Organized by Professor Shing Tung Yau" |
January 08, 2010, 230 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
DAVID HELM (UNIVERSITY OF TEXAS) |
Algebraic families of admissible representations of GL_n(Q_p) |
Abstract The local Langlands correspondence for GL_n relates n-dimensional representations of (essentially) the Galois group of a local field F toe complex representations of GL_n(F). An interesting question is how the objects on both sides of this correspondence vary in algebraic families, and in particular if the correspondence can be extended to such families. We discuss joint work with Matt Emerton that suggests that the answer is yes." |
December 09, 2009, 3 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
DAVID KAZHDAN () |
Classical vs. Geometric Langlands |
" |
December 08, 2009, 530 pm at MIT (2-139) |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
DENNIS ERIKSSON (UNIVERSITY OF TOKYO) |
The determinant of the cohomology revisited |
Deligne has proposed a program to study the Riemann-Roch theorem up to higher equivalences. I will report on some progress on this, in particular in constructing a Riemann-Roch isomorphism for the determinant of the cohomology and then deduce some geometric consequences for the same." |
December 08, 2009, 3 pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
BENJAMIN WEINKOVE (UNIVERSITY OF CALIFORNIA SAN DIEGO) |
Complex Monge-Ampere equation |
Organized by Professor Shing Tung Yau" |
December 07, 2009, 1 - 2 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
ANDREW COTTON-CLAY (HARVARD UNIVERSITY) |
Symplectic field theory, tightness, and dynamics of vector fields |
" |
December 07, 2009, 3 pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
SI LI (HARVARD UNIVERSITY) |
Picard Fuchs equations of relative period on Calabi-Yau hypersurface |
Organized by Professor Shing Tung Yau" |
December 04, 2009, 2 - 3 pm at Science Center, Room 507 |
| RANDOM MATRIX SEMINARS |
T. KEMP (MIT) |
Chaos and the Fourth Moment |
Abstract The Wiener Chaos is an orthogonal decomposition of the L^2 space of a Brownian motion, naturally associated to stochastic integration theory; the orders of chaos are given by the range of multiple Wiener-lto integrals. In 2006, Nualart and collaborators proved a remarkable central limit theorem in the context of the chaos. If $X_K$ is a sequence of $n$th Wiener-lto integrals (in the $n$th chaos), then necessary and sufficient conditions that $X_K$ converge weakly to a normal law are that its (second and) fourth moments converge--all other moments are controlled by these. In this lecture, I will discuss recent joint work with Roland Speicher in which we prove an analogous theorem for the empirical eigenvalue laws of high-dimensional random matrices" |
December 03, 2009, 3 pm at Science Center, Room 232 |
| THE THURSDAY SEMINAR |
MIKE HOPKINS (HARVARD UNIVERSITY) |
Homotopy invariance of the cohomology of special linear groups |
" |
December 03, 2009, 3 - 5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
ANDREW KNIGHTLY (UNIVERSITY OF MAINE) |
Explicit relative trace formulas on GL(2) |
Abstract In many applications of the trace formula, one tries to match orbital integrals to deduce a relationship between the spectral data on two different groups. On the other hand, as originally conceived by Selberg, one can input a test function and compute the orbital integrals explicitly to obtain spectral information for a single group. I will present several such examples of explicit relative trace formulas on the group GL(2). Applications include a vertical Sato-Tate law for Hecke eigenvalues, and asymptotics for averages of modular L-values. This is joint work with Charles Li" |
December 02, 2009, 3 pm at Science Center, Room 507 |
| DYNAMICS AND GEOMETRY SEMINAR |
GIULIO TIOZZO (HARVARD UNIVERSITY) |
The entropy of $\alpha$-continued fractions |
Abstract We consider a one-parameter family of interval maps arising from generalized continued fraction expansions known as $\alpha$-continued fractions. For such maps, we investigate the behavior of Kolmogorov-Sinai entropy as a function of the parameter; we will discuss numerical evidence that this function has a self-similar structure, as well as theoretical results about its regularity." |
December 02, 2009, 4 - 5 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
GREGORY PEARLSTEIN (MICHIGAN STATE UNIVERSITY) |
Zero loci of normal functions |
I will discuss recent work with Patrick Brosnan on the algebraicity of the zero loci of normal functions, and applications to the study of algebraic cycles" |
December 01, 2009, 3 - 4 pm at MIT (26-204) |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
DUSTIN CLAUSEN () |
Quantization |
" |
December 01, 2009, 530 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
CLARK BARWICK (HARVARD UNIVERSITY) |
Descent problems for K-theory |
" |
November 30, 2009, 3 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
JOHN VOIGHT (UNIVERSITY OF VERMONT) |
Algebraic curves uniformized by congruence subgroups of triangle groups |
Abstract We construct certain subgroups of hyperbolic triangle groups which we call congruence subgroups. These groups include the classical congruence subgroups of SL(2,Z), Hecke triangle groups, and 19 families of Shimura curves associated to arithmetic triangle groups. We determine the field of muduli of the curves associated to these groups and thereby realize the Galois groups PSL(2,q) and PGL(2,q) regularly in many cases over explicitly given abelian number fields. This is joint work with Pete L. Clark" |
November 25, 2009, 3 - 4 pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
YNG-ING LEE (NATIONAL TAIWAN UNIVERSITY) |
Special solutions to Lagrangian mean curvature flow |
Organized by Professor Shing Tung Yau" |
November 25, 2009, 2 - 3 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
MIHNEA POPA (UNIVERSITY OF ILLINOIS AT CHICAGO) |
BGG correspondence and the cohomology of compact kaehler manifolds |
The cohomology algebra of the sheaf of holomorphic functions on a compact Kahler manifold can be naturally viewed as a module over the exterior algebra of a vector space. A well-known result of Bernstein-Gel fand-Gelfand gives a correspondence between such exterior modules and linear complexes of modules over the polynomial ring. I will explain how one can use a modern view on this correspondence, together with the Generic Vanishing theory developed by Green and Lazarsfeld via Hodge-theoretic methods, in order to understand new algebraic structures of the cohomology algebra. As a bonus, homological and commutative algebra tools can be applied on the polynomial ring side to obtain inequalities for the holomorphic Euler characteristic and the Hodge numbers of compact Kahler manifolds. This is joint work with R. Lazarsfeld." |
November 24, 2009, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
MELISSA LIU (COLUMBIA UNIVERSITY) |
Coherent-Constructible Correspondence for Toric Varieties and Toric Orbifolds |
" |
November 24, 2009, 130 - 300 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
DENNIS GAITSGORY (HARVARD UNIVERSITY) |
Quantum Langlands |
Organized by Professor Shing Tung Yau" |
November 23, 2009, 3 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
HANS SCHOUTENS (NEW YORK CITY COLLEGE OF TECHNOLOGY) |
Schemic Grothendieck rings and motivic rationality |
Abstract We propose a suitable substitute for the classical Grothendieck ring of an algebraically closed field, in which any quasi-projective scheme is represented, while maintaining its non-reduced structure. This yields a more subtle invariant, called the schemic Grothendieck ring, in which we can formulate a form of integration resembling Kontsevich s motivic integration via arc schemes. In view of its more functorial properties, we can present a characteristic-free proof of the rationality of the geometric Igusa zeta series for certain hypersurfaces, thus generalizing the ground-breaking work on motivic integration by Denef and Loeser. The construction uses first-order formulae, and some infinitary versions, called formularies, which in turn can be translated to some notions from topos theory sieves and formal motives" |
November 23, 2009, 315 pm at MIT 3-442 |
| RANDOM MATRIX SEMINARS |
P. DEIFT (COURANT INSTITUTE) |
Integrable systems a modern view |
Abstract The modern theory of integrable systems began with the solution of the Korteweg de Vries equation by Gardner, Greene, Kruskal and Miura in 1967. This led to the development of a variety of new mathematical techniques, and over time, and quite unexpectedly, these techniques have found applications in areas far beyond their dynamical origins. The applications include problems in algebraic geometry, numerical analysis, analytic number theory, combinatorics and random matrix theory, among many others. The speaker will discuss some of these developments" |
November 19, 2009, 3 pm at Science Center, Room 232 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
JACOB LURIE (HARVARD UNIVERSITY) |
Crystals of schemes |
" |
November 19, 2009, 6 pm at MIT (2-139) |
| DYNAMICS AND GEOMETRY SEMINAR |
GENEVIEVE WALSH (TUFTS) |
Commensurability of knot complements |
" |
November 18, 2009, 4 - 5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
XINYI YUAN (HARVARD UNIVERSITY) |
Okounkov bodies for arithmetic line bundles |
Abstract We construct convex bodies, called Okounkov bodies, associated to a Hermitian line bundle in the setting of Arakelov theory. As consequences, we derive many properties of the volume of the Hermitian line bundle" |
November 18, 2009, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
CRAIG VAN COEVERING (MIT) |
Asymptotically conical manifolds and the Monge-Amp\'{e}re equation |
Abstract Some analysis is considered on manifolds with a conical end. Then we show that in the K\{a}hler case the complex Monge-Amp\ {e}re equation can be solved with the same regularity as is known in the ALE case. This can be used to produce many Calabi-Yau manifolds with a conical end." |
November 17, 2009, 130 - 300 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
JACOB LURIE (HARVARD UNIVERSITY) |
Crystals |
" |
November 17, 2009, 530 - 800 pm at MIT (2-139) |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
JOSEPH RABINOFF (HARVARD UNIVERSITY) |
Tropical intersection numbers and canonical subgroups |
Tropical algebraic geometry was originally invented as a way of reducing problems in complex algebraic geometry to questions about a combinatorial object, its tropicalization. I ll talk a bit about tropical varieties, and in particular why one is led naturally to consider varieties over non-Archimedean fields, for instance the field of Puiseaux series over C. I ll then talk a bit about the simplest case of tropical intersection theory, namely the computation of intersection numbers of dimension-zero complete intersections. I ll finish by giving an application to the arithmetic of abelian varieties" |
November 17, 2009, 3 - 4 pm at MIT (26-204) |
| BASIC NOTIONS SEMINAR |
JOSEPH RABINOFF (HARVARD UNIVERSITY) |
Beyond Newton polygons locating the zeros of polynomials over a non-Archimedean field |
Organized by Professor Shing Tung Yau" |
November 16, 2009, 3 pm at Science Center, Room 507 |
| RANDOM MATRIX SEMINARS |
W. DE ROECK (ETH ZURICH) |
Diffusion of a massive quantum particle in coupled to a thermal medium in dimension $d\geq 4$ |
Abstract We consider a heavy quantum particle with an internal degree of freedom moving on the $d$-dimensional lattice $\bbZ^d$ (e.g., a heavy atom with finitely many excited states). The particle is coupled to a thermal medium (bath) consisting of free relativistic bosons through an interaction of strength $\|a$ linear in creation and annihilation operators. The mass of the quantum particle is assumed to be of order $\|a^{-2}$, and we assume that the internal degree of freedom is coupled effectively to the thermal medium. We prove that the motion of the quantum particle is diffusive in $d\geq 4$ and for $\|a$ small enough. The talk is based on joint work with J. Frohlich, reported in arXiv0906.5178" |
November 12, 2009, 3 pm at Science Center, Room 232 |
| THE THURSDAY SEMINAR |
JACOB LURIE (HARVARD UNIVERSITY) |
Fundamental groups of A^1-invariant sheave (continued) |
Abstract End of the proof of Morel s theorem of the strong A^1-invariance of the fundamental group of an A^1-invariant sheaf of spaces" |
November 12, 2009, 3 - 5 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
ANDREI NEGUT (HARVARD UNIVERSITY) |
D-schemesjet schemes and conformal blocks in the commutative case |
" |
November 12, 2009, 530 - 7pm at Science Center, Room 507 |
| DYNAMICS AND GEOMETRY SEMINAR |
DAN MARGALIT (TUFTS) |
Small dilatation pseudo-Anosovs and 3-manifolds |
" |
November 11, 2009, 4 - 6 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
BIANCA VIRAY (BERKELEY) |
Failure of the Hasse principle for Enriques surfaces |
Abstract Most counterexamples to the Hasse principle can be explained by an algebraic Brauer-Manin obstruction. We define some of the other possible obstructions and exhibit an Enriques surfaces where the failure of the Hasse principle is not explained by an algebraic Brauer-Manin obstruction." |
November 11, 2009, 3 - 4 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
DUSTIN CLAUSEN () |
Determinant line bundle and the Kac-Moody extension-II |
" |
November 10, 2009, 530-8 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
KIRSTEN WICKELGREN (HARVARD UNIVERSITY) |
Etale pie1 obstructions to rational points |
" |
November 10, 2009, 3 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
WILFRIED SCHMID (HARVARD UNIVERSITY) |
Hodge theory and unitary representations of reductive Lie groups |
Organized by Professor Shing Tung Yau" |
November 09, 2009, 3 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
() |
|
There will not be a Thursday Seminar today." |
November 05, 2009, 3 - 5 pm at Science Center, Room 507 |
| RANDOM MATRIX SEMINARS |
C. KING (NORTHEASTERN) |
Additivity counterexamples in quantum information theory via random matrix methods |
Abstract Random matrix methods have been recently used to prove the existence of counterexamples to several well-known conjectures in quantum information theory. In addition to reviewing these conjectures and their implications, this talk will explain some of the key ideas in the proofs of existence of counterexamples, including the recent work of Hastings. Some open questions in this area will also be discussed" |
November 05, 2009, 3 pm at Science Center, Room 232 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
ROMAN BEZRUKAVNIKOV () |
Hitchin fibration and affine Springer fibers-II |
" |
November 05, 2009, 530 - 700 pm at MIT (2-139) |
| SPECIAL SEMINAR |
LE DUNG TRANG () |
Geometry of singular maps |
Abstract Summary Consider a complex singular analytic germ of space. We shall define what is a general projection into the germ of an affine space. Usual techniques of differential topology have to be adapted to the singularities." |
November 04, 2009, 2 - 3 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
RICHARD TAYLOR (HARVARD UNIVERSITY) |
Potential automorphy for n dimensional Galois representations |
Abstract I will discuss recent improvements in the potential automorphy theorems available for Galois representations of any dimension. In particular I will discuss the case of ordinary Galois representations and applications to elliptic modular forms, in particular the proof of the Sato-Tate conjecture for all elliptic modular new forms. This is joint work with Barnet-Lamb, Geraghty and Harris" |
November 04, 2009, 3 - 4 pm at Science Center, Room 507 |
| DYNAMICS AND GEOMETRY SEMINAR |
ANDREW COTTON-CLAY (HARVARD UNIVERSITY) |
Holomorphic Pants in R times a Mapping Torus |
Abstract We review recent applications of Floer homology and holomorphic curves to the dynamics of area-preserving surface diffeomorphisms and to Reeb dynamics and present work in progress on counts of holomorphic pairs of pants in $\mathbb{R}times Y$ for $Y$ an Anosov or pseudo-Anosov mapping torus and potential applications." |
November 04, 2009, 4 - 6 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
YONG LIN (HARVARD UNIVERSITY) |
Ricci curvature on locally finite graphs |
Organized by Professor Shing Tung Yau" |
November 03, 2009, 130 - 300 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
DANIEL ERMAN (UNIVERSITY OF CALIFORNIA AT BERKELEY) |
Deformations of 0-dimensional schemes |
A natural question in the study of 0-dimensional schemes is to determine when such a scheme deforms to a disjoint union of points. I will discuss a syzygetic invariant which yields sharp information about this question. I will also give applications to the study of Hilbert schemes of points. This is joint work with M. Velasco" |
November 03, 2009, 3 pm at MIT (26-204) |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
DUSTIN CLAUSEN () |
Infinite-dimensional linear algebra, the determinant line bundle, and Kac-Moody extension |
" |
November 03, 2009, 530 pm at MIT (2-139) |
| BASIC NOTIONS SEMINAR |
HAO XU (HARVARD UNIVERSITY) |
Intersection theory on moduli spaces of curves |
Hao Xu will also be talking on November 3 at the Differential Geometry Seminar" |
November 02, 2009, 3 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
ROMAN BEZRUKAVNIKOV () |
Higgs bundles and the Hitchin base-II affine Springer fibers (introduction to the work of B.C. Ngo) |
" |
October 29, 2009, 530 - 700 PM at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
JACOB LURIE (HARVARD UNIVERSITY) |
Fundamental groups of A^1-invariant sheaves |
" |
October 29, 2009, 3 - 5 pm at Science Center, Room 507 |
| RANDOM MATRIX SEMINARS |
BENEDEK VALKO (WISCONSIN) |
Scaling limits of the beta-generalizations of classical ensembles |
Abstract The Hermite, Laguerre and Jacobi ensembles describe the joint eigenvalue distribution of classical random matrix models built from independent Gaussian random variables. There are versions using real, complex and real quaternion Gaussians which correspond to the beta=1, 2 and 4 cases of a more general family of models. I briefly review the known results about the scaling behavior of the general beta ensembles and report on some recent progress. The talk is based on joint work with B. Virag (Toronto) and also with S. Jacquot (Cambridge)." |
October 29, 2009, 3 pm at Science Center, Room 232 |
| NUMBER THEORY SEMINAR |
BEN HOWARD (BC) |
Hilbert modular surfaces, Hirzebruch-Zagier divisors, and CM points |
Abstract Hilbert modular surfaces arise as moduli spaces of abelian surfaces with real multiplication. Using the moduli interpretation one can define two families of special cycles on Hilbert modular surface the Hirzebruch-Zagier divisors, and the codimension two cycles of abelian surfaces which admit complex multiplication by a quartic CM field. In the spirit of Kudla s program and the Gross-Zagier theorem, we compute the arithmetic intersection multiplicities of these special cycles, and show that the intersection numbers appear as Fourier coefficients of the central derivative of an Eisenstein series. This is joint work with Tonghai Yang" |
October 28, 2009, 3 - 4 pm at Science Center, Room 507 |
| DYNAMICS AND GEOMETRY SEMINAR |
TOBIAS COLDING (MIT) |
Singularities of mean curvature flow |
" |
October 28, 2009, 4 - 5 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
DENNIS GAITSGORY (HARVARD UNIVERSITY) |
Higgs bundles and the Hitchin base-I local triviality of G-bundles (Steinberg's theorem) |
" |
October 27, 2009, 530 - 800 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
STEPHANIE YANG (KUNGLIGA TEKNISKA HOGSKOLAN STOCKHOLM) |
Tautological rings of moduli spaces of curves |
After reviewing the definition and know properties of tautological rings of moduli spaces of curves, we will discuss analogs of Faber s conjecture for various partial compactifications of the moduli space of smooth curves. We show that their tautological rings are one-dimensional in top degree but often do not satisfy Poincare duality" |
October 27, 2009, 3 PM at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
KWOK WAI CHAN (HARVARD UNIVERSITY) |
The Ooguri-Vafa Metric, Holomorphic Discs and Wall-Crossing |
Abstract I will discuss the new construction of the Ooguri-Vafa metric by the method of Gaiotto-Moore-Neitzke and its relation to wall-crossing formulas in mirror symmetry. In particular, we will see that the Ooguri-Vafa metric is closely related to nontrivial holomorphic discs with boundary in special Lagrangian torus fibers." |
October 27, 2009, 130 - 300 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
HONRG-TZER YAU (HARVARD UNIVERSITY) |
Eigenvalue distributions of random matrices - a dynamical approach |
Organized by Professor Shing Tung Yau" |
October 26, 2009, 3 pm at Science Center, Room 507 |
| SPECIAL DIFFERENTIAL GEOMETRY SEMINAR |
RICHARD SCHOEN (STANFORD UNIVERSITY) |
Extremal problems for low eigenvalues and minimal submanifolds |
Organized by Professor Shing Tung Yau" |
October 23, 2009, 130 - 230 pm at Science Center, Room 507 |
| RANDOM MATRIX SEMINARS |
R. KENYON (BROWN UNIVERSITY) |
Laplacians on graphs |
The uniform spanning tree (UST) on a graph is a basic model in discrete probability, with connections to loop-erased random walk, determinant processes and SLE. The classic matrix-tree theorem relates the determinant of the combinatorial laplacian on a graph to the number of spanning trees. We generalize this result to laplacians on vector bundles, giving a combinatorial interpretation of their determinants. This generalization allows us to study spanning trees and forests on graphs embedded on surfaces. In particular one can construct from this natural probability measures on the space of finite laminations on surfaces" |
October 22, 2009, 3 pm at Science Center, Room 232 |
| THE THURSDAY SEMINAR |
ANATOLY PREYGEL () |
The unstable connectivity theorem |
" |
October 22, 2009, 3 - 5 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
XINWEN ZHU (HARVARD UNIVERSITY) |
Global nilpotent cone and flatness of the Hitchin map |
" |
October 22, 2009, 530 - 7pm at MIT (2-139) |
| DYNAMICS AND GEOMETRY SEMINAR |
MARTIN BRIDGEMAN (BOSTON COLLEGE) |
The orthospectra of finite volume hyperbolic manifolds with totally geodesic boundary and associated volume identities |
Abstract Given a finite volume hyperbolic n-manifold $M$ with totally geodesic boundary, and orthogeodesic of $M$ is a geodesic arc which is perpendicular to the boundary. For each dimension n, we show there is $F_n$ such that the volume of any $M$ is the sum of values of $F_n$ on the orthospectrum (length of orthogeodesics). For $n=2$ the function $F_2$ is the Rogers L-function and the summation identities give dilogarithm identities on the Modluli space of surfaces." |
October 21, 2009, 4 - 5 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
JUN LI (STANFORD UNIVERSITY) |
Degeneration of Hilbert scheme of ideal sheaves and a proof of Goettsche conjecture |
Organized by Professor Shing Tung Yau" |
October 21, 2009, 2 - 3 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
DAVID GERAGHTY (HARVARD UNIVERSITY) |
The Sato-Tate conjecture for Hilbert modular forms |
Abstract I will discuss a recent joint work with Thomas Barnet-Lamb and Toby Gee in which we prove the Sato-Tate conjecture for non-CM regular algebraic cuspidal automorphic representations of GL_2 over a totally real field." |
October 21, 2009, 3 - 4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
ALINA MARIAN (UNIVERSITY OF ILLINOIS AT CHICAGO) |
The moduli space of stable quotients |
I will discuss features of a moduli space of stable quotients of the rank n trivial sheaf on stable curves. This gives a compactification of the moduli of maps from smooth curves to Grassmann varieties, distinct from the Kontsevich-Manin space. The construction connects with Gromov-Witten theory on the one hand, and leads to new relations in the tautological ring of the moduli space of curves on the other. This is joint work with Dragos Oprea and Rahul Pandharipande." |
October 20, 2009, 3 pm at MIT (26-204) |
| DIFFERENTIAL GEOMETRY SEMINAR |
CUMRUN VAFA (HARVARD UNIVERSITY, PHYSICS) |
Kontsevich-Soibelman Wall Crossing and Topological Strings |
Organized by Professor Shing Tung Yau" |
October 20, 2009, 130 - 300 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
ANDREI NEGUT (HARVARD UNIVERSITY) |
The Hitchin map, global vs. local |
" |
October 20, 2009, 530 - 800 pm at MIT (2-139) |
| BASIC NOTIONS SEMINAR |
CEDRIC VILLANI (IHP PARIS) |
Landau damping |
Abstract In 1946 Landau stunned the physical community by predicting relaxation effects for the nondissipative, nonlinear Vlasov-Poisson equation in plasma physics. Experimentally confirmed, the so-called Landau damping has become a cornerstone of plasma physics. However, as pointed out half a century ago, the linearization assumption used by Landau seems absurd. In a recent work with Clement Mouhot, we fill this gap and provide a mathematical explanation of Landau damping. Organized by Professor Shing-Tung Yau" |
October 19, 2009, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
CHARLES LIVINGSTON (INDIANA UNIVERSITY) |
Topologically slice knots with nontrivial Alexander polynomial |
Abstract A theorem of Freedman states that every knot in S3 that has trivial Alexander polynomial bounds a locally flat embedded disk in B4; that is, these knots are topologically slice. On the other hand, it follows from results of Donaldson that some knots with trivial Alexander polynomial are not smoothly slice. Built on these results, it is easy to construct examples of knots with nontrivial Alexander polynomial that are topologically slice, but not smoothly slice. However, there remained the possibility that the distinction between the two categories is completely explained by Freedman s theorem formally, it seemed possible that every topologically slice knot is smoothly concordant to an Alexander polynomial one knot. In this talk, based on joint work with Hedden and Ruberman, I will describe examples of topologically slice knots that are not concordant to polynomial 1 knots. More generally, the set of such examples is infinitely generated modulo concordance. ." |
October 16, 2009, 330 - 430 pm at Science Center, Room 507 |
| RANDOM MATRIX SEMINARS |
VAN VU (RUTGERS UNIVERSITY) |
Random Matrices The Universality Phenomenon |
Abstract It is believed that the limiting distributions of eigenvalues of random matrices are universal, i.e., they do not depend on the exact distributions of the entries. I am going to discuss several results concerning this general phenomenon." |
October 16, 2009, 12 - 1 pm at Science Center, Room 232 |
| SPECIAL DIFFERENTIAL GEOMETRY SEMINAR |
ZBIGNIEW BLOCKI (JAGIELLONIAN UNIVERSITY) |
Defining complex Monge-Ampere operator for non-smooth functions |
Abstract We will discuss the problem of defining a complex Monge-Ampere measure for non-smooth plurisubharmonic functions. The problem is much more subtle than in the real case, as it turns out in particular that such a measure cannot be always well defined. One of the result will be a precise characterization of the (local) domain of definition of the complex Monge-Ampere operator. We will also discuss the global problem on compact Kahler manifolds. Organized by Professor Shing-Tung Yau" |
October 14, 2009, 2 - 3 pm at Science Center, Room 232 |
| DYNAMICS AND GEOMETRY SEMINAR |
SARAH KOCH (HARVARD UNIVERSITY) |
Dynamics of maps on moduli space |
" |
October 14, 2009, 4 - 5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
NOAM ELKIES (HARVARD UNIVERSITY) |
On the areas of rational triangles |
Abstract By Heron s formula there exists a triangle of area $\sqrt{a}$ all of whose sides are rational if and only if $a > 0$ and $xyz(x + y + z) = a$ for some rationals $x, y, z$. In a 1749 letter to Goldbach, Euler constructed infinitely many such $(x, y, z)$ for any rational $a$ (positive or not), remarking that it cost him much effort but not explaining his method. We suggest one approach, using only tools available to Euler, that he might have taken, and use it to construct several other infinite families of solutions. Then we reconsider the problem as a question in arithmetic geometry $xyz(x+y+z) = a$ gives a K3 surface, and each family of solutions is a singular rational curve on that surface defined over {\bf Q}. The structure of that N\ {e}ron--Severi group of that K3 surface explains why the problem is unusually hard. Along the way we also encounter the Niemeier lattices (the even unimodular lattices in ${\bf R}^{24}$) and the non-Hamiltonian Petersen graph" |
October 14, 2009, 3-4 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
DENNIS GAITSGORY (HARVARD UNIVERSITY) |
The loop group and the affine Grassmannian |
" |
October 13, 2009, 530 - 800 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
WEI HO (HARVARD UNIVERSITY) |
Orbit parametrizations of curves |
We discuss parametrizations of geometric data, such as curves with specified line bundles, by orbits of representations of reductive algebraic groups. This point of view also allows us to recover several classical constructions relating different moduli spaces of curves. Moreover, such explicit realizations of these moduli spaces lend themselves to computations, arithmetic applications, and (uni) rationality results." |
October 13, 2009, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
SLAWOMIR KOLODZIEJ (JAGIELLONIAN UNIVERSITY) |
Volume of sublevel sets of plurisubharmonic functions |
Organized by Professor Shing Tung Yau" |
October 13, 2009, 130 - 300 pm at Science Center, Room 507 |
| SPECIAL DIFFERENTIAL GEOMETRY SEMINAR |
SERGIO CECOTTI (SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVANZATI) |
Yukawa couplings in F-theory and a non-commutative residue formula |
Organized by Professor Shing Tung Yau." |
October 13, 2009, 4 - 530 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
ALEXANDER GRIGORYAN (UNIVERSITAT BIELEFELD) |
On positive solutions of semi-linear elliptic inequalities on complete Riemannian manifods |
Organized by Professor Shing Tung Yau. Please note the change in time and location." |
October 09, 2009, 2 - 3 pm at Science Center, Room 507 |
| SPECIAL DIFFERENTIAL GEOMETRY SEMINAR |
LINYUAN LINCOLN LU (UNIVERSITY OF SOUTH CAROLINA) |
A random graph model for complex graphs |
Abstract It was observed that many real-world networks such as the Internet, social networks, biological networks, and Collaboration graphs have the so-called power law degree distributions. A graph is called a power law graph if the fraction of vertices with degree k is approximately proportional to k^{-b} for some constant b. The classical Erdos and Renyi random graph model G(n,p) is not suitable for modeling these power law graphs. Chung and Lu directly generalize G(n,p) into random graphs with given expected degree sequences. They determined the size and volume of the giant component, the average distance and the diameter, and the spectra. Some theoretic results will be compared to real data. (Joint work with Fan Chung Graham" |
October 09, 2009, 330 - 430 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
NIR AVNI (HARVARD UNIVERSITY) |
The loop group and its action on Bun (G). |
" |
October 08, 2009, 530 - 7pm at MIT (2-139) |
| THE THURSDAY SEMINAR |
MIKE HOPKINS (HARVARD UNIVERSITY) |
The A^1 connectivity theorems |
Abstract I ll describe the formulation and proof of Morel s A^1 connectivity theorems." |
October 08, 2009, 3 - 5 pm at Science Center, Room 507 |
| SPECIAL LECTURE |
HARVEY M. FRIEDMAN (OHIO STATE UNIVERSITY) |
Unprovable Theorems |
Abstract An unprovable theorem is a theorem about basic mathematical objects that can only be proved using more than the usual axioms for mathematics (ZFC=Zermelo Frankel set theory with the Axiom of Choice). The highlight of the talk is the presentation of a new unprovable theorem that involves only the usual ordering of the rationals, vectors of rationals, and the +1 function on rationals. We first review some previous examples of unprovable theorems in the weaker sense that the proof demonstrably requires some use of logical principles transcendental to the problem statement. These previous contexts include 1. Patterns in finite sequences from a finite alphabet. 2. Pointwise continuous embeddings between countable sets of reals (or, more concretely, rationals).3. Relations between f(n_1,...,n_k) and f(n_2,...,n_k+1). 4. Homeomorphic embeddings between finite trees. 5. Borel sets in the plane and graphs of one dimensional Borel functions. 6. Boolean relations between sets of integers and their images under integer functions." |
October 08, 2009, 430 - 600 pm at Science Center, Room 221 |
| DYNAMICS AND GEOMETRY SEMINAR |
SERGIO FENLEY (FSU/PRINCETON) |
Pseudo-Anosov flows and large scale geometry of 3-manifolds |
" |
October 07, 2009, 4 - 5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
WEI ZHANG (HARVARD UNIVERSITY) |
An arithmetic fundamental lemma for the unitary group of three variable |
Abstract In this talk, I will present a relative trace formula approach to the Gross-Zagier formula and its high dimensional generalization (a first derivative version of the global Gross-Prasad conjecture) for unitary group Shimura varieties. In particular, and arithmetic fundamental lemma (AFL) is proposed. Some results proved recently will be presented, including the AFL for unitary group of three variable." |
October 07, 2009, 3 - 4 pm at Science Center, Room 507 |
| SPECIAL ANALYSIS SEMINAR |
LOUIS NIRENBERG (NEW YORK UNIVERSITY COURANT INSTITUTE OF MATHEMATICAL SCIENCES) |
On Singular Solutions of Fully Nonlinear Elliptic Equation |
Organized by Professor Horng-Tzer Yau" |
October 07, 2009, 2 - 3 pm at Science Center, Room 507 |
| AHLFORS LECTURES |
PETER LAX (NYU) |
Degenerate Matrices |
Organized by Professors Shing-Tung Yau and Horng-Tzer Yau." |
October 06, 2009, 245 - 345 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
BRIAN LEHMANN (MIT) |
Pseudo-effective reduction maps |
" |
October 06, 2009, 3 - 4 pm at MIT (26-204) |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
SAM RASKIN () |
Contangent space and D-modules on an algebraic stack-III |
" |
October 06, 2009, 530 - 800 pm at MIT (2-139) |
| THE THURSDAY SEMINAR |
KIRSTEN WICKELGREN (HARVARD UNIVERSITY) |
Suslin's paper On the K-Theory of Algebraically Closed Fields |
Abstract I ll present Suslin s proof that for an extension F_0->F of algebraically closed fields, K_*(F_0,Z/n) -> K_*(F,Z/n) is an isomorphism. It follows that H_i(GL_n(F_0), Z/1) -> H_i (GL_n(F), Z/1) is an isomorphism when i<=n." |
October 01, 2009, 3 - 5 pm at Science Center, Room 507 |
| JOINT BRANDEIS-HARVARD-MIT NORTHEASTERN MATHEMATICS COLLOQUIUM |
GIOVANNI FELDER (ETH ZURICH) |
Holomorphic differential operators and the Riemann-Roch-Hirzerburch formula |
Abstract In 1956 Hirzebruch wrote a formula for the Euler characteristic of a holomorphic vector bundle on a compact complex manifold as the integral of a characteristic class, generalizing the classical Riemann-Roch formula for line bundles on a curve. In 1988, Feigin and Tsygan explained that the origin of this class lies in the Hochschild cohomology of the algebra of polynomial differential operators, which os one dimensional. Using ideas from formal geometry they constructed a map from this cohomology to de Rham cohomology of any complex manifold with a vector bundle and showed that the image of a canonically normalized cocycle is the Hirzebruch class. I will review these ideas and discuss recent developments, including an explicit formula for the cocycle and the extension of the Riemann-Roch-Hirzebruch formula to a formula for the alternating sum of traces of the action of a holomorphic differential operator on sheaf cohomology. This talk is based on joint papers with B. Feigin and B. Shoikhet, with M. Engeli and with X. Tang." |
October 01, 2009, 430 pm at Science Center, Hall A |
| RANDOM MATRIX SEMINARS |
M. RUDELSON (UNIVERSITY OF MISSOURI, COLUMBIA) |
Invertibility of random matrices |
" |
October 01, 2009, 3 - 410 pm at Science Center, Room 232 |
| NUMBER THEORY SEMINAR |
MATTHIAS SCHUETT (HARVARD UNIVERSITY) |
Arithmetic of Enriques surfaces |
In this talk, we will discuss arithmetic aspects of Enriques surfaces. We will be particularly concerned with fields of definition and Galois actions on surfaces or divisors. Our ideas are motivated by similar results for K3 surfaces which we will also review. This is joint work with Klaus Hulek" |
September 30, 2009, 3 - 4 pm at Science Center, Room 507 |
| DYNAMICS AND GEOMETRY SEMINAR |
HEE OH (BROWN UNIVERSITY) |
Equidistribution and Counting for geometrically finite hyperbolic groups |
" |
September 30, 2009, 4 - 5 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
SAMUEL GRUSHEVSKY (STONY BROOK UNIVERSITY) |
The geometry of Mg and differentials with real periods |
We use meromorphic differentials on Riemann surfaces with prescribed singular parts and real periods to define a real-analytic foliation of the moduli space of curves Mg, with complex leaves. Using this foliation we give a quick proof of Diaz bound on the dimension of complete subvarieties of Mg, and prove some vanishing results for the cohomology of Mg. We will also discuss the motivation for this construction, coming from integrable systems, and potential further applications of this construction to the study of cohomology and subvarieties of Mg. This is joint work with Igor Krichever." |
September 29, 2009, 3 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
JACOB LURIE (HARVARD UNIVERSITY) |
Categorification of the Fourier Transform |
Organized by Professor Shing Tung Yau" |
September 28, 2009, 3 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
DUSTIN CLAUSEN () |
An introduction to the A^1-homotopy category |
" |
September 24, 2009, 3 - 5 pm at Science Center, Room 507 |
| JOINT BRANDEIS-HARVARD-MIT NORTHEASTERN MATHEMATICS COLLOQUIUM |
MATTHEW EMERTON (NORTHWESTERN) |
The growth of cohomology in towers of manifolds |
Please note that this is a different location to past colloquia" |
September 24, 2009, 430 PM at Science Center, Hall A |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
SAM RASKIN () |
Cotangent space and D-modules on an algebraic stack-II |
Please note the change in location." |
September 24, 2009, 530 - 7pm at MIT (2-139) |
| RANDOM MATRIX SEMINARS |
IVAN CORWIN (COURANT INSTITUTE) |
Fluctuations in traffic flow, crystal growth and random matrices |
Abstract Analogous to the central limit theorem, we study the asymptotic behavior of the fluctuations of traffic flow, crystal growth height and eigenvalues of random matrices around their expectations. We show how the fluctuation limits of these random processes are related to their respective expectations (hydrodynamic limits)." |
September 24, 2009, 3 pm at Science Center, Room 232 |
| NUMBER THEORY SEMINAR |
MATTHEW EMERTON (NORTHWESTERN) |
On the p-adically completed cohomology of Shimura varieties for U(2,2) |
In this talk I will describe some calculations and speculations related to the p-adically completed cohomology of unitary Shimura varieties for a group of type U(2,2) attached to a quadratic imaginary field K. These are motivated by the fact that the hyperbolic 3-manifolds associated to congruence subgroups of GL_2(K) can appear as strata of the Borel--Serre boundary of these Shimura varieties, so that analysizing this completed cohomology presents one possible approach to the construction of Galois representations attached to Hecke eigenclasses (including torsion classes) in the cohomology of congruences subgroups of GL_2(K). The discussion will be based on work in progress, joint with Frank Calegari and Michael Harris." |
September 23, 2009, 3 - 4 pm at Science Center, Room 507 |
| DYNAMICS AND GEOMETRY SEMINAR |
ERIKO HIRONAKA (HARVARD UNIVERSITY) |
Small dilatation pseudo-Anosov mapping classes coming from the simplest pseudo-Anosov braid |
" |
September 23, 2009, 4 - 5 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
SAM RASKIN () |
Contangent space and D-modules on an algebraic stack-I |
Please note the change in location." |
September 22, 2009, 530 - 800 pm at MIT (2-139) |
| DIFFERENTIAL GEOMETRY SEMINAR |
LI-SHENG TSENG (HARVARD UNIVERSITY) |
Cohomolgoy and Hodge Theory on Symplectic Manifolds |
" |
September 22, 2009, 130 - 300 PM at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
YURI TSCHINKEL (NEW YORK UNIVERSITY) |
K3 surfaces and their higher dimensional analogs |
I will discuss the existence and distribution of rational curves on K3 surfaces and their punctual Hilbert schemes, with an emphasis on arithmetic applications." |
September 22, 2009, 3 pm at MIT (26-204) |
| BASIC NOTIONS SEMINAR |
BENEDICT GROSS (HARVARD UNIVERSITY) |
Self-dual and conjugate-dual Galois representations |
" |
September 21, 2009, 3 pm at Science Center, Room 507 |
| RANDOM MATRIX SEMINARS |
MIGUEL TIERZ (BRANDEIS) |
Random matrices, Stieltjes-Wigert polynomials and 1 D exactly solvable models. |
Abstract We study a Hermitian random matrix model with a log-normal weight function and show its relevance in topological quantum field theory. Generalizations of the model, including a biorthogonal version and the insertion of Schur polynomials are also studied, using orthogonal polynomials. Connections with 1 D exactly solvable models are also pointed out." |
September 17, 2009, 3 pm at Science Center, Room 232 |
| THE THURSDAY SEMINAR |
MICHAEL HOPKINS (HARVARD UNIVERSITY) |
Introduction to the Friedlander-Milnor conjecture |
Abstract This semester the Thursday Seminar will focus on A^1 homotopy theory, with the goal of going through Morel s proof of the Friedlander-Milnor conjecture. This first talk will consist of an introduction to the conjecture, and an overview of Morel s proof" |
September 17, 2009, 3 - 5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
MATTHEW EMERTON (NORTHWESTERN) |
Even Galois Representations and the Fontaine-Mazur Conjecture |
We prove, under mild hypotheses, there are no irreducible two-dimensional ordinary even Galois representations of the Galois group of Q with distinct Hodge-Tate weights, in accordance with the Fontaine-Mazur conjecture. We also show how this method can be applied to a related circle of problems" |
September 16, 2009, 3 - 4 PM at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
CHENYANG XU (MIT) |
Strong rational connectedness of surfaces and its applications |
I m going to talk about the various notions of rational connectedness and show that some rationally connected surfaces are indeed strongly rationally connected, including the smooth locus of log del Pezzo surfaces, which was conjectured by Hassett-Tschinkel." |
September 15, 2009, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
CLAY CORDOVA (HARVARD UNIVERSITY) |
Decoupling Gravity in F-Theory |
Organized by Professor Shing Tung Yau" |
September 15, 2009, 130 - 3 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
SAM RASKIN () |
Cotangent space and D-modules on an algebraic stack-I |
" |
September 15, 2009, 530-8pm at Science Center, Room 232 |
| SPECIAL SEMINAR |
JOEL SMOLLER (UNIVERSITY OF MICHIGAN, ANN ARBOR) |
Linear Waves in the Kerr Geometry |
Abstract I will give a survey of wave dynamics in the Kerr spacetime geometry, the mathematical model of rotating black hole in equilibrium. After a brief introduction to the Kerr metric, I will review the separability properties of linear wave equations of general spin, s=0,1/2,1,2, corresponding to scalar, Dirac, electromagnetic fields, and linearized gravitational waves. Results on the long-time dynamics of Dirac and scalar waves, including decay rates for massive Dirac fields, will be discussed. For scalar waves, we give a rigorous treatment of superradiance, and describe the open problem of linear stability of the Kerr metric and present partial results. Organized by Professor Shing Tung Yau and Lydia Bier" |
September 11, 2009, 1030 am at Science Center, Room 530 |
| THE TRIVIAL NOTIONS SEMINAR |
JACK HUIZENGA (HARVARD UNIVERSITY) |
How to count like Michel Chasles (and not like Jacob Steiner) |
" |
September 10, 2009, 207 pm at Science Center, Room 507 |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY |
DENNIS GAITSGORY AND TOLY PREYGEL (HARVARD UNIVERSITY) |
Background on algebraic stacks |
" |
September 10, 2009, 530 - 7pm at MIT (2-139) |
| JOINT BRANDEIS-HARVARD-MIT NORTHEASTERN MATHEMATICS COLLOQUIUM |
JOEL SMOLLER (UNIVERSITY OF MICHIGAN, ANN ARBOR) |
Expanding Wave Solutions of the Einstein Equations that Induce an Anomalous Acceleration into the Standard Model of Cosmology |
abstract
| September 10, 2009, 430 pm at Science Center, Hall D |
| RANDOM MATRIX SEMINARS |
ANTTI KNOWLES (HARVARD UNIVERSITY) |
Recent development on Quantum Brownian Motion |
Abstract Antti will report a recent work by Frohlich and Wojciech. This is the first of a series of lectures on this subject and we will meet twice a week (Tue, Wed, 310 - 420" |
September 10, 2009, 3pm at Science Center, Room 232 |
| NUMBER THEORY SEMINAR |
TIM DOKCHITSER (CAMBRIDGE UNIVERSITY) |
On the parity conjecture for elliptic curves |
For an elliptic curve E over a number field K, there are various modulo 2 versions of the Birch-Swinnerton-Dyer Conjecture, each sometimes called the Parity Conjecture. One asserts that the Mordell-Weil rank of E/K has the same parity as the analytic rank, as given by the root number. Another one is the same statement for the p-infinity Selmer rank for some prime p. I will explain the proof of the second conjecture for all E/Q and all p (this completes earlier work by Greenberg, Guo, Monsky, Nekovar and Kim), and show that over all number fields the first conjecture follows from finiteness of the Tate-Shafarevich group. This is joint work with Vladimir Dokchitser" |
September 9, 2009, 3-4PM at SC 507 |
| RANDOM MATRIX SEMINAR |
Alexei Borodin (CALTECH) |
Interlacing Particle Systems |
The goal of the talk is to survey recent results on interlacing particle systems that arise in representation theory, random matrices, and dimer models" |
September 3, 2009, 3PM at SC 232 |
| SUMMER TOPOLOGY SEMINAR |
MARK MAHOWALD (NORTHWESTERN UNIVERSITY) |
Homotopy theory of the Kervaire invariant |
Organized by Professor Mike Hopkins." |
August 10, 2009, 3 - 4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
AMNON NEEMAN (MATHEMATICAL SCIENCES INSTITUTE-ANU) |
A New Approach to Dualizing Complexes |
In the last four years there has arisen a completely new way of looking at dualizing complexes, and we will try to outline the theory. We will begin with a quick review of Grothendieck duality, done classically. Then we will discuss some of the results in the 2005 and 2006 articles by Iyengar, Jorgensen and Krause which began the new approach. Their results were limited to the case of affine schemes; we will explain this, and then show how, using recent work of the speaker and of his student Daniel Murfet, it is possible to also handle the global case." |
May 19, 2009, 3 pm at Science Center, Room 507 |
| RANDOM MATRIX SEMINARS |
J. QUASTEL (TORONTO) |
Effect of noise on traveling fronts |
Abstract Noisy perturbations of reaction-diffusion equations arise naturally when approximating by more basic models involving particles. Traveling fronts are the most important qualitative feature of such systems and we describe how they are affected by the noise in the simplest case of the one dimension KPP equation. In particular, we prove the Brunet-Derrida conjecture that the speed is reduced by a factor CIVog\epsilonI^{-2" |
May 14, 2009, 11 am at Science Center, Room 232 |
| WORKSHOP IN STRING THEORY, GENERAL RELATIVITY, AND PARTIAL DIFFERENTIAL EQUATIONS |
ERIC ZASLOW (NORTHWESTERN UNIVERSITY) |
Constructible Sheaves and the Fukaya Category |
Organized by Professor Shing Tung Yau" |
May 14, 2009, 315 - 415 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
PAOLO ALUFFI (FLORIDA STATE UNIVERSITY) |
Unexpected applications of characteristic classes for singular varieties |
Abstract There is a well-developed theory of characteristic classes for singular varieties, stemming from work of Marie-Helene Schwartz and Robert MacPherson. These CSM (=Chern-Schwartz-MacPherson) classes and the corresponding calculus of constructible functions have been applied in recent years to study questions in a wide variety of fields, ranging from classical enumerative geometry, to birational invariants, to new formulas for Donaldson-Thomas invariants, to computations related to high energy physics. In this talk I will review the theory underlying CSM classes, and survey several of these applications, including work in collaboration with Mboyo Esole on elliptic fibrations and with Matilde Marcolli on the study of motives related to Feynman integrals." |
May 12, 2009, 4 - 5 pm at Science Center, Room 507 |
| SPECIAL GEOMETRY SEMINAR |
IVAN CHELTSOV (UNIVERSITY OF EDINBURGH) |
Alpha-invariants of Fano orbifolds |
Abstract The only known sufficient condition for the existence of a Kaher-Einstein metric on Fano manifold can be formulated in terms of so-called alpha-invariant introduced by Tian and Yau more than 20 years ago. This invariant can be naturally defined for log Fano varieties with log terminal singularities using purely algebraic language. Using a global-to-local results of Shokurov, one can define a similar invariants for a germ of log terminal singularity. We describe the role played by alpha-invariants in birational geometry and singularity theory. We consider many explicit examples. We prove the existence of kahler-Einstein metrics on many quasismooth well-formed weighted del Pezzo hypersurface and compare this result with new obstructions found by J. Gauntlett, D. Martelli, J. Sparks and S.-T. Yau. We apply our technique to classify weakly-exceptional quasismooth well-formed weighted del Pezzo hypersurface using the classification of isolated rational quasihomogeneous three-dimensional singularities obtained by S.T. Yau and Y. Yu" |
May 11, 2009, 4 - 5 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
MICHAEL HOPKINS (HARVARD UNIVERSITY) |
The Kervaire invariant problem |
Organized by Professor Shing Tung Yau" |
May 11, 2009, 3 pm at Science Center, Room 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
THOMAS KOBERDA (HARVARD UNIVERSITY) |
Braids and Their Dilatations The Burau, Gassner and Bigelow representations. |
" |
May 06, 2009, 4 pm at Science Center, Room 507 |
| SPECIAL LECTURE |
ROBERT MERTON (HARVARD UNIVERSITY) |
On the Science of Finance in the Practice of Finance Observations on the Financial Crisis |
" |
May 05, 2009, 1115 - 1230 pm at Science Center, Room 507 |
| SPECIAL NUMBER THEORY SEMINAR |
JEAN-LOUP WALDSPURGER (PARIS) |
An integral formula related to the local Gross-Prasad conjecture, for tempered representations |
" |
May 04, 2009, 3 - 4 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
TIAN-JUN LI (UNIVERSITY OF MINNESOTA) |
Symplectic cones of almost complex 4-manifolds |
Please note the change in time" |
May 01, 2009, 230 - 330 pm at Science Center, Room 507 |
| THE TRIVIAL NOTIONS SEMINAR |
ALEKSANDAR SUBOTIC (HARVARD UNIVERSITY) |
Homological Mirror Symmetry for the Elliptic Curve |
" |
April 30, 2009, 207 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
OLGA STROILOVA (MIT) |
Classification of p-compact groups, part I reflection and realization |
" |
April 30, 2009, 4 - 6 pm at Science Center, Room 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
() |
|
No meeting--Simons Lectures by Ghys at MIT, 430pm in 34-10" |
April 29, 2009, at |
| NUMBER THEORY SEMINAR |
DAVID GERAGHTY (HARVARD UNIVERSITY) |
Modularity Lifting Theorems for Nearly Ordinary Galois Representations |
Abstract Building on work of Clozel, Harris and Taylor we prove modularity lifting theorems for certain l-adic Galois representations which are nearly ordinary at decomposition groups over l. We apply the Taylor-Wiles method, with innovations due to kisin and Taylor, to compare universal nearly ordinary Galois deformation rings with Hecke algebras associated to Hida families. A key step in the proof is to determine the irreducible components of the appropriate framed Galois deformation rings at the places dividing I" |
April 29, 2009, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
SERGEY GRIGORIAN () |
Betti numbers of barely G2 manifolds |
Organized by Professor Shing Tung Yau" |
April 28, 2009, 130 - 300 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
ALICE GUIONNET (LYON) |
Random matrices, free probability and enumerations of maps |
Random matriced appear in many different topics such as number theory, statistics or integrable systems. We shall discuss in this talk two fascinating theories which appear when one considers several rendom matrices, and more precisely their joint moments. Free probability is a theory of noncommutative operators which appears naturally when considering random matrices with size going to infinity. The relation between large random matirces and the question of enumerating graphs sorted by their genus goes back to Brezin, Itzykson, Parisi and Zuber. We will describe these two topics, their relation and how classical ideas from probability theory can be applied in this setting" |
April 27, 2009, 3 pm at Science Center, Room 507 |
| SPECIAL RANDOM MATRIX SEMINAR |
ALICE GUIONNET (LYON) |
Large random matrices with heavy tailed entries |
" |
April 24, 2009, 12 noon at Science Center, Room 232 |
| GAUGE THEORY AND TOPOLOGY |
JONATHAN WEITSMAN (NORTHEASTERN) |
Fermionization, convergent perturbation theory, and correlations in quantum gauge theories with cutoffs. |
" |
April 24, 2009, 330 - 430 pm at Science Center, Room 507 |
| SPECIAL PROBABILITY SEMINAR |
YUVAL PERES (MICROSOFT RESEARCH) |
Markov chains and embeddings in Hilbert space |
Abstract There is a surprisingly strong connection between the rate of escape of Random walk in a graph G and the distortion of embeddings of G into Hilbert space. One example of a fact where the only known proof uses this connection, is the result of Erschler based on an embedding due to Mok, that for any random walk on an infinite group it escapes at least at rate constant times t^{1/2} from its starting point. This is also true on a finite group, but only for a limited time of course-it is an open problem for how long this persists. When does a random walker recognize that he is stuck in a finite group? (Talk based on joint works with Assaf Naor and James Lee)" |
April 23, 2009, 12 noon at Science Center, Room 232 |
| THE TRIVIAL NOTIONS SEMINAR |
JACK THORNE (HARVARD UNIVERSITY) |
Toric Varieties |
Abstract Toric varieties are algebraic varieties which can be written down in terms of simple combinatorial data, of the type of convex bodies in Euclidean space. Their geometry and intersection theory can then be described completely in terms of these objects. The aim here will be to shine a light on some of these correspondences, and to give some fun examples. No more than a nodding acquaintance with algebraic geometry will be assumed" |
April 23, 2009, 207 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
JOHN DUNCAN (HARVARD UNIVERSITY) |
Discrete groups and formal series |
Abstract We describe a method for associating bivariate formal series to discrete groups of isometries of the hyperbolic plane. We find that these series are rather sensitive to certain arithmetic and geometric properties of the groups to which they correspond, and the association allows us to define an interesting class of groups. It turns out that there is an interesting moduli problem naturally associated to each group in our class" |
April 22, 2009, 3 pm at Science Center, Room 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
A. BUFETOV () |
Suspension flows over Vershik's automorphisms |
" |
April 22, 2009, 4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
DIANE MACLAGAN (UNIVERSITY OF WARWICK) |
Tropical Bounds on Nef Cones |
I will describe ways to obtain bounds on the nef cone of a variety X using a suitably chosen embedding of X into a toric variety. The techniques come from tropical geometry, and suggest a tropical approach to completely describing the nef cone of X. This is joint work with Angela Gibney" |
April 21, 2009, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
WILLIAM MEEKS (UNIVERSITY OF MASSACHUSETTS, AMHERST) |
The geometry, regularity and topological properties of CMC laminations and foliations of Riemannian 3-manifolds |
Abstract I will go over the basic properties of laminations and foliations with leaves having constant mean curvature, varying from leaf to leaf or all having the same constant mean curvature. In particular I will try to explain what are the CMC foliations of R^3-S where S is any closed countable set. Differential Geometry Seminars are organized by Professor Shing-Tung Yau" |
April 21, 2009, 130 - 300 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
JUN YIN (HARVARD UNIVERSITY) |
Mathematical problems in quantum many-body physics |
Organized by Professor Shing Tung Yau" |
April 20, 2009, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
JIM SIMONS (RENAISSANCE TECHNOLOGIES) |
Structured Bundles and Differential Cohomology |
" |
April 17, 2009, 330 - 430 pm at Science Center, Room 507 |
| THE TRIVIAL NOTIONS SEMINAR |
DAVID GERAGHTY (HARVARD UNIVERSITY) |
Representations of the absolute Galois group of Q |
Abstract We will discuss representations of the absolute Galois group of Q and look at some examples coming from modular forms and algebraic geometry. The goal will be to provide a brief introduction to the Langlands program. No background in number theory will be assumed" |
April 16, 2009, 207 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
MAT GELVIN (MIT) |
Dwyer-Kan obstruction theory |
" |
April 16, 2009, 4 - 6 pm at Science Center, Room 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
CLIFFORD TAUBES (HARVARD UNIVERSITY) |
An introduction to geometric quantization |
" |
April 15, 2009, 4 pm at Science Center, Room 507 |
| RANDOM MATRIX SEMINARS |
YIN JUN (HARVARD UNIVERSITY) |
Sine beta process for local statistics of random matrix |
" |
April 15, 2009, 2 pm at Science Center, Room 232 |
| NUMBER THEORY SEMINAR |
JUNECUE SUH (MIT) |
Nonhomeomorphic conjugates of connected Shimura varieties |
Abstract Joint with J. S. Milne. Start with a complex algebraic variety and make a conjugate of it by applying an automorphism of \C to its defining equations. While, by Grothendieck, the two conjugate varieties have the same algebraic fundamental group, Serre showed that the _topological_fundamental groups can still be different. Other examples followed later. In this talk, we construct connected Shimura varieties whose conjugates have nonisomorphic topological fundamental groups, by using Margulis s super-rigidity. In particular, we get examples, whose fundamental groups change under conjugation, that are moduli spaces of abelian varieties with prescribed PEL structure and Eilenberg-MacLane spaces at the same time." |
April 15, 2009, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
ANDREW NEITZKE (HARVARD UNIVERSITY) |
Wall-crossing and hyperkahler geometry |
Abstract I will discuss recent work with Davide Gaiotto and Greg Moore on a geometric interpretation of the Kontsevich-Soibelman wall-crossing formula. We identify this formula as an ingredient in a new construction of hyperkahler metrics. This seminar is organized by Professor Shing-Tung Yau" |
April 14, 2009, 130 - 300 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
LYDIA BIERI (HARVARD UNIVERSITY) |
Geometric Analysis and General Relativity |
Organized by Professor Shing Tung Yau" |
April 13, 2009, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
ANDY COTTON-CLAY (MIT) |
Fixed point bounds for symplectic mapping classes |
" |
April 10, 2009, 330 - 430 pm at Science Center, Room 507 |
| COLLOQUIUM |
HENRYK IWANIEC (RUTGERS UNIVERSITY) |
Is there a ghost in the house of prime numbers? |
" |
April 09, 2009, 430 pm at Science Center, Hall D |
| THE TRIVIAL NOTIONS SEMINAR |
YU-SHEN LIN () |
Mirror Symmetry and Predicting Enumerative Invariants |
Abstract Mirror symmetry relates the A-model of a given Calabi-Yau manifold with the B-model of its mirror. The former associates its Yukawa coupling with counting rational curves on the ambient Calabi-Yau manifold while the latter associates its Yukawa coupling with period integrals and variation of Hodge structure. The amazing thing is that period integrals involve no quatum corrections and are easier to compute. Assuming some physics, one can predict the number of rational curves of given degree on a generic quintic via a simple period calculation." |
April 09, 2009, 207 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
ANATOLY PREYGEL (MIT) |
p-compact groups The Weyl Group |
" |
April 09, 2009, 4 - 6 pm at Science Center, Room 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
NIMISH SHAH () |
Limits of expanding translates of shrinking curves on hyperbolic manifolds |
" |
April 08, 2009, 4 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
EDWARD FRENKEL (UNIVERSITY OF CALIFORNIA AT BERKELEY) |
A rigid irregular connection on the projective line |
Abstract From the trace formula and the global Langlands correspondence one can infer the existence of a particular rigid l-adic local system on the projective line with tame ramification at 0 and wild ramification, of the mildest possible kind, at infinity, for any simple algebraic group. These l-adic local systems and their characteristic 0 counterparts have been constructed in some cases by Deligne and Katz. We will explain how to construct such a local system in the characteristic 0 case, uniformly for an arbitrary simple algebraic group, using the formalism of opers introduced by Beilinson and Drinfeld. Among other things, it provides an example of the geometric Langlands correspondence with wild ramification." |
April 08, 2009, 3 PM at Science Center, Room 507 |
| RANDOM MATRIX SEMINARS |
THOMAS LAM (HARVARD UNIVERSITY) |
Random Partitions and random matrices, II |
" |
April 08, 2009, 2 pm at Science Center, Room 232 |
| FACULTY COLLOQUIUM |
LI-SHENG TSENG (HARVARD UNIVERSITY) |
Non-Kahler Geometry |
" |
April 06, 2009, 3pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
STEFAN FRIEDL (UNIVERSITY OF WARWICK) |
Symplectic 4-manifolds and fibered 3- manifolds |
" |
April 03, 2009, 330 - 430 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
JACOB LURIE (HARVARD UNIVERSITY) |
p-Compact Groups Finding a Maximal Torus |
" |
April 02, 2009, 4 - 6 pm at Science Center, Room 507 |
| THE TRIVIAL NOTIONS SEMINAR |
RYAN REICH (HARVARD UNIVERSITY) |
Evaluating Bezout's Theorem |
Abstract Tropical geometry is a combinatorial field with a strong formula analogy to algebraic geometry and many strange connections that allow similar theorems to be proved using sickeningly elementary methods. I will prove a tropical Bezout s Theorem and then deduce the real Bezout s Theorem from it." |
April 02, 2009, 207 pm at Science Center, Room 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
DANIJELA DAMJANOVIC (HARVARD UNIVERSITY) |
Perturbations of some higher rank unipotent actions |
" |
April 01, 2009, 4 pm at Science Center, Room 507 |
| RANDOM MATRIX SEMINARS |
THOMAS LAM (HARVARD UNIVERSITY) |
Random Partitions and random matrices, I |
" |
April 01, 2009, 2 pm at Science Center, Room 232 |
| NUMBER THEORY SEMINAR |
NOAM ELKIES (HARVARD UNIVERSITY) |
On the rank of elliptic curves with a 2-torsion point |
Abstract We use K3 surfaces parametrized by a rational Shimura curve to construct nonconstant elliptic curves over Q(T) with a rational 2-torsion point and Mordell-Weil rank at least 11." |
April 01, 2009, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
VALENTINO TOSATTI (HARVARD UNIVERSITY) |
Large Kahler limits of Calabi-Yau metrics |
" |
March 31, 2009, 130 - 3 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
ROBERT POLLACK (BU) |
Fitting ideals of Selmer groups of modular forms |
" |
March 31, 2009, 3 - 4 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
DANIJELA DAMJANOVIC (HARVARD UNIVERSITY) |
Perturbations of some higher rank unipotent actions |
Organized by Professor Shing Tung Yau" |
March 30, 2009, 3 PM at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
ZOLTAN SZABO (PRINCETON) |
Heegaard Floer homology and complete decomposing systems |
" |
March 20, 2009, 330 - 430 pm at Science Center, Room 507 |
| THE TRIVIAL NOTIONS SEMINAR |
TANYA KOBYLYATSKAYA (HARVARD UNIVERSITY) |
A Gentle Introduction to Heegaard Floer Homology |
Abstract Heegaard Floer homology was introduced by Peter Ozsvath and Zoltan Szabo around the year 2000. The theory provides very strong invariants for closed oriented 3-manifolds. The aim of this talk is to go over some of the elements that go into its construction." |
March 19, 2009, 207 pm at Science Center, Room 507 |
| DIFFERENTIAL SPHERICAL AND WHITTAKER FUNCTIONS (A NEW TAKE ON CLASSICAL HARMONIC ANALYSIS) |
IVAN CHEREDNIK (UNC CHAPEL HILL) |
Nonsymmetric Bessel Functions Via Spinors (Part II) |
The technique of spinors (in a similar sense) was used in my proof of Matsuo-Cherednik theorem establishing a connection between KZ and QMBP. In mathematics, the latter is the eigenvalue problem for the radial parts of Laplace operators on the symmetric spaces (with k). They are simple to define (not new) by real spinors, we mean functions on the disjoint union of all Weyl chambers (respectively, the imaginary parts must be in this union for complex spinors). However, this definition coupled with Dunkl operators readily lead to a significant extension of the theory of Bessel functions (to be discussed) and well beyond it. Interestingly, spinors provide representations of DAHA which are not exactly induced ones; in the Whittaker limit, far from the induced ones. There are quite a few open problems (to be formulated and discussed)." |
March 19, 2009, 5 - 630 pm at Science Center, Room 232 |
| THE THURSDAY SEMINAR |
ANDRE HENRIQUES () |
Towards a Geometric Description of Elliptic Cohomology |
" |
March 19, 2009, 4 - 6 pm at Science Center, Room 507 |
| COLLOQUIUM |
ZOLTAN SZABO (PRINCETON) |
Heegaard diagrams and invariants for three-manifolds |
Abstract This talk will give an introduction to Heegaard Floer homology for closed oriented three-dimensional manifolds. After describing the construction we will discuss applications and also some techniques to compute Heegaard Floer homology." |
March 19, 2009, 430 pm at Science Center, Hall D |
| UPCOMING TALK |
STEPHEN T. YAU (UNIVERSITY OF ILLINOIS AT CHICAGO) |
Explicit construction of moduli space of bounded complete Reinhardt domains in Cn and Hilbert 14th problems |
Abstract One of the most fundamental problems in complex geometry is to determine when two bounded domains in Cn are biholomorphically equivalent. Even for complete Reinhardt domains, this fundamental problem remains unsolved for many years. Using the Bergman function theory, we construct an infinite family of numerical invariants from the Bergman functions for complete Reinhardt domains in Cn. These infinite family of numerical invariants are actually a complete set of invariants if the domains are pseudoconvex with C1 boundaries, the complete set of numerical invariants can be reduced dramatically although the set is still infinite. We shall also discuss the role of the Hilbert 14th problem in the construction of numerical biholomorphic invariants of complete Reinhardt domains in Cn" |
March 18, 2009, 2 - 3 pm at Science Center, Room 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
A.WILKINSON () |
Absolute continuity, Lyapunov exponents and rigidity. |
" |
March 18, 2009, 4 pm at Science Center, Room 507 |
| RANDOM MATRIX SEMINARS |
ARNAV TRIPATHY (HARVARD UNIVERSITY) |
Matrix Integrals and Map Enumeration |
" |
March 18, 2009, 2 pm at Science Center, Room 232 |
| NUMBER THEORY SEMINAR |
BRIAN CONRAD (STANFORD) |
Finiteness theorems for algebraic groups over global function fields |
Abstract If X is a smooth variety over a global field k, G is an algebraic group over k equipped with an action on X, and x is a point in X(k) then it is natural to ask how the property of x in X(k) being in the G(k)-orbit of x compares with it being in the G(k_v)-orbit of x for all places v of k. The relevant local-to-global obstruction space for this problem is the Tate-Shafarevich set of the isotropy group G_x that is generally not connected or reductive (or smooth when char(k)>0), even when G is connected and semisimple. In the number field case the finiteness of these sets was proved by Borel and Serre long ago, but their method used characteristic 0 in an essential way. Recently in joint work with Gabber and G. Prasad we have developed a theory of pseudo-reductive groups which is a very useful tool to prove results for general affine algebraic groups in the function field case that were previously known only in the reductive case. In particular, this work makes it possible to prove the finiteness of Tate-Shafarevich sets of all affine algebraic group schemes over global function fields (away from char. 2 for now), as well as a number of other new finiteness results over local and global function fields. The first part of the talk will explain a bit about the theory of pseudo-reductive groups (more details of which were given in my talk yesterday at BC), and the rest of the talk will show how it is used." |
March 18, 2009, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
DAN MANGOUBI (UNIVERSITY OF MONTREAL) |
A Local Version of Courant's nodal domains theorem |
Abstract Let (M,g) be a compact Riemannian manifold. Given a smooth real function F on M, any connected component of the open set {F\neq 0} is called a nodal domain of F. In 1923 Courant proved that the number of nodal domains which correspond to the k-th eigenfunction of the Laplacian on M cannot exceed k. In 1990 H. Donnelly and C. Fefferman proved a nonsharp local version of Courant s theorem. We will explain this, and show how one can obtain a sharp form of the local Courant theorem on real analytic manifolds. Differential Geometry Seminars are organized by Professor Shing-Tung Yau" |
March 17, 2009, 130 - 300 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
SHIHOKO ISHII (TOKYO INSTITUTE OF TECHNOLOGY) |
Properties of Jet Schemes |
" |
March 17, 2009, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL SPHERICAL AND WHITTAKER FUNCTIONS (A NEW TAKE ON CLASSICAL HARMONIC ANALYSIS) |
IVAN CHEREDNIK (UNC CHAPEL HILL) |
Nonsymmetric Bessel Functions Via Spinors (Part I) |
This lecture is actually independent of the previous ones, a good introduction for those who are interested in modern vision of the classical theory of Bessel functions, Hankel transform and related harmonic analysis. In the A(1)-case, we will reduce the difference theory to the differentia one using the trigonometric and rational Dunkl operators. We will use this (operator) approach to prove the classical theorem about the Gaussian integrals of Bessel functions. The first neoclassical generalization will concern the non-symmetric solutions of the classical DE for Bessel functions. The second one will be the theory of eigenfunctions of the rational Dunkl operator. The new technique of spinors is needed to address these and many related problems. In spite of simple setting, the rational rank one theory is a great starting point for the DAHA harmonic analysis" |
March 17, 2009, 5 - 630 pm at Science Center, Room 232 |
| FACULTY COLLOQUIUM |
JOHN DUNCAN (HARVARD UNIVERSITY) |
Poincare Series |
Organized by Professor Shing Tung Yau" |
March 16, 2009, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
DANIEL RUBERMAN (BRANDEIS) |
Seiberg-Witten invariants and periodic Dirac operations |
Abstract We study the Seiberg-Witten equations on a 4-manifold X with the homology of S^1 x S^3. The count of such solutions, called the Seiberg-Witten invariant, depends on choices of Riemannian metric and perturbation of the equations to make a smooth moduli space. A similar issue is resolved in dimension 3 by relating the jumps in the Seiberg-Witten invariant to the spectral flow of the Dirac operator; the resulting invariant is then Casson s invariant. In dimension 4, we use Taubes theory of periodic-end operators to relate the jumps in the Seiberg-Witten invariant to the index theory of the Dirac operator on the infinite cyclic cover of X. This circle of ideas has applications to classification of smooth manifolds homeomorphic to S^1 x S^3. to questions about positive scalar curvature, and to homology cobordisms. This is joint work with Tom Mrowka nd Nikolai Saveliev" |
March 13, 2009, 330 - 430 at SCience Center, Room 507 |
| THE TRIVIAL NOTIONS SEMINAR |
SI LI (HARVARD UNIVERSITY) |
Feynman Integrals and Three-fold Invariants |
Abstract Starting from the physics idea of the Feynman Integral, I will discuss Witten s insight of constructing invariants of three dimensional manifold from Chern-Simons theory. The first example will be the Ray-Singer Torsion constructed from the spectrum of Laplacian operator. I will explain the reason to believe its topological property. Then by adding Wilson lines, we show how to obtain the linking number of two circles in R3 from Chern-Simons point of view. This is the simplest but intuitive example of Witten s construction of knot invariants." |
March 12, 2009, 207 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
JACOB LURIE (HARVARD UNIVERSITY) |
p-compact groups Existence of a Nontrivial Torus |
" |
March 12, 2009, 4 - 6 pm at Science Center, Room 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
E. HIRONAKA () |
Pseudo-Anosov mapping classes with small dilatation constructed from graphs |
" |
March 11, 2009, 4 pm at Science Center, Room 507 |
| DIFFERENTIAL SPHERICAL AND WHITTAKER FUNCTIONS (A NEW TAKE ON CLASSICAL HARMONIC ANALYSIS) |
IVAN CHEREDNIK (MIT) |
Dunkl Operators Under Whittaker Limit |
Abstract We will continue the theory of the limits of DAHA of rank one; the most challenging is the Whittaker limit. As it was found by Pavel Etingof, the Macdonald q, t-operators for A(n) behave nicely under the special (Whittaker) modification of the limit t->0 or the limit t->infinity, extending the construction well known in the differential case (from QMBP to Toda lattice). We will generalize it to Dunkl operators (including a new interpretation of the q-Toda lattice via mil-DAHA). A new method, the technique of spinors, was used for this generalization. The terminology comes from the rank one differential case (to be considered later), where the Dunkl operator is nothing but the Dirac operator (square root of the Laplace operator) of the corresponding symmetric space. Due to the novelty (and importance) of this topic, we will discuss the construction in full detail (for A(1) only). The conceptual aspects of the technique of spinors are not clear at the moment; there can be interesting connections to modern analysis (including microlocal functions) and (hopefully) to the theories where the q-Whittaker functions are used (Givental-Lee, the geometric Langlands program)" |
March 10, 2009, 5 - 630 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
CARLOS LOUSTO (CENTER FOR COMPUTATIONAL RELATIVITY AND GRAVITATION (CCRG), ROCHESTER INSTITUTE OF TECHNOLOGY) |
New results in numerical relativity |
Abstract We review the formulation that led to a breakthrough in numerical relativity and finally allowed, after three decades, to stably evolve binary black holes for many orbits. We discuss some of its implications to mathematical relativity and astrophysics The orbital hung-up effect and the cosmic censorship conjecture. The discovery of the large recoil velocities (up to 4000 km/s) acquired by the merger remnant of two spinning black holes and its astrophysical consequences. The space-time characterization of the final black hole and the no-hair theorem. Generic binary black hole configurations and the evolution of three (an N) black holes. This seminar is organized by Professor Shing-Tung Yau" |
March 10, 2009, 130 - 300 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
BENEDICT GROSS (HARVARD UNIVERSITY) |
Connections on algebraic curves |
Organized by Shing Tung Yau" |
March 09, 2009, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
YI NI (MIT) |
Non-separating spheres and twisted Heegaard Floer homology |
" |
March 06, 2009, 330 - 430 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
MICHAEL HOPKINS (HARVARD UNIVERSITY) |
Cohomology of p-compact groups |
Abstract This talk will begin our journey through the Dwyer-Wilkerson paper Homotopy fixed point methods for Lie groups and finite loop space" |
March 05, 2009, 4 - 6 pm at Science Center, Room 507 |
| THE TRIVIAL NOTIONS SEMINAR |
ANA CARAIANI (HARVARD UNIVERSITY) |
Stacks for Dummies |
Abstract A problem number theorists often encounter is getting a handle on their moduli spaces. There is no such thing as a moduli scheme of elliptic curves, because the non-trivial automorphisms some of them have get in the way. Fortunately, there is something called a moduli stack of elliptic curves. This talk is meant to b a gentle introduction to stacks we ll build our way to understanding what one is, we ll provide as few key examples and we ll see what makes stacks so useful for representing moduli problems." |
March 05, 2009, 207 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
BENEDICT GROSS (HARVARD UNIVERSITY) |
On the restriction of irreducible representations of classical groups |
Abstract J-L. Waldspurger has recently made an important advance, establishing a weak form of a conjecture I made with D. Prasad on restriction from SO(n) to SO(n-1) over local fields. I will review these conjectures, which are an interesting mix of representation theory and number theory, in the framework of restriction from U(n) to U(n-1). The local conjectures involve symplectic root numbers, and the global conjectures involve the central critical values and first derivatives of L-functions" |
March 04, 2009, 3 pm at Science Center, Room 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
R. DEVANEY (BOSTON UNIVERSITY) |
Dynamics of z n + C/zn Why n=2 is crazy |
" |
March 04, 2009, 4-5 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
EDUARDO ESTEVES (INSTITUTO NACIONAL DE MATEMATICA PURA E APLICADA) |
Compactified Jacobians and Abel maps for singular curves |
Abstract We will discuss the problem of extending the construction of the classical Abel maps for smooth curves to the case of singular curves. The construction of degree-1 Abel maps will be shown, together with an approach for constructing higher degree Abel maps. Possible applications will be discussed as well" |
March 03, 2009, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL SPHERICAL AND WHITTAKER FUNCTIONS (A NEW TAKE ON CLASSICAL HARMONIC ANALYSIS) |
IVAN CHEREDNIK (MIT) |
Daha in Rank One Inner Product, Links , Limits |
Abstract I will continue with the rank one case, making it as explicit as possible. We will focus on the inner product (old and new theory), the connection with the p-adic theory and links to the Q-Hermit polynomials. Th main results from the previous lecture will be repeated and supported by explicit formulas. Also, I will be preparing the technical tools for the switch to the real theory (March 10). At the end, we will discuss the p-adic Whittaker functions (I do not know what are their nonsymmetric counterparts)" |
March 03, 2009, 5 - 630 pm at Science Center, Room 232 |
| FACULTY COLLOQUIUM |
NOAM ELKIES (HARVARD UNIVERSITY) |
How to Solve Diophantine Equations |
Abstract Solving Diophantine equations is even harder than you think already the theoretically trivial case of a rational variety of dimension 0 may arise as a system of equations whose solution is not obvious. We describe one technique, adapted from numerical analysis, that often solves such equations where traditional elimination techniques fail. We illustrate with the problem of finding relatively prime polynomials x(t), y(t) of degrees 8 and 12 that satisfy deg (x^3-y^2)=5 -- an example that lies at a fascinating crossroads of Belyi functions, singular K3 surfaces, and the Hall conjecture. This colloquium is organized by Professor Shing Tung Yau" |
March 02, 2009, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
YI-JEN LEE (PURDUE UNIVERSITY) |
Periodic Floer homology and Seiberg-Witten Floer cohomology |
" |
February 27, 2009, 330 - 430 pm at Science Center, Room 507 |
| THE TRIVIAL NOTIONS SEMINAR |
DAVID ROE (HARVARD UNIVERSITY) |
The Weil Conjectures |
Abstract The Weil conjectures (proved in 1974 by Deligne) provide strong constraints on the number of points on a variety over extensions of finite fields. I will expound upon the statements of the conjectures, sketch a proof using etale cohomology, and give some reasons that we might care about the number of points on a variety" |
February 26, 2009, 207 pm at Science Center, Room 507 |
| BRANDIES-HARVARD-MIT-NORTHEASTERN JOINT MATHEMATICS COLLOQUIUM |
VAUGHAN JONES (UNIVERSITY OF CALIFORNIA AT BERKELEY) |
Large N limit of random matrices, free probability and the graded algebra of a planar algebra |
Abstract The suitably normalized limit of the average trace of a word on n independent random matrices defines a trace (the Voiculescu trace) on the algebra of noncommutative polynomials on n self-adjoint variables. In joint work with Guionnet and Shlyakhtenko we showed that this trace may be generalized to the case of an arbitrary planar algebra and one obtains interesting von Neumann algebras on completion. Of perhaps even greater interest is when the random matrices are distributed according to the Gaussian plus a hjgher order perturbation. It is possible that a judicious choice of this perturbation may lead to a model that is solvable by generalizations of Conway s skein theory method from knot theory." |
February 26, 2009, 430 pm at Science Center, Hall D |
| DIFFERENTIAL GEOMETRY SEMINAR |
Antoine Song (PRINCETON UNIVERSITY) |
Existence of infinitely many minimal hypersurfaces in closed manifolds |
In the early 80 s, S.-T. Yau conjectured that in any closed $3$-manifold there should be infinitely many minimal surfaces. I will review previous contributions to the question and present a proof of the conjecture, which builds on min-max methods developed by F. C. Marques and A. Neves. A key step is the construction by min-max theory of a sequence of closed minimal surfaces in a certain manifold N with non-empty stable minimal boundary, and I will explain how to achieve this via the construction of a non-compact manifold with cylindrical ends" |
February 26, 2009, 4:00 PM at Sci Center 507 |
| NUMBER THEORY SEMINAR |
DIMITAR JETCHEV (HUDSON RIVER TRADING LLC/IHES) |
Global divisibility of Heegner points and Tamagawa numbers |
Abstract We improve Kolyvagin s upper bound on the order of the p-primary part of the Shafarevich-Tate group of an elliptic curve of rank one over a quadratic imaginary field. In many cases, our bound is precisely the one predicted by the Birch and Swinnerton-Dyer conjectural formula" |
February 25, 2009, 3 - 4 pm at Science Center, Room 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
D. MARGALIT (TUFTS) |
Torelli groups and the complex of minimizing cycles. |
" |
February 25, 2009, 4 - 5 pm at Science Center, Room 507 |
| DIFFERENTIAL SPHERICAL AND WHITTAKER FUNCTIONS (A NEW TAKE ON CLASSICAL HARMONIC ANALYSIS) |
IVAN CHEREDNIK (MIT) |
Daha in Rank One Gaussians, The Form, Coinvariants |
Abstract Switching to the rank one, we will be able to restart the previous theory of DAHA, namely, the E-polynomials, Gaussians and coinvariants, practically from scratch. The form in terms of the affine symmetrizer from the previous talk (Affine Hall functions) will be in the focus of this one, including its interpretation as a Shapovalov form. Its rational counterpart (to be discussed later) is the analytic continuation (to negative k) of the key pairing in the theory of Bessel functions. If the time allows, we will begin preparations for the theory of Whittaker functions. The plan A. DAHA for A_1; E-polynomials. B. Q-Gauss integrals )level 1 theory). C. The invariant form and coinvariants. D. P-adic theory as the limit q->0" |
February 24, 2009, 5 - 630 pm at Science Center, Room 232 |
| DIFFERENTIAL GEOMETRY SEMINAR |
CHI-WANG SHU (BROWN UNIVERSITY) |
Local discontinuous Galerkin method for surface diffusion and Willmore flow of graphs |
Abstract We present the recent development of a local discontinuous Galerkin (LDG) finite element method for solving the surface diffusion equations and equations for Willmore flow of graphs. We will start with a general introduction to the discontinuous Galerkin method for nonlinear diffusion equations and then move on to the specific LDG scheme, including a discussion on its L^2 stability for the equation of surfsce diffusion and energy stability for the equation of Willmore flow of graphs. Finally, we will provide numerical simulation results for different solutions of these two types of the equations to illustrate the accuracy and capability of the LDG method. This is a joint work with Yan Xu" |
February 24, 2009, 130 - 300 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
MARTIN NOWAK AND CORINA TARNITA (HARVARD UNIVERSITY) |
Evolutionary Dynamics on Sets |
Organized by Professor Shing Tung Yau" |
February 23, 2009, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
TAMAR FRIEDMANN () |
Orbifold Singularities, Lie Algebras of the Third Kind (LATKes), and Pure Yang-Mills with Matter |
" |
February 20, 2009, 330 - 430 pm at Science Center, Room 507 |
| TRIVIAL NOTIONS SEMINAR |
CHEN-YU CHI (HARVARD UNIVERSITY) |
Be Rational, Geometry! |
" |
February 19, 2009, 207 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
DUSTIN CLAUSEN () |
Weyl Groups of p-Compact Groups |
Abstract p-Compact Groups are an at p analog (and generalization) of compact Lie groups in the world of homotopy theory. Following a paper of Dwyer, Miller, and Wilkerson, we ll show that p-compact groups have a similar structural anatomy to compact Lie groups, for instance supporting a good theory of maximal tori and Weyl groups" |
February 19, 2009, 4 - 6 pm at Science Center, Room 507 |
| BRANDIES-HARVARD-MIT-NORTHEASTERN JOINT MATHEMATICS COLLOQUIUM |
ALEXANDER GONCHAROV (BROWN UNIVERSITY) |
The quantum dilogarithm and quantization of cluster varieties |
abstract
| February 19, 2009, 430 pm at Science Center, Hall D |
| RANDOM MATRIX SEMINARS |
HONRG-TZER YAU (HARVARD UNIVERSITY) |
FIRST MEETING |
Format The aim is to understand a few papers in this subject in details. At this point, the selection is Virag papers on the beta ensembles and Pastur s paper on Dyson s Sine Kernel. In this first meeting, we ll decide what papers we will focus on. Also in the first meeting, I ll give a proof of Dyson s sine kernel for GUE. Jun Yin will present the paper by Virag. Occasionally, we ll have guest speakers" |
February 18, 2009, 207 - 330 pm at Science Center, Room 232 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
H. OH (BROWN UNIVERSITY) |
Apollonian circle packings and horospherical flows on hyperbolic 3-manifolds |
" |
February 18, 2009, 4 - 5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
DAVID KAZHDAN (HUJI) |
A computation of an endoscopic transform (joint work with Y. Varshavsky) |
Please view abstract in the following link." |
February 18, 2009, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL SPHERICAL AND WHITTAKER FUNCTIONS (A NEW TAKE ON CLASSICAL HARMONIC ANALYSIS) |
IVAN CHEREDNIK (UNC) |
Daha and Affine Hall Functions |
Abstract This lecture is essentially independent from the previous two ones; for those who want to join this mini-course please contact Xiaoguang Ma at xma@math.mit.edu for notes. We continue with the same program. The operator Macdonald formula (a modern revision of his formula for Zonal p-adic spherical functions), proven and discussed last time, will be moved to the DAHA level and the theory of Affine Hall Functions, AHF. Here the plan is A. The definition of DAHA (any root systems, A_1). B. Proof of the operator affine Macdonald formula. C. The convergence problem for AHF at level 0. D. Gaussians; the complete theory in level 1. E. A sketch of the AHF theory in higher ranks" |
February 17, 2009, 5 - 630 pm at Science Center, Room 232 |
| DIFFERENTIAL GEOMETRY SEMINAR |
CHRISTINA SORMANI (LEHMAN COLLEGE AND CUNY GRADUATE CENTER) |
Intrinsic Flat Convergence of Riemannian Manifolds |
Please note the change in time for this week only. Abstract We define a new distance between oriented Riemannian manifolds that we call the {\em intrinsic flat distance} based upon Ambrosio-Kirchheim s theory of integral currents on metric spaces. Limits of sequence of manifolds, $M^m_j$, with $vol(M_j)\le V_0$, $vol(\partial M_j)\le V_1$ and $diam(M_j)\le D$ are countably $H^m$ rectifiable metric spaces with an orientation and multiplicity that we call {\em integral current spaces}. In general the Gromov-Hausdorff and intrinsic flat limits do not agree. However, we show that they do agree when the sequence of manifolds has nonnegative Ricci curvature and a uniform lower bound on volume and also when the sequence of manifolds has a uniform linear local geometric contractibility function. These results are proven using work of Greene-Petersen, Gromov, Cheeger-Colding and Perelman. We present an example of three manifolds with positive scalar curvature constructed using Gromov-Lawson connected sums attaching two standard 3 spheres with increasingly many tiny wormholes which converge in the Gromov Hausdorff sense to the standard three sphere but in the intrinsic flat sense to the 0 space due to the canceling orientation of the two spheres. We conjecture this cannot occur in we exclude spaces with interior minimal surfaces. This is joint work with S. Wenger" |
February 17, 2009, 430 - 600 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
INANC BAYKUR (BRANDEIS) |
Finite group actions and smooth structures on four-manifolds. |
Abstract In this talk, I will introduce an equivariant version of Fintushel-Stern s reverse engineering technique, and discuss its applications to the construction of new smooth and symplectic four-manifolds, group actions and embeddings of surfaces. The first part of the talk would contain a survey of the current state of the art, and I can possibly include one or two sample & simple constructions for graduate students in the audience" |
February 13, 2009, 330 - 430 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
JACOB LURIE (HARVARD UNIVERSITY) |
Uniqueness of HP ^{infty} and the T functor |
" |
February 12, 2009, 4 - 6 pm at Science Center, Room 507 |
| TRIVIAL NOTIONS SEMINAR |
SAMIK BASU (HARVARD UNIVERSITY) |
Hirzebruch Problem 8 |
" |
February 12, 2009, 207 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
THOMAS BARNET-LAMB (HARVARD UNIVERSITY) |
Potential automorphy for certain Galois representations to GL(n) |
Abstract I will describe recent generalizations of mine to a theorem of Harris, Shepherd-Barron, and Taylor, showing that have certain Galois representations become automorphic after one makes a suitably large totally-real extension to the base field. The main innovation is that the result applies to Galois representations to GL_n, where the previous work dealt with representations to Sp-n; I can also dispense with certain congruence conditions which existed in the earlier work, and work over a CM, rather than a totally-real, field. The main technique is the consideration of the cohomology the Dwork hypersurface, and in particular, of pieces of this cohomology other than the invariants under the natural group action." |
February 11, 2009, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
BOHAN FANG (NORTHWESTERN UNIVERSITY) |
SYZ transformation and coherent-constructible correspondence for toric varieties |
Abstract I will describe a theorem equating the derived category of coherent sheaves for toric varieties and the derived category of constructibles sheaves supported on polytopes in a real vector space. This correspondence is obtained by performing the SYZ transformation, which produces a Lagrangian in the mirror space from a holomorphic line bundle on the toric variety. Applying Nadler-Zaslow s theorem we can go further to constructible sheaves from Lagrangians. Passing to K-theory recovers the isomorphism given by Morelli" |
February 10, 2009, 130 - 3 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
THOMAS LAM (HARVARD UNIVERSITY) |
The Edrei-Thoma Theorem |
" |
February 09, 2009, 3 pm at Science Center, Room 507 |
| TRIVIAL NOTIONS SEMINAR |
VALENTINO TOSATTI (HARVARD UNIVERSITY) |
Metric Sociology |
Abstract I will introduce the notion of Gromov-Hausdorff distance and convergence of compact metric spaces, and discuss the question of deciding whether a given set of compact metric spaces is precompact. I will then apply this to the study of closed Riemannian manifolds with diameter and lower Ricci curvature bounds, and I will present several examples of convergence, from the differential and algebro-geometric points of view." |
February 05, 2009, 207 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
HAYNES MILLER (MIT) |
What is a -compact group? |
" |
February 05, 2009, 4 - 6 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
NOAM ELKIES (HARVARD UNIVERSITY) |
Questions on quadratically recurrent sequences |
Abstract If the sequence s(n) is of the form f(P+nQ) where f is a theta function in n and P,Q are any vectors, then the sequence s(n) = f(P+nQ) satisfies a homogeneous quadratic recurrence s(n) s(n+w) = a_1 s(n+1) s(n+w-1) + a_2 s(n+2) s(n+w-2) + ... for some width w and coefficients a_i (0 < 2i <= w). The reverse implication is not true in general, but does hold in many cases, some known (e.g. all w<8) and some conjectural (e.g. when only two a _i are nonzero) that hint at connections with various moduli spaces arising in number theory and algebraic geometry. Besides these theoretical questions, there is much scope for numerical experimentation, as with the" |
February 04, 2009, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
SPYROS ALEXAKIS (MIT) |
Global Conformal Invariants A conjecture of Deser and Schwimmer |
Abstract Global Conformal Invariants are integrals of local geometric scalars, which remain invariant under conformal changes of the underlying metric. I will discuss my proof of a conjecture of Deser and Schwimmer, which asserts that any such global invariant admits a decomposition into standard building blocks of three types. I will present some ideas from the proof, putting emphasis on an algebraic question which lies at the heart of the problem. Time permitting, some analogous questions in Kahler geometry will also be discussed." |
February 03, 2009, 130 - 300 PM at Science Center, Room 507 |
| DIFFERENTIAL SPHERICAL AND WHITTAKER FUNCTIONS (A NEW TAKE ON CLASSICAL HARMONIC ANALYSIS) |
IVAN CHEREDNIK () |
This is an introduction to the course. Lectures will take place every Tuesday. |
Abstract This mini-course will be devoted to the new theory of q,t-spherical (difference) functions based on double affine Hecke algebras, DAHA. Its foundation is actually algebraic the polynomial representation of DAHA plays the key role, including the theory of symmetric and nonsymmetric Macdonald polynnomials. These topics will be reviewed systematically in the course. We will begin with the classical and nonsymmetric Bessel one-dimensional functions (eigenfunctions of the Dunkl operator) and then switch to their q,t-counterparts. The analytic theory includes the generalization of Harish-Chandra s growth estimates for spherical functions and related problems (many are open). The q-Whittaker functions constitute an important limiting case (t->0). The q-Whittaker functions have or are expected to have various applications in the representation theory of Kac-Moody algebras, quantum groups, quantum K-theory of flag varieties and, which maybe the most challenging, in the geometric quantum Langlands program. Among other features, they interpolate between real/complex and the p-adic theory. The Shintani-Casselman-Shalika-type formulas for the special values of spherical and Whittaker functions provide a natural bridge to the Langlands program; they will be in the focus of this course. It is a research course; however, due to the novelty of quite a few topics, the exposition will be practically from scratch and mainly in the one-dimensional setting" |
February 03, 2009, 5 - 630 pm at Science Center, Room 232 |
| FACULTY COLLOQUIUM |
GERALD SACKS (HARVARD UNIVERSITY) |
Infinitely Long Formulas A Short Introduction |
" |
February 02, 2009, 3 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
BENEDICT GROSS (HARVARD UNIVERSITY) |
On discriminants and their roots |
Abstract Modular forms and Hilbert modular forms give rise to Galois extensions of totally real number fields with non-abelian Galois groups. I will discuss a recent example studied by L. Dembele and J.-P. Serre, which involves a totally complex Galois extension K of Q whose degree is equal to 2251731094732800, which is unramified away from 2, and whose root discriminant is less than 55.4. The Galois group if K/Q is isomorphic to an extension of Z/8Z by the non-solvable SL(2,256) x SL(2,256). I will begin the talk with a review of the theory of discriminants and root discriminants, as well as the ramification properties of the Galois extensions associated to Hilbert modular forms." |
January 07, 2009, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
PAUL SEIDEL (MIT) |
Homological Mirror Symmetry for the Genus Two Curves |
Organized by Professor Shing Tung Yau" |
December 16, 2008, 430 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
MICHAEL TEMKIN (UNIVERSITY OF PENNSYLVANIA) |
Relative Riemann-Zariski Spaces |
In this lecture I ll define relative Riemann-Zariski spaces attached to a morphism of schemes and generalizing the classical Riemann-Zariski space of a field over C. We will see that similarly to the classical RZ space, the relative ones can be described either as projective limits of schemes in the category of locally ringed spaces, or as certain spaces of valuations. As an application, we will prove that any separated morphism between quasi-compact and quasi-separated schemes factors as a composition of an affine morphism followed by a proper morphism. In particular, this gives a new proof of Nagata compactification theorem. If time permits, I ll try to illustrate analogies between the new spaces and this work, and the non-Archimedean analytic spaces and Raynaud s theory. There will be a related talk at STAGE at 100 on Monday, MIT 26-302. ." |
December 16, 2008, 3 pm at Science Center, Room 507 |
| THE TRIVIAL NOTIONS SEMINAR |
THOMAS KOBERDA (HARVARD UNIVERSITY) |
How to Abelianize Groups That Are Difficult to Abelianize |
Abstract If we are given a finite presentation for a group, computing the abelianization is a mechanical task. If on the other hand the group is defined as the set of symmetries of a certain object or as the group of connected components of some Lie group, computing the abelianization might become highly nontrivia. We will consider the mapping class group of a closed surface and compute its abelianization, and discuss the abelianizations of some finite index subgroups. We will motivate this discussion with some aspects of the representation theory of the mapping class group" |
December 11, 2008, 207 pm at Science Center, Room 507 |
| BRANDIES-HARVARD-MIT-NORTHEASTERN JOINT MATHEMATICS COLLOQUIUM |
LAI-SANG YOUNG (COURANT INSTITUTE) |
Markov towers over chaotic dynamical systems |
Abstract About 10 years ago, I proposed a unified approach for obtaining statistical information on a class of chaotic dynamical systems. The idea is to exchange the inherent messiness of dynamical structures for the relative simplicity of certain countable state Markov chains. This can sometimes be done by constructing a Markov tower over the dynamical system in question, but the construction is not without cost, and the comparison is not perfect after all, dynamical systems are not Markov chains. I would like to report on some of the results that have been obtained since. Via examples, I will address the following two questions (1) what kind of information does the method yield, and (2) for which types of systems has it been fruitful? In relation to (1) I will report on results on rates of correlation decay, large deviations, escape rates and surviving distributions for systems with leaks. As examples of (2) I will discuss billiards and strange attractors arising from the periodic forcing of oscillators." |
December 11, 2008, 430 - 530 pm at Science Center, Hall D |
| NUMBER THEORY SEMINAR |
KATHERINE STANGE (HARVARD UNIVERSITY) |
Elliptic Nets |
Abstract The collection of division polynomials of an elliptic curve form a sequence satisfying a recurrence relation. Evaluated at a fixed curve and point, this becomes a sequence of elements in a field, analogous to (and precisely generalising) Lucas and Fibonacci numbers and their relationship to cyclotomic polynomials. We will generalise this to higher rank arrays, briefly outline the geometric information contained in the sequence or array, and briefly sketch two of the many paths one might follow from her the first is an application to pairing-based elliptic curve cryptography and the second is a natural question about primes which has potential application to Hilbert s Tenth Problem for the rationals." |
December 10, 2008, 3 PM at Science Center, Room 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
R. MUKAMEL (MIT) |
Surfaces with Triangular Veech Groups |
" |
December 10, 2008, 4 pm at Science Center, Room 507 |
| SPECIAL LECTURE |
AVRAHAM AIZENBUD (WEIZMANN INSTITUTE OF SCIENCE) |
Gelfand pairs and invariant distributions |
Abstract First we shall remind the notion of Gelfand pair, and discuss its relevance to classical representation theory harmonic analysis, automorphic forms, and number theory. We shall then discuss the relation between Gelfand pairs and invariant distributions. We shall review some recent results on Gelfand pairs and explain the tools used to prove these results in a simple example $(GL_2, GL_1)$. This talk gives motivation and introduction to a subsequent talk by D. Gurevich on December 10 at the MIT, where the pair $(GL_{n+1}, GL_n)$ will be discussed" |
December 09, 2008, 130 - 230 pm at Science Center, Room 232 |
| DIFFERENTIAL GEOMETRY SEMINAR |
HUAI-DONG CAO (LEHIGH UNIVERSITY) |
Geometry of Gradient Ricci Solitons |
" |
December 09, 2008, 130 - 230 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
SHING TUNG YAU (HARVARD UNIVERSITY) |
Conserved quantities in classical general relativity |
" |
December 08, 2008, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
ANDY NEITZKE (HARVARD UNIVERSITY) |
Wall-crossing formulae and hyperkahler geometry |
" |
December 05, 2008, 330 - 430 pm at Science Center, Room 507 |
| TRIVIAL NOTIONS SEMINAR |
MARYANTHE MALLIARIS (UC BERKELEY) |
Pseudoinfinite Sets |
Abstract The regular ultrapower construction is a lens for looking at the relationship between finite and infinite combinatorics. Ultrapowers produce large generic extensions of a given object which exaggerate certain features and suppress others, but it is a deep question to determine which families of features can be separated in this way. I ll sketch techniques due to Shelah and Kunen for constructing regular ultrapowers which vary the sizes of certain sets and the cuts realized in models of linear orders, and explain the connection to classification theory. Little to no prior knowledge of model theory or ultraproducts will be assumed." |
December 04, 2008, 207 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
DAVID NADLER (NORTHWESTERN UNIVERSITY) |
Constructible Sheaves and the Fukaya Category |
" |
December 04, 2008, 3 - 5 pm at Science Center, Room 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
S. SHEFFIELD (MIT) |
Hamburgers, cheeseburgers, and scaling limits of discrete random surfaces |
" |
December 03, 2008, 4 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
TATHAGATA BASAK (UNIVERSITY OF CHICAGO) |
A Complex hyperbolic reflection group and the bimonster |
Abstract Let R be the reflection group of the complex leech lattice plus a hyperbolic cell. Let D be the incidence graph of the projective plane over the finite field with 3 elements. Let A(D) be the Artin group of D generators of A(D) correspond to vertices of D. Two generators braid if there is an edge between the, other wise they commute. It is surprising that both the bimonster and the reflection group R are quotients of A(D) when the generators are mapped to elements of order 2 and 3 respectively. A conjecture by Daniel Allocock seeks to explain this connection between R and the bimonster. We shall try to explain some of the evidence for the conjecture so far. We shall see that D behaves like the Coxeter-Dynkin diagram for the reflection group R. This imprecise analogy with Weyl groups actually makes our proofs work. There is a parallel story for a quaternionic hyperbolic reflection group where the analogies repeat" |
December 03, 2008, 3 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
JENIA TEVELEV (UNIVERSITY OF MASSACHUSETTS) |
Effective divisors and curves on moduli spaces of curves |
In a joint work with Ana-Maria Castravet, we discovered a sort ofmirror correspondence extremal effective (but not boundary) divisors on the moduli space of stable rational curves with n punctures correspond to maximal degenerations of genus g = n − 3 curves to the union of lines. For example, the non-boundary extremal divisor for n = 6 (the Keel-Vermeiredivisor) corresponds to the degeneration of a genus 3 curve (a plane quartic) to the union of four lines. Related results about extremal effective curveswill also be discussed.correspondence extremal effective (but not boundary) divisors on" |
December 02, 2008, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
SHLOMO STERNBERG (HARVARD UNIVERSITY) |
A report on recent work of Alexeev, Bursztyn and Meinrenken |
" |
December 02, 2008, 430 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
SOPHIE MOREL (INSTITUTE FOR ADVANCED STUDY) |
On the cohomology of certain noncompact Shimura varieties |
" |
November 26, 2008, 3PM at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
BRUNO DE OLIVEIRA (UNIVERSITY OF MIAMI/ VISITING SCHOLAR HARVARD UNIVERSITY) |
Symmetric differentials and the geometry of projective varieties |
Please note this seminar will take place at MIT" |
November 25, 2008, 3 pm at MIT (4-231) |
| DIFFERENTIAL GEOMETRY SEMINAR |
LE DUNG TRANG (ICTP TRIESTE ITALY) |
Rational Polynomials |
Organized by Professor Shing Tung Yau" |
November 25, 2008, 430 pm at Science Center, Room 507 |
| RANDOM MATRIX SEMINARS |
JOE BLITZSTEIN (HARVARD UNIVERSITY STATISTICS DEPARTMENT) |
Random walks on graphs with bottlenecks |
Abstract Random walks on undirected graph give natural, easily visualized examples of Markov chains. Conversely, any reversible Markov chain can be so-represented (with weighted edges). Bounds on how fast the chain converges to its stationary distribution are generally obtained by studying the eigenvalues of the transition matrix. A bottleneck in a graph is a structural feature impeding convergence We will describe approaches to identifying and quantifying bottlenecks, using a local version of the Poincare coefficient. This suggests an adaptive algorithm for obtaining a chain that converges faster, by creating shortcuts that bypass the bottlenecks. Based in part on joint work with Nike Sun" |
November 20, 2008, 310 - 410 pm at Science Center, Room 232 |
| TRIVIAL NOTIONS SEMINAR |
CARL ERICKSON () |
Modular Forms and You |
Abstract Do you wake up each day feeling overwhelmed by arithmetic data? Do your L-functions have a functional equation shaped holes that can t be left empty any longer? Are you getting tired of leaving those enormous symmetry groups just sitting around, doing nothing? Rankin at the bottom of the ladder? Well what the hecke are you waiting for? Modular forms will solve all your problems and lift you to the next level. You ll be fitter, happier, and even more popular. How can you start finding out if modular forms are right for you? Come to our free, no-strings-attached, introductory seminar! We ll explain the most basic contexts in which modular forms arise and describe some things that they re useful for" |
November 20, 2008, 207 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
FUCHENG TAN (MIT) |
Galois Eigenvarieties |
Abstract Kisin constructed the finite slope subspace parameterizing 2-dimensional p-adic Galois representaions of G_Q carrying a non-zero crystalline period, which we proved years later to be the same as the Coleman-Mazur eigencurve. Following him, we define Galois eigenvarieties for arbitrary dimensions and arbitrary number fields, prove that a classical point in a Galois eigenvariety is smooth when the refinement on this point is non-critical. As an application, we prove (under mild condition) that the Galois representation attached to Siegel modular form of weitht 2 is de Rham (at p) if and only if it is Hodge-Tate" |
November 19, 2008, 3 pm at Science Center, Room 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
N. AVNI (HARVARD UNIVERSITY) |
Dynamics on representation varieties -- finite, compact and hyperbolic |
" |
November 19, 2008, 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
CHEN-YU CHI (HARVARD UNIVERSITY) |
Pseudonorms and Birational Equivalence |
Organized by Professor Shing Tung Yau. Please note the change in time and place" |
November 18, 2008, 145 pm at Science Center, Room 232 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
HSIAN-HUA TSENG (UNIVERSITY OF WISCONSIN) |
Hodge integrals on Hurwitz spaces and Gromov-Witten theory of orbifolds |
Abstract Inside moduli spaces of stable pointed curves one can consider loci which parameterizes curves that admit Hurwitz cover structures to over curves. These loci are called Hurwitz loci. Hurwitz-Hodge integrals are by definition integrals over these loci of Chern classes of suitably defined Hodge bundles. Hurwitz-Hodge integrals arise naturally as Gromov-Witten invariants of local orbifolds. In this talk we ll review the definition of Hurwitz-Hodge integral. We ll discuss a result, proven with Paul Johnson and Rahul Pandharipande, which expresses cycle Hurwitz-Hodge integrals with one Hodge class as double Hurwitz numbers." |
November 18, 2008, 3 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
LAUREN WILLIAMS (HARVARD UNIVERSITY) |
What does the non-negative part of a flag variety look like? |
This is a new series in which our senior faculty give talks aimed at first year graduate students who want to get a feel for different areas of research" |
November 17, 2008, 3 PM at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
MATT HEDDEN (MIT) |
On the knot theory of complex and symplectic curves |
" |
November 14, 2008, 330 - 530 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
SHEEL GANATRA () |
Derived Fukaya Categories and Lefschetz Fibrations |
" |
November 13, 2008, 3 - 5 pm at Science Center, Room 507 |
| THE TRIVIAL NOTIONS SEMINAR |
JACK HUIZENGA (HARVARD UNIVERSITY) |
How to Count Like Schubert |
" |
November 13, 2008, 207 pm at Science Center, Room 507 |
| RANDOM MATRIX SEMINARS |
BALINT VIRAG (TORONTO) |
Large gaps between random eigenvalues and the Brownian carousel |
Abstract In the 1950s Wigner suggested modeling atomic nuclei by random matrices. He proposed a formula for the chance of large gaps between eigenvalues. Dyson (1962) improved and generalized this formula for a large class of models called beta ensembles. I will show how random matrix eigenvalues can be described via Brownian motions in the hyperbolic plane. This leads to a proof of modified version of Dyson s predictions via stochastic calculus." |
November 13, 2008, 310 - 410 pm at Science Center, Room 232 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
J. DUNCAN (HARVARD UNIVERSITY) |
Fuchsian groups and affine Dynkin diagrams |
" |
November 12, 2008, 4 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
RALPH GREENBERG (UNIVERSITY OF WASHINGTON) |
Iwasawa Theory and Projective Modules |
" |
November 12, 2008, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
NICOLAOS KAPOULEAS (BROWN UNIVERSITY) |
The Gluing Constructions of Special Lagrangian Cones |
Please notice the change in date. Differential Geometry Seminars are organized by Professor Shing Tung Yau" |
November 10, 2008, 4 pm at SCience Center, Room 507 |
| FACULTY COLLOQUIUM |
CLARK BARWICK (HARVARD UNIVERSITY) |
Schematic Homotopy Types |
" |
November 10, 2008, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
LAWRENCE ROBERTS (MICHIGAN STATE UNIVERSITY) |
Knot Floer homology for fibered knots in double branched covers |
" |
November 07, 2008, 330 - 430 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
MOHAMMED ABOUZAID (MIT) |
Fukaya categories of open lagrangians in cotangent bundles |
" |
November 06, 2008, 3 - 5 pm at Science Center, Room 507 |
| THE TRIVIAL NOTIONS SEMINAR |
KATY KORNER (HARVARD UNIVERSITY) |
A Brief Overview of the Philosophy of Mathematics |
Abstract We will discuss various schools of thought on the nature of mathematical truth. Emphasis will be on the development of mathematical philosophy throughout the last two hundred years, aided by historical anecdotes of dubious origin and accuracy." |
November 06, 2008, 207 pm at Science Center, Room 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
D. FISHER (INDIANA UNIVERSITY, RADCLIFFE INSTITUTE) |
The space of discrete linear groups |
" |
November 05, 2008, 4 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
MARC-HUBERT NICOLE (CENTRE DE MATHEMATIQUES DE JUSSIEU) |
Purity of level m stratifications |
Abstract We will discuss stratifications coming from truncations of Barsotti-Tate groups (also called p-divisible groups), generalizing the Ekedahl-Oort stratification. We will recall some background material about stratifications, explain the hierarchy of purity properties, and describe in detail the situation for level m stratifications. We will illustrate our main result in the case of the Siegel modular varieties, and mention how our techniques apply to good reductions of Shimura varieties of Hodge type. Joint work with A. Vasiu and T. Wedhorn" |
November 05, 2008, 3 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
JAROD ALPER (COLUMBIA UNIVERSITY) |
Constructing Moduli Spaces of Objects with Infinite Automorphisms |
Abstract Moduli problems parameterizing objects with infinite automorphisms (eg. semi-stable vector bundles) often do not admit coarse moduli schemes but may admit moduli schemes identifying certain non-isomorphic objects. In particular, the moduli stack parameterizing such objects is not Deligne-Mumford. I will introduce techniques to study such moduli stacks and address the question of how such moduli schemes can be intrinsically constructed. The crucial ingredient is the notion of a good moduli space for an Artin stack, which generalizes Mumford s geometric invariant theory and characterizes the desired geometric properties of a moduli scheme parameterizing objects with infinite automorphisms" |
November 04, 2008, 300 pm at MIT (4-231) |
| DIFFERENTIAL GEOMETRY SEMINAR |
ARTEM PULEMOTOV (CORNELL UNIVERSITY) |
The Li-Yau-Hamilton Inequalities and the Yang-Mills Heat Equation |
" |
November 04, 2008, 430 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
PETER KRONHEIMER (HARVARD UNIVERSITY) |
Using instantons to see the Thurston norm |
This is a new series in which our senior faculty give talks aimed at first year graduate students who want to get a feel for different areas of research" |
November 03, 2008, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
CAGATAY KUTLUHAN (MICHIGAN STATE UNIVERSITY) |
Seiberg-Witten Floer homology and symplectic forms on S1 Ś M3 |
" |
October 31, 2008, 330 - 430 pm at Science Center, Room 507 |
| RANDOM MATRIX SEMINARS |
MING-JUN LAI (UNIVERSITY OF GEORGIA) |
On Sparsest solutions of underdetermined linear systems |
Abstract . I shall first give a few examples on image compression, noised will be introduced and numerical results will be demonstrated that our approach works very, and cryptography to motivate why we need to find sparsest solution of linear systems and give a short overview for the $\ell_1$ approaches, the greedy algorithms and the $\ell_q$ methods with $0
| October 30, 2008, 310 - 410 pm at Science Center, Room 232 | |
| THE THURSDAY SEMINAR |
CLARK BARWICK (HARVARD UNIVERSITY) |
Floer Homotopy and String Topology |
" |
October 30, 2008, 3 - 5 pm at Science Center, Room 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
R. SCHWARTZ (BROWN, HARVARD) |
Outer billiards and the modular group |
" |
October 29, 2008, 4 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
RACHEL OLLIVIER (HARVARD UNIVERSITY & ECOLE NORMALE SUPERIEURE) |
Mod p representations of p-adic GL(n) and Hecke modules |
Abstract We will review the structure of the (pro-p) Iwahori-Hecke ring of p-adic GL(n) (integral Satake transform, integral Bernstein presentation...) and of its modules with mod p coefficients (and central character). We will then explore some properties of the natural link between those modules and the smooth mod p representations of p-adic GL(n) (with central character), and as far as possible, compare these properties with those of the analogous link in the case of the mod p representations of the associated Chevalley group" |
October 29, 2008, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
TAMAR FRIEDMANN (MIT) |
Orbifold Singularities, The Latke, and Pure Yang-MiIls With Matter |
Organized by Professor Shing Tung Yau" |
October 28, 2008, 430 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
WENCHUAN HU (MIT) |
The topological structure of Chow varieties |
I will discuss the homotopy theoretic methods in the algebraic cycles theory and their applications to Chow varieties. In particular, we will talk about an elementary proof of Lawson-Yau formula on the Euler characteristic as well as its generalization. We also compute some homotopy and homology groups of Chow varieties. This leads to a negative answer to a question of Lawson-Michelsohn on algebraic cycles of a fixed degree in complex projective spaces." |
October 28, 2008, 3 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
JOE HARRIS (HARVARD UNIVERSITY) |
The interpolation problem |
This is a new series in which our senior faculty give talks aimed at first year graduate students who want to get a feel for different areas of research" |
October 27, 2008, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
MIKHAIL KHOVANOV (COLUMBIA UNIVERSITY) |
How to categorify one-half of a quantum group |
Today s Gauge Theory and Topology Seminar is cancelled" |
October 24, 2008, 330 - 430 pm at Science Center, Room 507 |
| RANDOM MATRIX SEMINARS |
A. HARROW (MIT) |
Random matrices in quantum information theory |
Abstract Quantum information theory contains many surprising phenomenon that are not present in Shannon s classical information theory. Two examples are data hiding, in which a secret message is distributed to two parties who cannot access the message if they only communicate classically; and the recent counter-example to the long-standing additivity question, which shows that the best codes for quantum channels need to use entanglement. In these examples, and many others, random matrices are used for either the best-known or the only constructions. My talk will explain the quantum information background, survey the application of random matrices and identify open problems. Some of the work it reviews can be found in arXivquant-ph/0307104, arXivquant-ph/0407049 andarXiv0809.3972" |
October 23, 2008, 310 - 410 pm at Science Center, Room 232 |
| THE THURSDAY SEMINAR |
JACOB LURIE (MIT) |
The Fukaya category II |
Abstract I will discuss some aspects of the definition of the Fukaya category, with particular emphasis on the Lagrangian Grassmannian and its role in coherently orienting the relevant moduli spaces" |
October 23, 2008, 3 - 5 pm at Science Center, Room 507 |
| MATH COLLOQUIUM |
MIKHAIL KHOVANOV (COLUMBIA UNIVERSITY) |
Categorification of quantum groups |
Abstract In 1990 Beilinson, Lusztig, and MacPherson defined an idempotented form of quantum sl(n). I ll discuss a joint work with Aaron Lauda on categorification of quantum sl(n) and explain the conjectural role of this categorification in representation theory." |
October 23, 2008, 430 pm at Science Center, Hall D |
| THE TRIVIAL NOTIONS SEMINAR |
THOMAS BARNET-LAMB (HARVARD UNIVERSITY) |
How to Vote |
Abstract With the November elections approaching, our minds naturally turn to voting problems. This talk will be a smorgasbord of topics connected by this common theme. For example, I will talk about Arrow s theorem, which shows that if there are more than two possible outcomes, designing a reasonable voting system is not possible with a finite population. Applications or otherwise to contemporary politics will not be covered" |
October 23, 2008, 207 pm at SCience Center, Room 507 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
C. MCMULLEN (HARVARD UNIVERSITY) |
Brad groups and Hodge theory |
" |
October 22, 2008, 4 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
MARK BEHRENS (MIT) |
Orientations and Eisenstein series |
Abstract Using a theorem of Jacob Lurie, Tyler Lawson and I have associated cohomology theories of topological automorphic forms (TAF) to certain unitary Shimura varieties. These cohomology theories generalize the theory of topological modular forms (TMF). Mike Hopkins and his collaborators were able to show that TMF admitted a cannonical string(MO<8>) orientation. Their construction rested on the p-adic interpolation of the classical eisenstein series (due to Katz). In this talk I will describe the current state of affairs of a joint project with Hopkins to find orientations of the TAF theories. I will explain how orientations are related to p-adic L-functions. Our attempts are related to the existence and properties of the p-adic interpolation of scaler valued Eisenstein series on the associated shimura varieties" |
October 22, 2008, 3 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
NIR AVNI (HARVARD UNIVERSITY) |
Motivic Integration |
This is a new series in which our senior faculty give talks aimed at first year graduate students who want to get a feel for different areas of research" |
October 20, 2008, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
KATRIN WEHRHEIM (MIT) |
Lagrangian correspondences and holomorphic quilts |
" |
October 17, 2008, 330 - 430 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
MICHAEL HOPKINS (HARVARD UNIVERSITY & ECOLE NORMALE SUPERIEURE) |
Preliminary construction of the Fukaya category |
Abstract I plan to sketch the construction of the Fukaya category in a simplified situation, following the treatment in chapter 9 of Seidel s book Fukaya Categories and Picad-Lefschetz Theory" |
October 16, 2008, 3 - 5pm at Science Center, Room 507 |
| RANDOM MATRIX SEMINARS |
S. SHEFFIELD () |
Liouville Quantum Gravity and KPZ |
Abstract Brownian motion is a random path, but what is the most natural way to define a random two dimensional Riemannian manifold? I will give both physical and mathematical answers to this question. I will also explain a recent proof, joint with Bertrand Duplantier, of the so called KPZ formula, which relates the scaling dimensions of random fractals on random surfaces with the dimensions of analogously defined random fractals Euclidean surfaces." |
October 16, 2008, 310 - 410 pm at Science Center, Room 232 |
| INFORMAL DYNAMICS AND GEOMETRY SEMINAR |
CURT MCMULLEN (HARVARD UNIVERSITY) |
Random walks on the hyperbolic plane and barycentric subdivision |
" |
October 15, 2008, 4 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
JOEL BELLAICHE (COLLUMBIA UNIVERSITY) |
Endoscopic tempered points on unitary eigenvarieties. |
Abstract {\it Unitary Eigenvarieties} are the universal families parameterizing the p-adic automorphic forms on unitary groups. Due to recent progresses on the Langlands program for those groups, the unitary eigenvarieties are now known to carry a family of Galois representations, which is worth studying, especially near points whose attached Galois representation is reducible. When those points are classical, that is, correspond to automorphic forms, they come in two types tempered and non-tempered. The non-tempered points are closely related to the Bloch-Kato conjecture, and have been the object of an ongoing series of works by various people, leading to new cases of that conjecture. In this talk, I will focus on tempered points. It turns out that the geometry of the eigenvariety near those points can be completely described, unlike the non-tempered case. I will explain how, and deduce some surprising consequences on Galois cohomology that are related not to Bloch-Kato s conjecture, but to the Jannsen s conjecture" |
October 15, 2008, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
LIMING GE (UNIVERSITY OF NEW HAMPSHIRE) |
Kadison-Singer Algebras |
Organized by Professor Shing Tung Yau" |
October 14, 2008, 430 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
MIKIO FURUTA (UNIVERSITY OF TOKYO AND MIT) |
Torus fibration and localization of Riemann-Roch number |
" |
October 10, 2008, 330 - 430 pm at Science Center, Room 507 |
| TRIVIAL NOTIONS SEMINAR |
AARON SILBERSTEIN (HARVARD UNIVERSITY) |
Intersection Homology Saving Poincare' Duality |
" |
October 09, 2008, 207 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
CURTIS MCMULLEN (HARVARD UNIVERSITY) |
Diophantine numbers in a fixed real quadratic field and Poincaré's periodic portrait |
" |
October 08, 2008, 3PM at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
VALENTINO TOSATTI (HARVARD UNIVERSITY) |
Kahler-Ricci flow and stability |
Please notice the change in hour and place for this time only" |
October 07, 2008, 400 - 500 pm at Science Center, Room 232 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
AMNON YEKUTIELI (BEN GURION UNIVERSITY) |
Twisted Deformation Quantization of Algebraic Varieties |
Abstract Let X be a smooth algebraic variety over a field of characteristic 0, endowed with a Poisson bracket. A quantization of this Poisson bracket is a formal associative deformation of the structure sheaf OX, which realizes the Poisson bracket as its first order commutator. More generally one can consider Poisson deformations of OX and their quantizations. I will explain what these deformations are. Then I ll state a theorem which says that when X is affine, there is a canonical quantization map (up to gauge equivalence). This is an algebro-geometric analogue of the celebrated result of Kontsevich (which talks about differentiable manifolds). In the second half of the lecture I ll talk about twisted Poisson deformations, and twisted associative deformations (aka stacks of algebroids). We recently proved that there is a canonical twisted quantization map, and I will describe this result. I will end with a question regarding twisted quantization of symplectic Poisson brackets. Some of this work is joint with F. Leitner" |
October 07, 2008, 3 pm at MIT (4-231) |
| FACULTY COLLOQUIUM |
CLIFF TAUBES (HARVARD) |
Inexpensive quantum field theories |
" |
October 06, 2008, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
CLARK BARWICK (HARVARD) |
The Rognes approach to the algebraic K-theory of the sphere spectrum |
" |
October 03, 2008, 330 - 430 pm at Science Center, Room 507 |
| RANDOM MATRIX SEMINARS |
A. EDELMAN (MIT) |
The Random Matrix Technique of Ghosts and Shadows |
Abstract On and off, I have been interested in novel computational approaches in random matrix theory for theoretical and practical use. I will review a few of my favorites, and then discuss current work on realizing schemes that include reals, complexes, and quaternions as special cases in the hopes of getting to the bottom of some key random matrix facts as well as building useful numerical approaches" |
October 02, 2008, 310 - 410 pm at Science Center, Room 232 |
| THE THURSDAY SEMINAR |
ANATOLY PREYGEL (HARVARD UNIVERSITY) |
A_infinity, associahedra, and little disks |
" |
October 02, 2008, 3 - 5 pm at Science Center, Room 507 |
| TRIVIAL NOTIONS SEMINAR |
ERIC WOFSEY () |
How I Learned to Stop Worrying and Love Transfinite Induction |
Abstract Many mathematicians think of transfinite induction as some spooky incomprehensible unconstructive device frought with logical technicalities. In reality, ordinal numbers, much like puppies, are warm fuzzy cuddly creatures that make your dreams come true! In this talk I ll explain how transfinite induction works, why it s more natural than Zorn s lemma, and how you can use transfinite induction even if you don t like the axiom of choice. I ll also show how tranfinite induction can turn naive intuitions into rigorous proofs of the intermediate value theorem and related results." |
October 02, 2008, 207 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
TOBY GEE (HARVARD UNIVERSITY) |
The conjectural relationship between Galois representations and automorphic |
Abstract We discuss joint work with Kevin Buzzard, in which we formulate conjectures relating automorphic representations and Galois representations in maximal possible generality, generalising work of Clozel and Gross" |
October 01, 2008, 3PM at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
SABIN CAUTIS (RICE UNIVERSITY) |
Equivalences from Geometric sl2 Actions |
Abstract We explain how sl2 actions on derived categories of coherent sheaves can be used to construct new derived equivalences. The examples I will describe in detail is an sl2 action via correspondences on the cotangent bundles of Grassmannians which generalizes the basic Mukai flop. More generally we can construct an action on the derived category of coherent sheaves on quiver varieties which lifts Nakajima s action on their cohomology. (joint with Joel Kamnitzer and Anthony Licata" |
September 30, 2008, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
WEI SONG (HARVARD UNIVERSITY PHYSICS DEPARTMENT) |
Quantum gravity in Three Dimensions |
Sponsored by Professor Shing Tung Yau" |
September 30, 2008, 430 - 530 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
DENNIS GAITSGORY (HARVARD) |
Geometric representation theory |
" |
September 29, 2008, 3 pm at Science Center, Room 507 |
| GUAGE THEORY AND TOPOLOGY |
GIOVANNI FORNI (UNIVERSITY OF MARYLAND) |
On the Greenfield-Wallach and Katok conjectures |
" |
September 26, 2008, 330 - 430 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
DENIS AUROUX (MIT) |
An overview of Lagrangian Floer homology |
" |
September 25, 2008, 3 - 5 pm at Science Center, Room 507 |
| RANDOM MATRIX COURSE AND SEMINARS |
VAHID TAROKH (DEAS, HARVARD) |
Shannon Theoretic Approach to Sparse Representation, Sparse Signal detection and Compressed Sampling |
We consider approximations of signals by the elements of a redundant frame/dictionary of size M>=N in a complex vector space of dimension N and formulate both the noiseless and the noisy sparse representation problems. The noiseless representation problem is to find sparse reresentations of a signal r given that such representations exist. First we construct a frame, referred to as the Vandermonde frame, for which the noiseless sparse representaion problem can be solved uniquely using O(N^2) operations, as long as the number of non-zero coefficients in the sparse representaion of r is L=\epsilon N for some 0<= epsilon <=0.5. It is known that epsion <= 0.5 can not be relaxed without violating uniqueness. This improves significantly on a construction of Candes and Tao based on random matrices. The noisy sparse representation problem is to find sparse representations of a signal r satisfying a distortion criterion. In this case, we establish a lower bound on the trade-off between the sparsity of the representation, the underlying distortion and the redundancy of any given frame. We then study an associated problem, namely the number of measurements required to recover a sparse signal in C^M with L non-zero coefficients from it s compressed samples in the presence of noise. For a number of different recovery criteria, we prove that O(L) (an asymptotically linear multiple of L) measurements are necessary and sufficient if L grows linearly as a function of M. This improves on the existing literature that is mostly focused on variants of a specific recovery algorithm based on convex programming, for which O(L log(M ? L)) measurements are required (e.g. results due to Tibshirani, Donoho, Candes and Tao). We also show that O(L log(M ? L)) measurements are required in the sublinear regime (L = o(M)). Finally, we discuss detection of sparse parameters in the presence of noise. We show that the lack of knowledge of the location of sparse elements do not cause any asymptotic mean square error penalties, contrary to common belief in the literature. This is a joint work with Mehmet Akcakaya and Behtash Babadi" |
September 25, 2008, 310 pm at Science Center, Room 232 |
| TRIVIAL NOTIONS SEMINAR |
YI LI () |
Combinatorics of Hodge Integrals |
Abstract I will give an introduction to the combinatorial aspects of Hodge integrals over the moduli space of curves, including the famous Faber intersection numbers recently proved by K. Liu and H. Xu" |
September 25, 2008, 207 PM at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
TAKAYUKI ODA (UNIVERSITY OF TOKYO) |
Spherical functions of chomological automprphic forms, case sudies for the groups $Sp(2,\mathbf{R})$ and $SU(2,2)$ |
Abstract In spite that we had the Matsushima isomorphism long time ago (in 60 s), we can derive little substances from that except for general results for cohomological representations of real semisimple Lie groups. And even this archemedean part of cohomological automorphic forms is not understood deeply yet. We take the cases of Siegel modular varieties of genus 2, or Hermitian modular varieties of type (2+2-), to review some effectively computable results on spherical functions, especially the matrix coefficeints of discrete series representations of $Sp (2,\mathbf{R})$ or $SU(2,2)$" |
September 24, 2008, 3PM at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
JANOS KOLLAR (PRINCETON) |
Cremona transformations and homeomorphisms of topological surfaces |
Joint work with Frederic Mangolte" |
September 23, 2008, 3 pm at MIT (4-231) |
| SPECIAL LECTURE AT HARVARD |
HEISUKE HIRONAKA () |
Resolution of Singularities of Algebraic varieties over characteristic p |
" |
September 22, 2008, 9 AM at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
PAUL SEIDEL () |
Introduction to the Fukaya category |
Abstract This semester the Thursday Seminar will focus on the Fukaya category. The first talk will be an introduction and overview of the subject." |
September 18, 2008, 3 - 5 pm at Science Center, Room 507 |
| RANDOM MATRIX COURSE AND SEMINARS |
JOSE RAMIREZ (UNIVERSIDAD DE COSTA RICA AND HARVARD) |
Diffusion limits of eigenvalues of random matrices |
Abstract We discuss the behavior of the distribution of the edge eigenvalues for beta-ensembles when the matrices get large. First, we talk about the convergence of the soft-edge eigenvalues to the eigenvalues of a certain stochastic Airy operator acting on the half line. This allows for a description in terms of explosion times according to the Ricatti Correspondence. Second, we will talk about more recent work on the limit of the hard-edge eigenvalues to a stochastic Bessel operator. Again this allows for a drescription in terms of explosion times. The methods used in each proof are different. This is a joint work with B. Rider and B. Virag" |
September 18, 2008, 310 - 410 pm at Science Center, Room 232 |
| NUMBER THEORY SEMINAR |
FLORIAN HERZIG (NORTHWESTERN UNIVERSITY) |
Weight Cycling and Serre-type Conjectures |
Abstract Suppose that rho is a three-dimensional modular mod p Galois representation whose restriction to the decomposition groups at p is irreducible and generic. If rho is modular in some (Serre) weight, then a representation-theoretic argument shows that it also has to be modular in certain other weights (we can give a short list of possibilities). This goes back to an observation of Buzzard for GL_2. Previously we formulated a Serre-type conjecture on the possible weights of rho. Under the assumption that the weights of rho are contained in the predicted weight set, we apply the above weight cycling argument to show that rho is modular in precisely all the nine predicted weights. This is joint work with Matthew Emerton and Toby Gee" |
September 17, 2008, 3 PM at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
MARK GROSS (UNIVERSITY OF CALIFORNIA SAN DIEGO) |
Mirror symmetry for P^2 and tropical geometry |
Organized by Professor Shing-Tung Ya" |
September 16, 2008, 430 pm at Science Center, Room 507 |
| ALGEBRAIC GEOMETRY SEMINAR |
DAVID SPEYER (MIT) |
Positroid Varieties - a Beautiful Stratification of the Grassmannian |
George Lusztig and Alex Postnikov have studied those points on the Grassmannian all of whose Plucker coordinates are nonnegative, and found that they can be grouped into strata indexed by combinatorial objects called positroids. We follow these positroids into the rest of the Grassmannian and find that their Zariski closures form an elegant stratification which refines the classical stratification into Schubert cells. In particular, the strata are Cohen-Macaulay and normal, are defined by explicit equations and have expicit Grobner degenerations. Studying the cohomology classes of these varieties gives geometrical meaning to Stanley s symmetric functions and Postnikov s toric Schur functions. Joint work with Allen Knutson and Thomad Lam" |
September 16, 2008, 3 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
BENEDICT GROSS (HARVARD UNIVERSITY) |
Integral zeta values and the number of automorphic representations |
Abstract Euler proved that the values of Zeta(s)* (1 - 2^(1-s)) at negative integers are elements of the ring Z[1/2]. Cassou-Nogues and Deligne/Ribet generalized this to an integrality result for the values of arbitrary partial zeta functions at negative integers. I will review their results, and show how these special values can be used to compute the number of irreducible automorphic representations of G with prescribed local behavior, where G is a simple group over a global field k. Via the global Langlands correspondence for k = F(t), I will compare this result with work of Katz and Deligne on Kloosterman sheaves. This is joint work with Mark Reeder" |
September 10, 2008, 3PM at Science Center, Room 232. Please notice change of place for this Wednesday only. |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
MARK GROSS (UC SAN DIEGO) |
Mirror symmetry via degenerations |
I will give a (hopefully gentle) overview of my program with Bernd Siebert to understand mirror symmetry via degenerations of Calabi-Yau manifolds to unions of toric varieties. I will try to explain what the current state of the program is, and show why we expect it to be a powerful tool for proving many different aspects of mirror symmetry" |
September 09, 2008, 3 pm at MIT (4-231) |
| DIFFERENTIAL GEOMETRY SEMINAR |
KWOK WAI CHEN (HARVARD UNIVERSITY) |
SYZ Mirror Transformation |
" |
September 09, 2008, 430 PM at Science Center, Room 232. PLEASE NOTICE THE CHANGE IN PLACE THIS TIME ONLY. |
| DIFFERENTIAL GEOMETRY SEMINAR |
JENS HOPPE (KTH STOCKHOLM) |
Membrane Equations and Singularities |
" |
June 06, 2008, 4 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
TOSHIYUKI KOBAYASHI (TOKYO AND HARVARD) |
Restriction of unitary representations of real reductive groups |
Abstract Branching problems ask how an irreducible representation of a group decomposes when restricted to its subgroup. Having an observation of bad features of branching problems in a general non-compact setting even for real reductive symmetric pairs, I will discuss how to find a nice setting for branching problems, and give an upper estimate on multiplicities. If time allows, some applications are also presented" |
May 28, 2008, 3 - 4 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
KIRAN S. KEDLAYA (MIT) |
Semistable reduction for overconvergent F-isocrystals |
Abstract As part of Berthelot s program for constructing a theory of coefficients in p-adic cohomology one repeatedly encounters the following problem given an overconvergent F-isocrystal on variety X, show that one can pull back along an alteration to get an F-isocrystal which extends (with logarithmic singularities) to some proper variety. This amounts to eliminating some monodromy obstruction along all divisors on all blowups of X. We describe our recent solution of this problem, using a valuation-theoretic approach to reduce to a local calculation in relative dimension 1" |
May 21, 2008, 3 - 4 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
MARK REEDER (BC) |
Pro-p-Sylow subgroups and supercuspidal representations |
Abstract We construct supercuspidal representations of a reductive p-adic group using the pro-p-Sylow subgroup of an Iwahori subgroup. We then give implications for the corresonding Langlands parameters, based on the formal degree conjecture of Hiraga-Ichino-Ikeda. This is joint work with Benedict Gross" |
May 14, 2008, 3 - 4 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
GORDAN SAVIN (UTAH) |
On the inverse problem in Galois theory |
I will discuss some aspects of recent joint work with C. Khare and M. Larsen which uses l-adic representations attached to automorphic forms to construct Galois groups of Lie type over the rational numbers" |
May 07, 2008, 3 - 4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
PAOLO CASCINI (UC SANTA BARBARA) |
On the Minimal Model Program |
Abstract The aim of the Minimal Model Program is to generalize the classification of complex projective surfaces, known in the early 20th century, to higher dimensional varieties. Besides providing a historical introduction, we will discuss some recent results and new aspects of this program" |
May 06, 2008, 3 pm at MIT (4-149) |
| BRANDEIS-HARVARD-MIT-NORTHEASTERN JOINT MATHEMATICS COLLOQUIUM |
RICHARD HAMILTON (COLUMBIA UNIVERSITY) |
Geometry of the Ricci flow |
Tea in the Common Room 4 - 430 p" |
May 01, 2008, 430 - 530 pm at Science Center, Hall D |
| THE THURSDAY SEMINAR |
MIKE HOPKINS (HARVARD) |
State sums and 2 dimensional topological field theories (ctd) |
" |
May 01, 2008, 3 - 5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
ANDREA MILLER (HARVARD) |
Chow motives of some mixed Shimura varieties |
Abstract We prove an absolute Chow-Kuenneth decompositions for universal families over some compact unitary Shimura surfaces, thus proving a strengthening (conjectured by J.Murre) of Grothendieck s conjecture C in these cases" |
April 30, 2008, 3 - 4 pm at Science Center, Room 507 |
| SPECIAL EVENT |
A FILM BY AGNES HANDWERK AND HARRIE WILLEMS () |
Wolfgang Doeblin- a mathematician rediscovered |
Abstract The documentary The film shows the biography of Wolfgang Doeblin, the intriguing history of his sealed letter with the manuscript, his mathematics, the Brownian motion and the applications in the financial world. It documents scientific and human aspects of the amazing discovery of the manuscript and throws new light on the startling circumstances of Doeblin s death at the age of 25. The film takes almost 1 hour. In a second independent part prof. Marc Yor explains the manuscript" |
April 30, 2008, 415 PM at Maxwell Dworkin G115, Harvard University |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
MIKE ROTH (QUEEN'S UNIVERSITY) |
Cup products for line bundles on complete flag varieties |
" |
April 29, 2008, 3 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
DAVID JERISON (MIT) |
Free boundary problems |
This is a new series in which our senior faculty give talks aimed at first year graduate students who want to get a feel or different areas of researc" |
April 28, 2008, 3 PM at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
ROSA SENA-DIAS (MIT) |
Spectral measure and asymptotics of algebraic metrics on toric varieties |
" |
April 25, 2008, 330 - 430 PM at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
MIKE HOPKINS (HARVARD) |
State sums and 2 dimensional topological field theories |
" |
April 24, 2008, 3 - 5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMNAR |
ROBERT POLLACK (BU) |
Stickelberger elements of non-ordinary modular forms |
Abstract In this talk, we will discuss progress on attaching analytic Iwasawa invariants to modular forms with non-ordinary reduction at some prime p. We proceeed by making a systematic study of congruences between the associated Stickelberger elements." |
April 23, 2008, 3 - 4 PM at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
ALESSANDRO TOMASIELLO (HARVARD) |
Generalized Complex Geometry and String Vacua |
Organized by Professor Shing-Tung Ya" |
April 22, 2008, 430 PM at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
JAMES BORGER (AUSTRALIAN NATIONAL UNIVERSITY & UNIVERSITY OF CHICAGO) |
Witt vectors, Lamb da-rings, and absolute algebraic geometry |
I will explain how the closely related concepts of Witt vector and Lambda-ring give rise to a kind of algebraic geometry that is , in a precise sense, over a deeper base than the ring of integers. I will also say something about how this relates to other issues in arithmetic algebraic geometry" |
April 22, 2008, 3 pm at MIT (4-149) |
| FACULTY COLLOQUIUM |
WILFRIED SCHMID (HARVARD) |
L-Functions and functional equations |
" |
April 21, 2008, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
RON STERN (UNIVERSITY OF CALIFORNIA AT IRVINE) |
Reverse engineering 4-manifolds |
" |
April 18, 2008, 330 - 430 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
BRIAN MUNSON (HARVARD) |
Higher order linking & the Blakers-Massey theorem II |
" |
April 17, 2008, 3 - 5 pm at Science Center, Room 507 |
| BRANDEIS-HARVARD-MIT-NORHTEASTERN JOINT MATHEMATICS COLLOQUIUM |
RONALD STERN (UNIVERSITY OF CALIFORNIA, IRVINE) |
4-manifolds, big and small |
Tea is from 400 to 430" |
April 17, 2008, 430 - 530 pm at Science Center, Hall D |
| MATHEMATICS EDUCATION SEMINAR SERIES |
WILFRIED SCHMID (HARVARD) |
Current Trends in US K-12 Mathematics Education, as Exemplified by TERC's Investigations' Program |
Professor Schmid is also a member of the National Mathematics Advisory Panel" |
April 17, 2008, 1 - 2 pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
DINESH THAKUR (IAS) |
Multi-zeta and related structures in function field arithmetic |
Abstract We will discuss algebraic relations between gamma, zeta and multi-zeta values and related structures such as mixed motives and Ihara power series" |
April 16, 2008, 3 - 4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
CONCETTINA GALATI (UNIVERSITY OF CALABRIA) |
Degenerating curves and surfaces first results and applications to enumerative geometry of curves on surfaces |
" |
April 15, 2008, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
MARCO GUALTIERI (MIT) |
Constructions of Generalized Kaehler Metrics |
Organized by Professor Shing-Tung Yau" |
April 15, 2008, 430 PM at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
CUMRUN VAFA (HARVARD) |
Topological Strings |
This is a new series in which our senior faculty give talks aimed at first year graduate students who want to get a feel for different areas of research" |
April 14, 2008, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
YONGBIN RUAN (UNIVERSITY OF MICHIGAN) |
Written equation and its moduli theory |
" |
April 11, 2008, 330 - 430 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
BRIAN MUNSON (HARVARD) |
Higher order linking & the Blakers-Massey theorem |
" |
April 10, 2008, 3 - 5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
OLIVER BULTEL (HEIDELBERG) |
PEL moduli spaces without C-valued points |
Abstract We give several moduli interpretations of the fibres of certain Shimura varieties over several prime numbers. As a corolary we obtain that for every prescribed odd prime characteristic p every symmetric Hermitian domain possesses quotients by congruence subgroups whose canonical models have potentially good reduction at p" |
April 09, 2008, 3 - 4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
RAGNI PIENE (UNIVERSITY OF OSLO) |
Classifying lattice polytopes via toric fibrations |
A recent conjecture of Batyrev and Nill concerns lattice polytopes without interior points. In joint work with Alicia Dickenstein and Sandra Di Rocco we give a proof in the case of regular polytopes, by linking such polytopes to toric fibrations" |
April 08, 2008, 3 pm at MIT (4-149) |
| DIFFERENTIAL GEOMETRY SEMINAR |
GIORGIOS DASKALOPOULOS (BROWN UNIVERSITY) |
Harmonic Maps Between Singular Spaces |
Organized by Professor Shing-Tung Yau" |
April 08, 2008, 430 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
ALBERTO DE SOLE (HARVARD) |
Hamiltonian equation, their integrals of motion and related algebraic structure. |
" |
April 07, 2008, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
ANDRAS STIPSICZ (COLUMBIA) |
Invariants of Legendrian knots in Heegaard Floer homology |
" |
April 04, 2008, 330 - 430 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
TOM GOODWILLIE (HARVARD) |
What is pseudoisotopy? (Part 3) |
" |
April 03, 2008, 3 - 5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
NOAM ELKIES (HARVARD) |
Genus-2 Jacobians with real multiplication via K3 surfaces |
Abstract We use K3 surfaces of Picard number at least 18 to parametrize genus-2 curves whose Jacobians have real multiplication. This approach goes considerably beyond what has been done with more direct constructions. For instance, we find some genus-2 curves over Q whose Jacobians have endomorphisms by the ring of algebraic integers in Q(sqrt(53))" |
April 02, 2008, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
STEPHEN YAU (UNIVERSITY OF ILLINOIS - CHICAGO) |
Classification of Weighted dual graphs with only complete intersection singularities structures |
Organized by Professor Shing-Tung Ya" |
April 01, 2008, 430 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
CRISTIAN GONZALEZ MARTINEZ (TUFTS UNIVERSITY) |
The Hodge-Poincare' polynomial of the moduli space of stable vector bundles |
" |
April 01, 2008, 3 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
MIKE HOPKINS (HARVARD) |
Algebraic topology and topological field theories |
This is a new series in which our senior faculty give talks aimed at first year graduate students who want to get a feel for different areas of research" |
March 31, 2008, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
MAKSIM LIPYANSKI (MIT) |
A semi-infinite cycle construction of Floer homology |
" |
March 21, 2008, 330 - 430 pm at Science Center, Room 507 |
| THE MATHEMATICS EDUCATION SEMINAR SERIES |
TOM JUDSON (HARVARD) |
High School Calculus in Japan and the United States |
Abstract Is High School Calculus in Japan different than high school calculus in the U.S ? How do high school calculus students from both countries compare? We examined and interviewed above average high school calculus students from Japan and the United States in order to determine any differences in their conceptual undestanding of calculus and their ability to use algebra to solve traditional claculus problems. We will discuss the Japanese high school curriculum, some of our findings from the study, and the problems that we encountered in doing a cross-cultural investigation of Japanese and American calculus students. We will also present pans for future research" |
March 20, 2008, 3 - 4 pm at Science Center, Room 530 |
| THE THURSDAY SEMINAR |
TOM GOODWILLIE (HARVARD) |
What is pseudoisotopy? (Part 2) |
" |
March 20, 2008, 3 - 5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
KAI-WEN LAN (HARVARD) |
Arithmetic compactifications of PEL-type Shimura varieties |
Abstract In this lecture, we will try to explain the essential ingredients in the construction of toroidal and mininal compactifications of smooth integral models of (general) PEL-type Shimura varieties, following the approaches of Faltings and Chai. Since this is rather an archaic problem, the goal will be to identify the main difficulties that are absent in the special cases worked out in the literature, and to explain why there could be a uniform solution to such difficulties." |
March 19, 2008, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
MU-TAO WANG (COLUMBIA UNIVERSITY) |
Isometric Embeddings and Quasi-Local Mass |
Organized by Professor Shing-Tung Yau" |
March 18, 2008, 430 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
FRED VAN DER WYCK (HARVARD) |
Moduli of curves with prescribed normalization and singularities |
Deligne and Mumford s stable curves are not the only singular curves which can be used to compactify the moduli spac eof smooth curves. Understanding alternative compactifications (such as those of Schubert, Hassett-Hyeon and Smyth) involves studying the deformation theory of singular curves. We will begin this talk by discussing that theory and its practice. This will lead us to define and analyze moduli spaces of curves with prescribed normalization and singularities, and then to consider possible compactifications of these spaces" |
March 18, 2008, 3 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
TOSHIYUKI KOBAYASHI (HARVARD) |
Existence Problem of Compact Locally Symmetric Spaces |
Abstract The local to global study of geometries was a major trend of 20th century geometry, with remarkable developments achieved particularly in Riemannian geometry. In contrast, in areas such as Lorentz geometry, familiar to us as the space-time of relativity theory, and more generally in pseudo-Riemannian geometry, as well as in various other kinds of geometry (symplectic, complex geomery,...), surprising little is known about global properties of the geomery even if we impose a locally homogeneous structure. I plan to give an exposition on the recent developments on the question about how the local geometric structure affects the global nature of non-Riemannian manifolds, with emphasis on the existence problem of compact forms, rigidity and deformation" |
March 17, 2008, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
VERONIQUE GODIN (HARVARD) |
Applications of string topology |
" |
March 14, 2008, 330 - 430 pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
LASZLO SZEKELYHIDI (UNIVERSITY OF DEBRECEN HUNGARY) |
Spectral Analysis and Spectral Synthesis |
" |
March 13, 2008, 4 pm at Science Center, Room 232 |
| THE THURSDAY SEMINAR |
TOM GOODWILLIE (HARVARD) |
What is pseudoisotopy? (Part 2) |
Cancelled." |
March 13, 2008, 3 - 5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
MICHAEL HARRIS (JUSSIEU) |
Endoscopic transfer and theta correspondences for close unitary groups |
Abstract The stabilization of the trace formula for unitary groups includes the construction of the endoscopic transfer from the group U(a)xU(b) to U(a+b). When b =1, the theta correspondence provides an alternative and more intuituve construction of this transfer" |
March 12, 2008, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
JIXIANG FU (FUDAN UNIVERSITY P. R. CHINA) |
Solving the strominger system for non-kahler complex manifolds |
This seminar is organized by Professor Shing-Tung Ya" |
March 11, 2008, 430 pm at Science Center, Room 507 |
| HARVARD- MIT ALGEBRAIC GEOMETRY SEMINAR |
KLAUS HULEK (UNIVERSITY OF HANNOVER) |
Moduli of polarized symplectic manifolds |
Abstract In many ways irreducible symplectic manifords behave similar to K3-surfaces, although it is known that the global Torelli theorem fails in general. Nevertheless, it is possible to relate moduli spaces of polarized irreducible symplectic manifolds to quotients of type IV domains by an arithmetic group. We analyse the situation and prove that certain moduli spaces of polarized irreducible symplectic manifolds are of general type. This is joint work with V. Gritsenko and G.K. Sankaran" |
March 11, 2008, 3 pm at MIT ( 4-149) |
| FACULTY COLLOQUIUM |
BEN WEINKOVE (HARVARD) |
The Calabi-Yau equation |
This is a new series in which our senior faculty give talks aimed at first year graduate students who want to get a feel for different areas of researc" |
March 10, 2008, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
MIKE HOPKINS (HARVARD) |
Algebraic topology of topological fields |
" |
March 07, 2008, 330 - 430 pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
TOM GOODWILLIE (HARVARD) |
What is pseudoisotopy |
Please notice the change in time just for this week only. Abstract Spaces of pseudoisotopies come up in the effort to understand the homotopy types of spaces of automorphisms of manifolds. I will survey some of the high points of this subject, including the fact that, by an argument involving algebraic K-theory, the space of diffeomorphisms of an n-sphere is rationally different from the Lie group O(n+1) except for small values of n" |
March 06, 2008, 330 - 530 pm at Science Center, Room 507 |
| SPECIAL ANALYSIS SEMINAR |
ZHIGANG SUO (SCHOOL OF ENGINEERING AND APPLIED SCIENCES, HARVARD.) |
Mechanics of soft active materials |
" |
March 06, 2008, 230 - 330 pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
PETER MARCH (DIRECTOR OF THE NSF DIVISION OF MATHEMATICAL SCIENCES.) |
An overview of NSF Division of Mathematical Sciences |
Abstract I will present a synopsis of activities supported by DMS; provide relevant budget and award information; and also discuss the context and prospects for federal funding of the mathematical sciences" |
March 05, 2008, 4 - 5 pm at Maxwell Dworkin 115 |
| NUMBER THEORY SEMINAR |
SUG WOO SHIN (IAS) |
Galois representations arising from some compact unitary Shimura varieties |
" |
March 05, 2008, 3 - 4 PM at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
JOHN LOFTIN (RUTGERS UNIVERSITY) |
Affine Hermitian-Einstein Metrics |
Organized by Professor Shing-Tung Ya" |
March 04, 2008, 430 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
STEVEN KLEIMAN (MIT) |
The Canonical model of a singular curve |
" |
March 04, 2008, 3 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
MARTIN NOWAK (HARVARD) |
Evolutionary dynamics |
This is a new series in which our senior faculty give talks aimed at first year graduate students who want to get a feel for different areas of researc" |
March 03, 2008, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
ANDREEA NICOARA (HARVARD) |
Equivalence of types |
" |
February 29, 2008, 330 - 430 pm at Science Center, Room 507 |
| JOINT MATHEMATICS COLLOQUIUM |
HENRI DARMON (MCGILL UNIVERSITY) |
Rational points on elliptic curves and cycles on Shimura varieties |
Abstract The theory of CM (Complex Multiplication) points on modular and Shimura curves provides one of the most fruitful approaches to the Birch and Swinnerton-Dyer conjecture, leading to the best known results for elliptic curves of analytic rank one. In this talk I will explore the possibility of more general constructions in which, loosely speaking, CM points on Shimura curves are replaced by higher dimensional (topological, or algebraic ) cycles on Shimura varieties. This is a joint Brandies-Harvard-MIT-Northeastern Seminar" |
February 28, 2008, 430 pm at Science Center, Hall D |
| THE THURSDAY SEMINAR |
VERONIQUE GODIN (HARVARD) |
Review of equivariant Morse theory and geodesics |
" |
February 28, 2008, 3 - 5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
SKIP GARIBALDI (EMORY) |
Dense orbits and Spin groups |
Abstract If a semisimple group G has a representation V such that there is a dense orbit in the projective space P(V), then one obtains some classification results about G-torsors. I will explain how this method has recovered some classical results about Spin-torsors (essentially, quadratic forms) and how it has produced some new ones" |
February 27, 2008, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
SPIRO KARIGIANNIS (OXFORD UNIVERSITY) |
G-2 Manifolds with isolated conical singularities |
This seminar is organized by Professor Shing-Tung Ya" |
February 26, 2008, 430 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
DAN ABRAMOVICH (BROWN UNIVERSITY) |
Counting curves with tangency conditions comparison of approaches |
" |
February 26, 2008, 3 pm at MIT ( 4-149) |
| FACULTY COLLOQUIUM |
PETER KRONHEIMER (HARVARD) |
Knots, slice genus and knot homologies |
This is a new series in which our senior faculty give talks aimed at first year graduate students who want to get a feel for different areas of research" |
February 25, 2008, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
DYLAN THURSTON (BARNARD COLLOGE) |
Using Combinatorial Link Floer Holomology to Detect Transverse Knots |
" |
February 22, 2008, 330 - 430 pm at Science Center, Room 507 |
| COLLOQUIUM |
PETER SARNAK (PRINCETON) |
Equidistribution and primes |
Dinner follows (at 615pm) at the Faculty Club. $5 for graduate students" |
February 21, 2008, 430 pm at Science Center, Hall D |
| NUMBER THEORY SEMINAR |
WEE TECK GAN (UCSD) |
Formal degree and local theta correspondence |
Abstract The formal degree conjecture of Hiraga-Ichino-Ikeda expresses the formal degree of a discrete series representation in terms of the adjoint gamma factor of its Langlands parameter. I will discuss the interaction of this conjecture with cases of Langlands functoriality given by the local theta correspondence. As an application, I will consider the conjecture for the group GSp(4)" |
February 20, 2008, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
YONGBIN RUAN (UNIVERSITY OF MICHIGAN) |
Dichotomy of uniruled submanifold in symplectic geometry |
Differential Geometry Seminars are organized by Professor Shing-Tung Yau" |
February 19, 2008, 430 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
ILYA TYOMKIN (MIT) |
Tropical curves, toric stacks, and enumerative geometry |
" |
February 19, 2008, 3 PM at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
THOMAS LAM (HARVARD) |
Graphs, towers, and categorifying Hopf algebras |
This is a new series in which our senior faculty give talks amined at first year graduate students who want to get a feel for different areas of research" |
February 18, 2008, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
CHRIS BEASLEY (HARVARD) |
More About Localization For Wilson Loops in Chern-Simons Theory |
" |
February 15, 2008, 330 - 430 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
CECILIA BUSUIOC (BU) |
Eisenstein Cohomology, The Steinberg Symbol and Special Values of L-functions. |
" |
February 13, 2008, 3 - 4 pm at Science Center, Room 507 |
| ALGEBRAIC GEOMETRY SEMINAR |
IVAN CHELTSOV (UNIVERSITY OF EDINBURGH) |
Birational automorphisms and alpha-invariants |
This is a joint Harvard- MIT Seminar" |
February 12, 2008, 3 pm at MIT 4-149 |
| SPECIAL DIFFERENTIAL GEOMETRY SEMINAR |
FRANCISCO MARTIN (UNIVERSITY OF GRANADA- SPAIN) |
Complete proper minimal sufaces in bounded domains of R^3 |
This seminar is organized by Professor Shing-Tung Yau" |
February 12, 2008, 3 pm at Science Center, Room 232 |
| SPECIAL DIFFERENTIAL GEOMETRY SEMINAR |
SERGEY GRIGORIAN (CAMBRIDGE UNIVERSITY - UNITED KINGDOM) |
Local Geometry of the G2 Moduli Space |
This seminar is organized by Professor Shing-Tung Ya" |
February 12, 2008, 430 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
HORNG-TZER YAU (HARVARD) |
A review on regularity of axisymmetric Navier-Stokes equations |
This is a new series in which our senior faculty give talks aimed at first year grduate students who want to get a feel for different areas of research" |
February 11, 2008, 3 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
YUM-TONG SIU (HARVARD) |
Analytic techniques in algebraic geometry and algebraic-geometric techniques in analysis. |
" |
February 08, 2008, 330- 430 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
BENEDICT GROSS (HARVARD) |
Some supercuspidal parameters for p-adic groups and their formal degrees |
Abstract I will give some examples which support the formal degree conjecture presented last week by Atsushi Ichino. I will also present a mild reformulation of the conjecture. This is joint work with Mark Reeder" |
February 06, 2008, 3 - 4 pm at Science Center, Room 507 |
| ALGEBRAIC GEOMETRY SEMINAR |
OVIDIU PASARESCU (INST. OF MATHEMATICS OF THE ROMANIAN ACADEMY AND COLORADE STATE.) |
On the classification of embedded curves |
" |
February 05, 2008, 3 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
JIN-YI CAI (UNIVERSITY OF WISCONSIN-MADISON) |
The Permanent and Determinant Problem |
This seminar is organized by Professor Shing-Tung Ya" |
February 05, 2008, 430 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
JOE HARRIS (HARVARD) |
Galois Groups of Enumerative Problems |
This is a new series in which our senior faculty give talks aimed at first year graduate students who want to get a feel for different areas of research" |
February 04, 2008, 3 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
ATSUSHI ICHINO (OSAKA CITY UNIVERSITY AND IAS) |
Formal degrees and adjoint gamma factors |
Abstract We give a conjectural formula for the formal degree of a deiscrete series representation in terms of the adjoint gamma factor. Our conjecture is supported by various examples and is compatible with the Weyl dimension formula. Using twisted endoscopy, we also verify the conjecture for a stable discrete series representation of U(3) over a non-archimedean local field of characteristic zero. This is a joint work with K.Hiraga and T.Ikeda" |
January 30, 2008, 3-4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
SEBASTIAN CASALAINA-MARTIN (HARVARD) |
The moduli space of cubic threefolds via degenerations of the intermediate Jacobian |
Abstract A well known result of Clemens and Griffiths says that a smooth cubic threefold can be recovered from its intermediate Jacobian. In this talk I will discuss the possible degenerations of these abelian varieties, and thus give a description of the compactification of the moduli space of cubic threefolds obtained in this way. The relation between this compactification and those constructed in the work of Allcock-Carlson-Toledo and Looijenga-Swierstra will also be considered, and is similar in spirit to the relation between the various compactifications of the moduli spaces of low genus curves. This is joint work with Radu Laza" |
December 18, 2007, 300 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
() |
NO SEMINAR |
" |
December 17, 2007, at |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
LENHARD NG (DUKE UNIVERSITY) |
Knot contact homology and string topology |
" |
December 14, 2007, 330- 430 pm at Science Center, Room 507 |
| SEMINAR ON CHIRAL ALGEBRAS |
KOBI KREMNIZER () |
Lattice algebras and their chiral homology ll |
" |
December 13, 2007, 3-5 PM at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
J. BELLAICHE (COLUMBIA/ BRANDEIS) |
Non smooth classical point on Eigenvarieties |
Abstract Eigenvarieties, the natural generalization of the Eigencurve discovered by Coleman and Mazur, are $p$-adic rigid analytic spaces that interpolate the finite slope algebraic automorphic forms for a given reductive group. Very little is known on their geometry. We shall show that, contrarily to the case of the Eigencurve, Eigenvarieties of higher rank have many non-smooth classical points. We shall also explain how that non-smoothness at a point $x$ implies that the eigenvariety sees several independent elements in a suitable Selmer group corresponding to $x$" |
December 12, 2007, 3- 4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
DAVID SMYTH (HARVARD) |
Compact Moduli of Singular Curves |
" |
December 11, 2007, 300 pm at MIT (2-142) |
| HARVARD-MIT ALGEBRAIC SEMINAR |
ALLEN KNUTSON (UC BERKELEY) |
Branchvarieties and automatically reduced flat limits |
" |
December 11, 2007, 430 pm at MIT (2-142) |
| SPECIAL LECTURE IN HONOR OF LEONHARD EULER'S 300TH BIRTHDAY |
WILLIAM DUNHAM (MUHLENBERG COLLEGE) |
Euler's Amicable Numbers |
Abstract In this talk, I first sketch the life and work of Leonhard Euler (1707-1783), whose 300th birthday is being celebrated this year. I then address a specific problem from number theory the construction of amicable pairs (recall that two positive integers are amicable if each is the sum of the proper divisors of the other). The Greeks knew the amicable pair 220 and 284, and two others were found prior to the 18th century, when Euler arrived on the scene. In an awesome display of mathematical power, he found 58 new ones! I shall examine how he did it - i.e., how he single-handedly increased the world s supply of amicable numbers twenty-fold. His argument is clever yet so easy to follow that we will genertae a new amicable pair right before your eye. This provides another reminder, if another is necessary, of why Euler is such a towering figure in the history of mathematics. Note Any mathematics major (or minor) should find the talk easily accessible" |
December 10, 2007, 4 pm at Maxwell Dworkin G-115 |
| BASIC NOTIONS SEMINAR |
MARK BEHRENS (MIT) |
Stable homotopy groups of spheres and modular forms |
" |
December 10, 2007, 3- 4 PM at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
CUMRUN VAFA (HARVARD) |
Free fermions and topological strings |
" |
December 07, 2007, 330- 430 pm at Science Center, Room 507 |
| ANALYSIS SEMINAR |
ANDREJ ZLATOS (UNIVERSITY OF CHICAGO) |
Dissipation Enhancement by flows in 2D |
Abstract We consider a passive scalar advection-diffusion equation in 2D with a periodic incompressible advecting vector field (flow). We provide a sharp characterization of all flow profiles that optimally enhance dissipation in the sense that solutions with compactly supported initial data become arbitrarily small arbitrarily quickly, provided the flow amplitude is large enough. Our characterization is expressed in terms of simple geometric and spectral conditions on the flow. Extensions to higher dimensions and applications to reaction-advection-diffusion equations will also be mentioned" |
December 07, 2007, 330 pm at Science Center, Room 232 |
| COLLOQUIUM |
DOUGLAS ARNOLD (IMA ( INSTITUTE OF MATHEMATICS AND ITS APPLICATIONS)) |
|
Please note the change in location for this time only" |
December 06, 2007, 430 pm at Science Center, Hall A |
| SEMINAR ON CHIRAL ALGEBRAS |
KOBI KREMNIZER () |
Lattice algebras and their chiral homology |
" |
December 06, 2007, 3- 5 pm at Science Center, Room 507 |
| TEACHING SEMINAR |
Carol Findell (BOSTON UNIVERSITY) |
How Can a Teacher Become an Expert Teacher? |
What are the qualities of an expert teacher? Important attributes are defined and illustrated. The following six ideas are explored in depth. An expert teacher |
| NUMBER THEORY SEMINAR |
CHRISTOPHE BREUIL (IHES/ COLUMBIA) |
From Diamond-Serre weights to representations of GL2(F) |
" |
December 05, 2007, 3-4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
YANIR RUBINSTEIN (MIT) |
Some discretizations of geometric evolution equations |
This seminar is organized by Prof. Shing-Tung Yau" |
December 04, 2007, 430 PM at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
JAROSLAW WLODARCZYK (PURDUE) |
Resolution algorithm in characteristic zero and its possible extension in positive characteristic |
We discuss basic ideas of the simplified Hironaka algorithm of resolution of singularities in characteristic zero and its possible extenion in positive characteristic" |
December 04, 2007, 300 pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
DANIJELA DAMJANOVIC (HARVARD) |
Stability of some abelian actions |
" |
December 03, 2007, 3- 4 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
WEIMIN CHEN (UMASS, AMHERST) |
Symmetry groups of exotic K3 surfaces |
" |
November 30, 2007, 330- 430 pm at Science Center, Room 507 |
| ANALYSIS SEMINAR |
A. PIZZO (ETH/ ZURICH) |
Multi-scale methods in atomic physics |
Abstract The purpose of this lecture is to report on recent progress in understanding atomic physics when the electrons are coupled to the quantized radiation field. First, it will be shown that a groundstate persists, then I will present a simple argument, based on a multi-scale virial theorem, showing that excited bound states of an atom turn into resonances. Some comments on Rayleigh scattering will conclude my lecture" |
November 30, 2007, 330 pm at MIT 2- 136 |
| SEMINAR ON CHIRAL ALGEBRAS |
DENNIS GAITSGORY (HARVARD) |
The chiral de Rhan complex and BRST cohomology |
" |
November 29, 2007, 3-5 pm at |
| NUMBER THEORY SEMINAR |
BJORN POONEN (BERKELEY) |
The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields |
" |
November 28, 2007, 3-4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
LYDIA BIERI (HARVARD) |
An extension of thie stability theorem of the Minkowski Space in general relativity |
This seminar is organized by Prof. Shing Tung Yau" |
November 27, 2007, 430 pm at Science Center, Room 507 |
| HARVARD -MIT ALGEBRAIC GEOMETRY SEMINAR |
JUNECUE SUH (MIT) |
Plurigenera of general type surfaces in mixed characteristic |
" |
November 27, 2007, 300 pm at MIT (2-142) |
| DIFFERENTIAL GEOMETRY SEMINAR |
SERGIO LUKIC (RUTGERS UNIVERSITY) |
Some balanced metrics, quantization and path integrals |
This seminar is organized by Prof. Shing-Tung Ya" |
November 27, 2007, 130 pm at Science Center, Room 232 |
| BASIC NOTIONS SEMINAR |
() |
NO SEMINAR |
" |
November 26, 2007, at |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
RAVI VAKIL (STANFORD) |
Reimagining universal covers and fundamental groups in algebraic and arithmetic geometry |
" |
November 20, 2007, 430 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
PENG PENG YU (DARTMOUTH COLLEGE) |
Studies of the limiting behavior of the Liu-Yau Quasi-Local Energy |
This seminar is organized by Prof. Shing-Tung Ya" |
November 20, 2007, 430 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
NOAM ELKIES (HARVARD) |
How many points can a genus-2 curve have? |
" |
November 20, 2007, 300 pm at Science Center, Room 507 |
| BASIC NOTIONS |
PAUL SEIDEL (MIT) |
Pair of Pants |
" |
November 19, 2007, 3- 4 pm at Science Center, Room 507 |
| COLLOQUIUM |
WILLIAM MINICOZZI (JOHN HOPKINS UNIVERSITY) |
The rate of change of width under flows |
Abstract I will discuss a geometric invariant, that we call the width, of a manifold and first show how it can be realized as the sum of areas of minimal 2-spheres. When $M$ is a homotopy 3-sphere, the width is loosely speaking the area of the smallest 2-sphere needed to" |
November 15, 2007, 430 pm at Science Center, Hall A |
| SEMINAR ON CHIRAL ALGEBRAS |
JOHN FRANCIS (HARVARD) |
Chiral homology of chiral envelopes |
" |
November 15, 2007, 3- 5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
LUIS DIEULEFAIT (BARCELONA) |
Remarks on Serre's modularity conjecture |
" |
November 14, 2007, 3- 4 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
MATTHIAS SCHUETT (HARVARD) |
Calabi-Yau threefolds as fibre products of rational elliptic surfaces |
Chad Schoen introduced the idea to construct Calabi-Yau threefolds as fibre products of rational elliptic surfaces. This construction has many interesting applications in algebraic geometry, number theory and physics. In this talk we will sketch three of them - rigid Calabi-Yau threefolds with a view towards modular forms, - examples with new pairs (h^1,1,h^1,2), - non-liftable Calabi-Yau threefolds in positive characteristic" |
November 13, 2007, 300 pm at MIT (2-142) |
| DIFFERENTIAL GEOMETRY SEMINAR |
TAO LUO (WORCESTER POLYTECHNIC INSTITUTE) |
Dynamical stability of rotating stars of compressible fluids with applications to white dwarfs |
This seminar is organized by Professor Shing-Tung Ya" |
November 13, 2007, 430 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
CHRIS BEASLEY (HARVARD) |
Localization for Wilson loops in Chern-Simons theory |
" |
November 09, 2007, 330 - 430 pm at Science Center, Room 507 |
| ANALYSIS /MATH PHYSICS SEMINAR |
WEI-MIN WANG (UNIVERSITE' PARIS-SUD) |
Bounds on Sobolev Norms for Time Dependent Schrödinger Equations |
This is a joint Harvard/MIT Semina" |
November 09, 2007, 330 pm at Science Center, Room 232 |
| SEMINAR ON CHIRAL ALGEBRAS |
JACOB LURIE (HARVARD) |
Chiral homology of commutative chiral algebras |
" |
November 8, 2007, 3- 5 pm at Science Center, Room 507 |
| MATHEMATICS EDUCATION SPEAKER SERIES SEMINAR |
Jon Star (HARVARD GRADUATE SCHOOL OF EDUCATION) |
Improving Students' Flexibility in Algebra The Benefits of Comparison |
Details" |
November 08, 2007, 100 pm at Science Center, Room 530 |
| MATHEMATICS EDUCATION SEMINAR SERIES |
JON STAR (HARVARD) |
Improving Students' Flexibility in Algebra The Benefits of Comparison |
" |
November 08, 2007, 1-2 pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
PIERRE CHAROLLOIS (JUSSIEU) |
On the argument of Stark units and periods of Hilbert modular forms. |
Abstract This is a report on joint work with Henri Darmon. Trying to generalize modular units to the setting of Hilbert modular forms, we are led to formulate a refinement of Stark s conjecture based on periods of Eisenstein series over some specific cycles. I ll give an overview of our contruction and some numerical evidences supporting our conjecture" |
November 07, 2007, 3- 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
MIHALIS DAFERMOS (UNIVERSITY OF CAMBRIDGE) |
The stability problem for black hole spacetimes in general relativity |
This seminar is organized by Professor Shing-Tung Ya" |
November 06, 2007, 2 pm at Science Center, Room 232 |
| DIFFERENTIAL GEOMETRY SEMINAR |
DENIS AUROUX (MIT) |
Mirror symmetry in the complement of an anticanonical divisor |
This seminar is organized by Professor Shing-Tung Ya" |
November 06, 2007, 430 pm at Science Center, Room 507 |
| BASIC NOTIONS / FACULTY COLLOQUIUM |
BENEDICT GROSS (HARVARD) |
On the parameters of discrete series |
This is a new series in which our senior faculty give talks aimed at first year graduate students who want to get a feel for different areas of research" |
November 05, 2007, 300 - 400 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
LYDIA BIERI (HARVARD) |
An extension of the stability theorem of the Minkowski space in general relativity. |
" |
November 02, 2007, 330-430 pm at Science Center, Room 507 |
| ANALYSIS/MATH PHYSICS SEMINAR |
JINHO BAIK (UNIVERSITY OF MICHIGAN) |
|
Abstract The Tracy-Widom distribution functions are certain probability distribution functions expressed in terms of a solution of second order nonlinear ODE (Painleve II equation). These distribution fuctions arise as universal limits in random matrix theory, statistics, combinatorics and probability. After reviewing some of the above models, we discuss the asymptotic tail behaviors of these functions. Especially we discuss the question of evaluating the constant terms in the asymptotics at negative infinity and related constant problems for other distribution functions" |
November 02, 2007, 330 pm at MIT 2-136 |
| SEMINAR ON CHIRAL ALGEBRAS |
JOHN FRANCIS (HARVARD) |
Chiral homology |
" |
November 01, 2007, 3 - 5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
DAVID WHITEHOUSE (MIT) |
Applications of the relative trace formula to central L-values |
Abstract I will describe a couple of applications of Jacquet s relative trace formula to central values of twisted quadratic base change L-functions for GL(2). The first is to prove explicit formulae, generalizing work of Gross and Zhang (amongst others), relating this central value to integrals of automorphic forms over tori. The second is to average value results for Hilbert modular forms and subconvexity. This talk is based on separate joint works with Kimball Martin and Brooke Feigon" |
October 31, 2007, 3 - 4 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
MAC CONAMHNA OISIN (IMPERIAL COLLEGE LONDON) |
Singularity resolutions by m-theory fivebranes-calibrated geometry, >ads solutions and special holonomy metrics |
Organized by Professor Shing-Tung Ya" |
October 30, 2007, 430 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
MAKSYM FEDORCHUK (HARVARD) |
Linear sections of the Severi variety and moduli of curves |
" |
October 30, 2007, 300 pm at MIT (2-142) |
| BASIC NOTIONS/ FACULTY COLLOQUIUM |
SLAVA KRUSHKAL (VISITING HARVARD) |
The chromatic polynomial. the golden ratio. and quantum topology |
This is a new series in which our senior faculty give talks aimed at first year graduate students who want to get a feel for different areas of research" |
October 29, 2007, 300-400 PM at Science Center, Room 507 |
| SERIES OF LECTURES BY SERRE |
JEAN-PIERRE SERRE (VISITING HARVARD UNIVERSITY) |
|
" |
October 26, 2007, 9-10 AM at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
MOHAMMED ABOUZAID (MIT) |
On homological mirror symmetry for toric varieties |
" |
October 26, 2007, 330-430 PM at Science Center, Room 507 |
| ANALYSIS/MATH PHYSICS SEMINAR |
HANS CHRISTIANSON (MIT) |
Phase space analysis near periodic orbits |
" |
October 26, 2007, 330 pm at Science Center, Room 232 |
| SEMINAR ON CHIRAL ALGEBRAS |
DENNIS GAITSGORY (HARVARD) |
Chiral differential operations |
" |
October 25, 2007, 3-5 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
JEAN-FRANCOIS BURNOL (LILLE) |
Relativistic causality and functional equations |
" |
October 24, 2007, 3 - 4 pm at Science Center, Room 507 |
| SERIES OF LECTURES BY SERRE |
JEAN- PIERRE SERRE (VISITING HARVARD UNIVERSITY) |
|
" |
October 24, 2007, 9-10 AM at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
BJORN ANDREAS (HUMBOLDT UNIVERSITY-BERLIN) |
Fourier-Moukai transforms and spectral covers for K3 fibrations |
Organized by Professor Shing-Tung Ya" |
October 23, 2007, 430 pm at Science Center, Room 507 |
| HARVARD MATHEMATICAL LOGIC SEMINAR |
PETER CHOLAK (UNIVERSITY OF NOTRE DAME) |
Coding, Orbits and Computably Enumerable Sets |
A recent result of Cholak, Downey, and Harrington is that there is a computably enumerable set A such that the arithmetic complexity of membership in the orbit of A (under automorphisms of the lattice of computably enumerable (c.e.) sets) is as hard as possible. Our focus will be on the underlying codings. We wish to understand why these codings work, how they are related, and why they are necessary." |
October 23, 2007, 430 pm at Science Center, Room 232 |
| FACULTY COLLOQUIUM |
JOE HARRIS (HARVARD) |
Uniformity of Rational Points on Curves |
" |
October 22, 2007, 300 - 400 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
BRIAN MUNSON (HARVARD) |
Link maps and linking for arbitrary manifolds |
" |
October 19, 2007, 330 - 430 pm at Science Center, Room 507 |
| ANALYSIS MATH / PHYSICS SEMINAR |
PETER SHORE (MIT) |
Matrix product states and simulating spin chains |
This is a Harvard/MIT joint seminar" |
October 19, 2007, 330 pm at MIT |
| SERIES OF LECTURES BY SERRE |
JEAN-PIERRE SERRE (VISITING HARVARD UNIVERSITY) |
|
" |
October 19, 2007, 9-10 AM at Science Center, Room 507 |
| CHIRAL ALGEBRAS SEMINAR |
JOHN DUNCAN (HARVARD UNIVERSITY) |
Chiral algebras versus vertex algebras who will triumph? |
" |
October 18, 2007, 3 - 5 pm at Science Center, Room 507 |
| MATHEMATICS EDUCATION SPEAKER SERIES SEMINAR |
HEATHER HILL (HARVARD GRADUATE SCHOOL OF EDUCATION) |
Well Enough to Teach It What More Does It Take? |
Details
| October 18, 2007, 100 pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
BRIAN CONRAD (MICHIGAN) |
Non-archimedean analytification of algebraic spaces |
" |
October 17, 2007, 300-400 pm at Science Center, Room 507 |
| SERIES OF LECTURES BY SERRE |
JEAN-PIERRE SERRE (VISITING HARVARD UNIVERSITY) |
|
" |
October 17, 2007, 9-10 AM at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
CHIEN-HAO LIU (HARVARD UNIVERSITY) |
Azumaya-Type noncommutative spaces and morphisms therefrom Polchinski's d-brane in string theory from grothedieck's viewpoint |
Organized by Professor Shing-Tung Ya" |
October 16, 2007, 430 pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
DAWEI CHEN (HARVARD) |
Mori's program on the Kontsevich space of stable maps |
" |
October 16, 2007, 300 pm at MIT 2-142 |
| FACULTY COLLOQUIUM |
RICHARD TAYLOR (HARVARD) |
Shimura Varieties and Rapoport-Zink Space |
" |
October 15, 2007, 300 - 400 pm at Science Center, Room 507 |
| ANALYSIS/MATH PHYSICS SEMINAR |
TODD KEMP (MIT) |
Semigroup contraction properties for q-Gaussian processes |
" |
October 12, 2007, 330 pm at Science Center, Room 232 |
| GAUGE THEORY AND TOPOLOGY |
DUONG PHONG (COLUMBIA) |
Monge-Ampere equations and Donaldson geodesic rays |
" |
October 12, 2007, 330 - 430 pm at Science Center, Room 507 |
| SERIES OF LECTURES BY SERRE |
JEAN-PIERRE SERRE (VISITING HARVARD UNIVERSITY) |
|
" |
October 12, 2007, 9-10 AM at Science Center, Room 507 |
| SEMINAR ON CHIRAL ALGEBRAS |
JACOB LURIE (HARVARD) |
Lie-* algebras, chiral envelopes and examples |
" |
October 11, 2007, 3 - 5 PM at Science Center, Room 507 |
| BRANDEIS-HARVARD-MIT-NORTHEASTERN JOINT COLLOQUIUM |
D.H. PHONG (COLUMBIA UNIVERSITY) |
The Kahler-Ricci flow and stability |
" |
October 11, 2007, 430 - 530 pm at Science Center, Hall D |
| SERIES OF LECTURES BY SERRE |
JEAN-PIERRE SERRE (VISITING HARVARD UNIVERSITY) |
|
" |
October 10, 2007, 9-10 AM at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
JUNECUE SUH (MIT) |
Newton integral motives over finite fields questions of Serre and of Katz |
" |
October 10, 2007, 300 - 400 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
GABOR SZEKELYHIDI (HARVARD UNIVERSITY) |
OptimalTest-Configuratin for toric varieties |
This seminar is organized by Professor Shing-Tung Ya" |
October 09, 2007, 430 pm at Science Center, Room 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
ANGELA GIBNEY (U PENN) |
A new candidate for the nef cone of the moduli space of n-pointed curves of genus g |
" |
October 09, 2007, 300 pm at MIT 2-142 |
| GAUGE THEORY AND TOPOLOGY |
SLAVA KRUSHKAL (UNIVERSITY OF VIRGINIA) |
Algebraic and geometric duality in dimension 4 |
" |
October 05, 2007, 330 - 430 pm at Science Center, Room 507 |
| JOINT MIT-HARVARD ANALYSIS SEMINAR |
JUERG FROEHLICH () |
|
Note special time and roo" |
October 05, 2007, 400 pm at Jefferson, Room 453, Harvard |
| SERIES OF LECTURES BY SERRE |
JEAN-PIERRE SERRE (VISITING HARVARD UNIVERSITY) |
|
" |
October 5, 2007, 9-10 AM at Science Center, Room 507 |
| SEMINAR ON CHIRAL ALGEBRAS |
SCOTT CARNAHAN () |
TBA |
Please note the change of tim" |
October 04, 2007, 300 - 500 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
MARK WATKINS (BRISTOL UNIVERSITY) |
Ranks of elliptic curves |
" |
October 03, 2007, 300 - 400 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
PING AO (UNIVERSITY OF WASHINGTON) |
|
Organized by Professor Shing-Tung Ya" |
October 03, 2007, 1210 pm at Science Center, Room 530 |
| INFORMAL SEMINAR |
MARYAM MIRZAKHANI (PRINCETON) |
Analogies between moduli spaces of hyperbolic surfaces and negatively curved manifolds |
" |
October 03, 2007, 400-600 pm at Science Center, Room 530 |
| SERIES OF LECTURES BY SERRE |
JEAN-PIERRE SERRE (VISITING HARVARD UNIVERSITY) |
|
" |
October 3, 2007, 9-10 AM at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
BJOERN SCHMEKEL (HARVARD UNIVERSITY) |
Quasi-Local energy and other related problems in general relativity |
This seminar is organized by Professor Shing-Tung Ya" |
October 02, 2007, 430 pm at Science Center, Room 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
MONTSERRAT TEIXIDOR I BIGAS (TUFTS) |
Maps between moduli spaces of vector bundles and the theta divisor |
Abstract There are several natural rational maps between moduli spaces of vector bundles on a curve of different ranks and degrees. We show that in many cases these maps are finite. The results are used then to give lower bounds for the dimension of the base locus of the generalized theta divisor in the moduli space of vector bundles" |
October 02, 2007, 300 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
CLIFFORD TAUBES (HARVARD) |
Smooth Manifolds in Dimension 4 |
This is a one time shift. Faculty Colloquiums are held at 300 pm." |
October 01, 2007, 330-430 pm at Science Center, Room 507 |
| JOINT MIT-HARVARD ANALYSIS SEMINAR |
ENNO LENZMANN (MIT) |
Dynamical evolution of self-gravitating relativistic matter in Hartree theory |
" |
September 28, 2007, 330 pm at Science Center, Room 232 |
| SERIES OF LECTURES BY SERRE |
JEAN-PIERRE SERRE (VISITING HARVARD UNIVERSITY) |
|
" |
September 28, 2007, 9-10 AM at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
ALVARO PELAYO (MIT) |
Symplectic actions of 2-tori on 4-manifolds |
" |
September 28, 2007, 330-430 pm at Science Center, Room 507 |
| SEMINAR ON CHIRAL ALGEBRAS |
JACOB LURIE () |
Review of Algebraic D-modules |
" |
September 27, 2007, 330 - 530 pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
JEAN-PIERRE SERRE (COLLEGE DE FRANCE) |
Examples of discrete rotation groups in 3- space |
" |
September 26, 2007, 300 - 400 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
PAN PENG (HARVARD UNIVERSITY) |
On a proof of the Labastida-Marino-Ooguri-Vafa Conjecture |
" |
September 25, 2007, 430 pm at Science Center, Room 507 |
| ALGEBRAIC GEOMETRY SEMINAR |
BJORN POONEN (UC BERKELEY) |
Existence of rational points on smooth projective varieties |
" |
September 25, 2007, 300 -400 pm at Science Center, Room 507 |
| ANALYSIS SEMINAR |
BENJAMIN SCHLEIN (MUNICH AND UNIV CAMBRIDGE) |
Hartee approximation for the dynamics of mean field systems |
Abstract In the first part of the talk I am going to review recent results concerning the rigorous derivation of the nonlinear Hartee equations (and the related Gross-Pitaevskii equation) from many body quantum dynamics. In the second part of the talk I am going to discuss some new bounds on the rate of convergence towards the limiting Hartree evolution" |
September 21, 2007, 330 pm at MIT 2-136 |
| NUMBER THEORY SEMINAR |
BYOUNG DU KIM (NORTHWESTERN UNIVERSITY) |
Iwasawa theory and the parity conjecture for non-ordinary reduction primes |
" |
September 19, 2007, 300 PM at Science Center, Room 507 |
| ALGEBRAIC GEOMETRY SEMINAR |
JOSEPH LANDSBERG (TEXAS A&M) |
Rigidity of homogeneous vrieties |
This is a joint seminar with MI" |
September 18, 2007, 300-400 pm at MIT 2-142 |
| SPECIAL SEMINAR |
Abe Othman, Ben Conlee and Chris Yetter (HARVARD UNIVERSITY) |
The contest modeling problem |
This year, Harvard s team of Chris Yetter, Abe Othman and Ben Conlee was one of the 5 Outstanding Winners of the 2007 Mathematical Modeling Contest. This was out of 351 teams representing institutions in 12 countries who worked on the given modeling problem. This team was also the INFORMS prize recipient. Chris, Abe and Ben will be describing the contest modeling problem and their solution. Cookies and Juice will be provided at the seminar. Please come if you are free" |
May 11, 2007, 2PM at Sci Center 232 |
| DYNAMICS AND GEOMETRY, INFORMAL SEMINAR |
CURTIS MCMULLEN (HARVARD) |
Complex dynamics on the unit disk measures, multipliers and R-trees |
Abstract We will discuss echoes of the theory of hyperbolic surfaces, curves on them, measured laminations and Teichmueller space, in the dynamical study of proper holomorphic maps of the unit disk to itself" |
May 09, 2007, 4 pm at Science Center, Room 530 |
| GAUGE THEORY AND TOPOLOGY |
PETER KRONHEIMER (HARVARD UNIVERSITY) |
knot homologies from singular instantons |
" |
May 04, 2007, 330- 430 pm at Science Center, Room 309 |
| COLLOQUIUM |
AKSHAY VENKATESH (COURANT INSTITUTE, NYU) |
Effective equidistribution on homogeneous spaces |
Abstract I ll talk about some relations between analytic number theory, and questions about equidistribution on homogeneous spaces. (For our purposes, a homogeneous space is the quotient of a Lie group by a lattice, e.g. the space of lattices in R^n). I will first discuss old work of Kloosterman an Selberg in that light. I will then discuss an effective equidistribution result, joint with M. Einsiedler and G. Margulis, which applies in some higher rank instances" |
May 03, 2007, 430 pm at Science Center, Hall D |
| NUMBER THEORY SEMINAR |
CHUNG PANG MOK (HARVARD UNIVERSITY) |
Exceptional Zero Conjecture for Hilbert modular forms |
" |
May 02, 2007, 300 pm at Science Center, Room 507 |
| DYNAMICS AND GEOMETRY, INFORMAL SEMINAR |
SHIMON BROOKS (PRINCETON) |
Halfway to quantum unique ergodicity |
" |
May 02, 2007, 4 pm at Science Center, Room 530 |
| GAUGE THEORY AND TOPOLOGY |
FANGYUN YANG (MIT) |
An index theorem for Dirac operators on manifolds with conic singularities |
" |
April 27, 2007, 330-430 PM at Science Center, Room 309 |
| COLLOQUIUM |
VENKATESAN GURUSWAMI (UNIVERSITY OF WASHINGTON) |
Reed-Solomon codes, low-degree automorphisms, and error-correction with optimal rate. |
The seminar will be preceded by tea at 400 PM in the Common Room" |
April 26, 2007, 430 PM at Science Center, Hall D |
| NUMBER THEORY SEMINAR |
BENJAMIN HOWARD (BOSTON COLLEGE) |
A twisted Gross-Zagier theorem and applications to Hida theory |
" |
April 25, 2007, 300 pm at Science Center, Room 507 |
| DYNAMICS AND GEOMETRY, INFORMAL SEMINAR |
Danijela Damjanovic (HARVARD UNIVERSITY) |
Litlewood's conjecture and SL_3(R)/SL_3(Z) |
This talk is about the Einsiedler-Katok-Lindenstrauss result Set of exceptions to the Littlewood s conjecture has Hausdorff dimension zero" |
April 25, 2007, 400 PM at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
DAVID KAZHDAN (HARVARD UNIVERSITY/HEBREW UNIVERSITY OF JERUSALEM) |
Alain Connes formulation of the Andre Weils theorem |
Abstract Discussion of Alain Connes formulation of the Andre Weil s theorem, [the Riemann conjecture for the functional filed case]. Alain Connes found a very interesting way to interpret the results as a computation of an asymptotic of a family of operators of finite rank" |
April 18, 2007, 300 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
EAMAN EFTEKHARY (HARVARD) |
Heegard Floer homology and existence of incompressible tori |
" |
April 13, 2007, 330 - 430 pm at Science Center, Room 309 |
| INFORMAL SEMINAR |
LIOR SILBERMAN (HARVARD) |
Measure rigidity for Cartan actions the low-entropy method |
A sketch of the ideas in Lindenstrauss s paper Invariant measures and quantum unique ergodicity" |
April 11, 2007, 4 pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
ADRIANO MARMORA (MCGILL UNIVERSITY) |
p-adic local constants |
" |
April 11, 2007, 300pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
BARRY MAZUR (HARVARD UNIVERSITY) |
Transcendence conjectures about units in algebraic number fields and deformation problems |
" |
April 09, 2007, 300 pm at Science Center, Room 507 |
| MATHEMATICS EDUCATION SEMINAR SERIES |
Bret Benesh (HARVARD UNIVERSITY) |
How students use books |
" |
April 06, 2007, 230 - 330 pm at Science Center, Room 309a |
| GAUGE THEORY AND TOPOLOGY |
YI NI (PRINCETON UNIVERSITY) |
Knot Floer homology detects fibered knots |
" |
April 06, 2007, 330 - 430 pm at Science Center, Room 309 |
| SPECIAL TOPOLOGY SEMINAR |
MAHMOUD ZEINALIAN (LONG ISLAND UNIVERSITY) |
Closed string TCFT for Calabi-Yau elliptic spaces |
" |
April 05, 2007, 200 PM at Science Center, Room 507 |
| COLLOQUIUM |
CLAIRE VOISIN (INSTITUTE DE MATHEMATIQUES DE JUSSIEU) |
Hodge loci and absolute Hodge classes |
Summary Hodge theory provides the notion of Hodge structure and of Hodge class on a compact Kaehler manifold. In the general Kaehler context, we proved that Hodge calsses may not be related to complex geometry. We shall explain in this talk why the Hodge conjecture has a completely different flavour in algebraic geometry, and some evidences for it coming from the study of Hodge loci" |
April 05, 2007, 430 pm at Science Center, Hall D |
| NUMBER THEORY SEMINAR |
JARED WEINSTEIN (BERKELEY) |
Local Langlands and the stable reduction of modular curves |
" |
April 04, 2007, 300 pm at Science Center, Room 507 |
| DYNAMICS AND GEOMETRY/ INFORMAL SEMINAR |
JASON BEHRSTOCK (UTAH) |
Asymptotic geometry of the mapping-class group |
" |
April 04, 2007, 400 pm at Science Center, Room 530 |
| FACULTY COLLOQUIUM |
DAN STROOCK (HARVARD UNIVERSITY) |
Most of DeGiorgi-Moser-Nash was already in Nash |
" |
April 02, 2007, 300 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
PEDRAM SAFARI (HARVARD UNIVERSITY) |
Gluing Seiberg-Witten monopoles an outline |
" |
March 23, 2007, 330- 430 pm at Science Center, Room 309 |
| DINAMICS AND GEOMETRY INFORMAL SEMINAR |
DIMITRY KLEINBOCK (BRANDEIS) |
|
" |
March 21, 2007, 400 pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
MARK KISIN (UNIVERSITY OF CHICAGO) |
Canonical integral models of shimura varieties |
" |
March 21, 2007, 300 PM at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
JOHN DUNCAN (HARVARD UNIVERSITY) |
Vertex algebra and elliptic genera |
Abstract This talk will be partly an introduction to vertex algebra, and partly an introduction to the construction of Malikov-Schechtman-Vaintrob which equips smooth manifolds with sheaves of vertex algebras in a such a way that one recovers (a normalization of ) Ochanine s elliptic genus at the level of characters" |
March 19, 2007, 300 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
HEE-JUNG KIM (MCMASTER UNIVERSITY) |
Topological triviality of smoothly knotted surfaces in 4-manifolds |
" |
March 16, 2007, 330-430 pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
BRUNO KINGLER (UNIVERSITE PARIS 7) |
On the Andre-Oort conjecture |
" |
March 14, 2007, 300 PM at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
DAVID KAZHDAN (HARVARD UNIVERSITY) |
Poisson summation formula and its applications to the representation theory |
" |
March 12, 2007, 300 pm at Science Center, Room 507 |
| TEACHING SEMINAR |
Tom Roby (UNIVERSITY OF CONNECTICUT) |
BL and the (Arnold) Ross Program |
" |
March 09, 2007, 200-300 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
DANIEL RUBERMAN (BRANDEIS UNIVERSITY) |
Heegard-Floer meets Casson-Gordon |
" |
March 09, 2007, 330-430 pm at Science Center, Room 309 |
| SPECIAL LECTURE |
VLADIMIR VOEVODSKY () |
Motivic Eilneberg-MacLane spaces |
" |
March 08, 2007, 300 - 430 pm at Science Center, Room 232 |
| NUMBER THEORY SEMINAR |
TERUYOSHI YOSHIDA (HARVARD UNIVERSITY) |
Converse of the weight-monodromy conjecture |
Abstract Weight-monodromy conjectue says that an l-adic Galois representatin of a local field is pure (in an appropriate sense) if it is geometric. Our work (with R. Taylor) on local-global compatibility for Langlands correspondence shows that a pure Galois representation is geometric (up to Frobenius semisimplification). Intended as an introduction to the subject for non-experts" |
March 07, 2007, 300 PM at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
YI NI (PRINCETON) |
Knot Floer homology detects fibered knots. |
" |
March 06, 2007, 330-430 pm at Science Center, Room 309 |
| FACULTY COLLOQUIUM |
GERALD SACKS (HARVARD UNIVERSITY) |
Differentially closed fields |
" |
March 05, 2007, 300 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
KARL LUTTINGER () |
|
" |
March 02, 2007, 330-430 pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
LIOR SILBERMAN (HARVARD UNIVERSITY) |
Equidistribution of Hecke Eigenforms |
" |
February 28, 2007, 300 PM at Science Center, Room 507 |
| SPECIAL LECTURE |
VLADIMIR VOEVODSKY () |
Motivic Eilenberg MacLane spaces |
" |
February 27, 2007, 1000-1130 am at Science Center, Room 232 |
| LOGIC SEMINAR |
PETER CHOLAK (UNIVERSITY OF NOTRE DAME) |
Classical Recursion Theory |
" |
February 26, 2007, 400 PM at Science Center, Room 530 |
| FACULTY COLLOQUIUM |
NOAM ELKIES (HARVARD UNIVERSITY) |
Belyi functions |
" |
February 26, 2007, 3pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
TIM PERUTZ (CAMBRIDGE UNIVERSITY) |
Symplectic models for gauge theory on 3- and 4-manifolds with singular fibrations |
" |
February 23, 2007, 330-430 pm at Science Center, Room 309 |
| JOINT COLLOQUIUM |
DANIEL TATARU (UC BERKELEY) |
Long term dynamics for wave and Schroedinger evolutions on a curved background |
Abstract We consider the question of long time behavior for linear wave and Schroedinger equations in $R^n$ for long range perturbations of the flat metric. This is related to spectral theory in the case of time independent coefficients, and to the dynamics of small data solutions for nonlinear evolutions. We discuss a phase space approach to the construction of global in tume outgoing parametrices, as well as the connection to localized emergy estimates and Strichartz type estimates" |
February 22, 2007, 430 pm at Science Center D |
| NUMBER THEORY SEMINAR |
JONATHAN POTTHARST (HARVARD UNIVERSITY) |
Triangulordinary Selmer groups |
" |
February 21, 2007, 300 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
DANIJELA DAMJANOVIC (HARVARD UNIVERSITY) |
Rigidity of higher-rank abelian actions review of some results, questions and methods |
" |
February 16, 2007, 330-430p.m. at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
JACOB LURIE (HARVARD UNIVERSITY) |
p-Divisible Groups in Algebraic Topology |
" |
February 14, 2007, 300 PM at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
CURT MCMULLEN (HARVARD UNIVERSITY) |
Thermodynamics, dimension and moduli of Riemann surfaces |
" |
February 12, 2007, 3 PM at SC 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
MATT HEDDEN (MIT) |
On knot Floer homology and complex curves |
" |
February 09, 2007, 330-430 p.m. at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
DAVID KAZHDAN () |
2-dimentional Hecke operators |
" |
February 07, 2007, 300-400 PM at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
Arthur Jaffe (HARVARD UNIVERSITY) |
Quantization and Renormalization |
" |
February 05, 2007, 300 p.m. at Science Center, Room 507 |
| LECTURE SERIES |
Vladimir Voevodsky (IAS) |
Motives and Motivic Homotopy |
" |
December 19, 2006, 100-300 PM at Science Center, Room 232 |
| FACULTY COLLUQUIUM |
Benedict Gross (HARVARD UNIVERSITY) |
Binary cubic forms and ternary quadratic forms classifying the orbits of some group actions. |
" |
December 18, 2006, 300 PM at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
Zoltan Szabo (PRINCETON UNIVERSITY) |
Knot Floer homology and combinatorical constructions |
" |
December 15, 2006, 330-430 PM at Science Center, Room 309 |
| LECTURE SERIES |
Vladimir Voevodsky (IAS) |
Motives and Motivic Homotopy |
" |
December 14, 2006, 1100am-100pm at Science Center, Room 232 |
| NUMBER THEORY SEMINAR |
John Duncan () |
Modular functions and sporadic simple groups |
Abstract Monstrous Moonshine is, in a word, the unexpected connection between modular functions, and the largest sporadic simple group--- the Fischer---Griess Monster. We will discuss an extension of this relating genus zero discrete groups commensurable with the modular group to a sporadic simple group that is not involved in the Monster" |
December 13, 2006, 300 PM at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Ilya Zharkov (HARVARD UNIVERSITY) |
Tropical curves and their Jacobians |
" |
December 12, 2006, 430-530 PM at Scienc Center, Room 507 |
| LECTURE SERIES |
Vladimir Voevodsky (IAS) |
Motives and Motivic Homotopy |
" |
December 12, 2006, 100-300 PM at Science Center, Room 232 |
| JOINT MIT/HARVARD ANALYSIS SEMINAR |
Youngmi Hur () |
Novel methodologies for effective wavelet constructions in high dimensions |
I will introduce new methodologies for representing data on regular grids. Among the new methodologies, the CAP and the L-CAMP will be discussed in detail. The CAP representation is a generalization of the Laplacian pyramidal representation.The CAP methodology works for any spatial dimension and for any integer dilation, and it is accompanied by solid mathematical theory that reveals its performance (i. e., its ability to rencode smoothness). The L-CAMP methodology is a descendent of the CAP. A subclass of the L-CAMP methodology provides effective wavelet constructions in high dimensions in the sense that it has fast algorithms(linear complexity with small constants) for both decomposition and reconstruction, its performance is completely understood, and the sum of the volumes of the supports of the underlying mother wavelets is extremely small. The above is joint work with Amos Ron. I will briefly talk about work in progress on near-optimal sparsity of wavelet coefficients, if time permits" |
December 08, 2006, 330 PM at Science Center, Room 221 |
| GAUGE THEORY AND TOPOLOGY |
John Sullivan (BERLIN) |
Rope length criticality for knots and links |
Abstract The Gehring ropelength problem asks us to minmize the length of a knot or link in space, subject to thickness constraint (keeping different strands of the knot at unit distance from each other). We derive a Balance Criterion giving necessary and sufficient cinditions for space curve to be ropelength-critical. Our approach is modeled on finite-dimensional rigidity theory for frameworks; we prove an infinite-dimensional generalization of the Kuhn-Tucker theorem. Some examples of ropelength minimizers exhibit surprising geometric behavior for two simply clasped ropes, there is a slight gap between them when they are pulled tight, and each has infinite curvature at its tip.This is joint work with Cantarella, Kusner, Fu and Wrinkle" |
December 08, 2006, 330-430 PM at Science Center, Room 309 |
| COLLOQUIUM |
David Eisenbud (MSRI AND UC BERKELEY) |
From Polynomial Interpolation to the Complexity of Ideals |
Abstract One natural question in interpolation theory is given a finite set of points in R^n, what is the least degree of polynomials on R^n needed to induce every function from the points to R? It turns out that this Interpolation degree is closely related to a fundamental measure of complexity in algebraic geometry called Castelnuovo-Mumford regularity. I ll explain these ideas and some of their current interest in algebraic geometry and commutative algebra" |
December 07, 2006, 430 PM with tea at 400 PM at Science Center, Hall D |
| LECTURE SERIES |
Vladimir Voevodsky (IAS) |
Motives and Motivic Homotopy |
" |
December 07, 2006, 1100AM-100PM at Science Center, Room 232 |
| SPECIAL SEMINAR |
Bernd Sturmfels (UNIVERSITY OF CALIFORNIA, BERKELEY) |
Semigraphoids, Permutohedra, and Mice |
Abstract Semigraphoids are combinatorial structures that arise in statistical learning theory. They are equivalent to convex rank tests and to polyhedral fans that coarsen the hyperplane arrangement associated with the symmetric group. This lecture gives an introduction to this theory. It centers around our recent answers to questions raised by Matus, Studeny, Postnikov, Reiner and Williams. The mice are in the title because everything started with the analysis of microarray data in molecular biology. Background referece Milan Studeny Probabilistic Conditional Independence Structures, Springer Series in Information Science and Statistics, 2005" |
December 06, 2006, 400 PM at Maxwell Dworkin, Rm. 115, 33 Oxford St. |
| NUMBER THEORY SEMINAR |
Jean-Francois Dat (UNIVERSITY OF PARIS 13) |
Non-abelian Lubin-Tate theory and elliptic representations |
Abstract By work of Harris-Taylor, the cuspidal part of the cohomology of Lubin-Tale towers is known to provide an explicit realization of the local Langlands correspondence. Recently Boyer described the whole cohomology and exhibited two defects i) the non-cuspidal constituents form a somehow asymmetric subset of the smooth dual of GL(N), ii) Langlands correpondence is only partially realized. We will show how to correct these defects by studying the cohomology complex of such towers in a suitable derived category. We also give an application to Drinfeld symmetric spaces" |
December 06, 2006, 300 PM at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Cumrun Vafa (HARVARD UNIVERSITY) |
Black Hole Entropy and Topological String |
" |
December 05, 2006, 430-530 PM at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
David Helm (HARVARD UNIVERSITY) |
Reduction of Shimura varieties and the Langlands program |
" |
December 04, 2006, 300 PM at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Elizabeth Denne (HARVARD) |
Simple closed curves in the plane have inscribed squares |
" |
December 01, 2006, 330-430 PM at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Marie-France Vigneras (PARIS 7 AND RADCLIFFE INSTITUTE FOR ADVANCED STUDIES) |
On the Colmez functor |
Abstract We will define the Colmez functor from locally constant representations of GL(2,Q_p) to etale (phi, Gamma)-modules, and a generalisation to GL(n, Q_p) suggested by Schneider" |
November 29, 2006, 300 PM at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
Horng-Tzer Yau (HARVARD UNIVERSITY) |
Brownian Motion in Quantum Mechanics |
" |
November 27, 2006, 300 PM at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Ben Weinkove (HARVARD UNIVERSITY) |
Kahler-Einstein metrics and Moser-Trudinger type inequalities |
" |
November 21, 2006, 430-530 PM at Science Center, Room 507 |
| SEMINAR ON DERIVED ALGEBRAIC GEOMETRY |
Jacob Lurie (HARVARD UNIVERSITY) |
Lecture X |
Please note change of time and place" |
November 21, 2006, 200-400 PM at MIT, Room 4-370 |
| FACULTY COLLOQUIUM |
Shing-Tung Yau (HARVARD UNIVERSITY) |
Hermitian metrics on complex manifolds and vector bundles |
" |
November 20, 2006, 3 PM at Science Center, Room 507 |
| CDM CONFERENCE |
Laurent Clozel, Kenneth Ribet, Paul Seidel, Yakov Sinai, Terence Tao, Edward Witten () |
Program details |
" |
November 17, 2006, Start 115 PM at Science Center, Hall D |
| MATHEMATICS EDUCATION SEMINAR SERIES |
Patrick Bahls (UNIVERSITY OF NORTH CAROLINA, ASHEVILLE) |
Change of Basis Inquiry-Based Linear Algebra |
" |
November 17, 2006, 330-430 PM at Science Center, Room 110 |
| SEMINAR ON DERIVED ALGEBRAIC GEOMETRY |
Jacob Lurie (HARVARD UNIVERSITY) |
Lecture IX |
" |
November 16, 2006, 300-500 PM at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Noam D. Elkies (HARVARD UNIVERSITY) |
Which bilinear recurrences give theta sequences? |
" |
November 15, 2006, 300 PM at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Clifford Taubes (HARVARD UNIVERSITY) |
A proof of the Weinstein conjecture in dimension 3 |
" |
November 14, 2006, 430-530 PM at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
Samit Dasgupta (HARVARD UNIVERSITY) |
Conjectures on Hilbert's 12th problem |
" |
November 13, 2006, 300 PM at Science Center, Room 507 |
| DERIVED ALGEBRAIC GEOMETRY |
Jacob Lurie (HARVARD UNIVERSITY) |
Lecture VIII |
" |
November 09, 2006, 300-500 PM at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Sug Woo Shin () |
Counting points on Igusa varieties |
Abstract We are led to study the bad reduction of Shimura varieties in order to prove instances of the local-global compatibility of the Langlands correspondence at ramified primes. Shimura varieties are closely related to Rapoport-Zink spaces and Igusa varieties in tems of geometry and cohomology, by results of Mantovan. We investigate the possibility of extending our knowledge of the local-global compatibility by studing Igusa varieties" |
November 08, 2006, 300 PM at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Denis Auroux (M.I.T.) |
The canonical pencils of Horikawa surfaces. |
" |
November 07, 2006, 430-530 PM at Science Center, Room 507 |
| HARVARD COLLOQUIUM (BASOC NOTIONS) |
Joe Harris (HARVARD UNIVERSITY) |
Specialization Methods in Algebraic Geometry |
" |
November 06, 2006, 300 PM at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY |
Tom Coates (IMPERIAL COLLEGE) |
Lagrangian Cones and Mirror Symmetry |
" |
November 03, 2006, 330- 430 PM at Science Center, Room 309 |
| JOINT MIT/HARVARD ANALYSIS SEMINAR |
Tsai Tai-Peng (UBC) |
Asymptotic stabolity of harmonic maps under the Schr/odinger flow |
Abstract For Schr/odinger maps from $/R^2times/R6+$ to the $2$-sphere $/S^2$, it is not known if finite energy solutions can form singularities (blowup) in finite time. We consider equivariant solutions with energy near the energy of the two-parameter family of equivariant harmonic maps. We prove that if the topological degree of the map is at least four, blowup does {/it not} occur, and global solutions converge (in a dispersive sense-i.e. scatter) to a fixed harmonic map as time tends to infinity. The proof uses, among other things, a time-dependent splitting of the solution, the generalized Hasimoto transform, and Strichartz (dispersive) estimates for a certain two space-dimensional linear Schr/odinger equation whose potentiol has critical power spatial singularity and decay. Along the way, we establish an energy-space local well-posedness result for which the existence time is determined by the length-scale of a nearby harmonic map. This is a joint with Stephen Gustafson and Kyungkeun Kang" |
November 03, 2006, 330 PM at MIT |
| SEMINAR ON DERIVED ALGEBRAIC GEOMETRY |
Jacob Lurie (HARVARD UNIVERSITY) |
|
" |
November 02, 2006, 300-500 PM at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Sug Woo Shin () |
Counting points on Igusa varieties |
Abstract We are led to study the bad reduction of Shimura varieties in order to prove instances of the local-global compatibility of the Langlands correspondence at ramified primes. Shimura varieties are closely related to Rapoport-Zink spaces and Igusa varieties in terms of geometry and cohomology, by results of Mantovan. We investigate the possibility of extending our knowledge of the local-global compatibility by studying Igusa varieties" |
November 01, 2006, 300 PM at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Jan-Erik Bjork (UNIVERSITY OF STOCKHOLM) |
Regularisation and meromorphic continuation of residue currents. |
Abstract [PDF]
| October 31, 2006, 430 - 530 pm at Science Center Room 507 |
| FACULTY COLLOQUIUM (BASIC NOTIONS) |
Shlomo Sternberg (HARVARD UNIVERSITY) |
The Ehrhart function for symbols and a generalization of Euler's constant |
" |
October 30, 2006, 3 PM at Science Center 507 |
| JOINT MIT-HARVARD ANALYSIS SEMINAR |
Vera Hur (MIT) |
Free-surface steady water waves with vorticity |
Abstract The water wave problem embodies the equation of hydrodynamics, the concepts of wave propagation, and the critically important role of boundary dynamics. I will give a precise account of the mathematical problem describing water waves and discuss its distinctive features. The emphasis is on the effects of the vorticity, which measures the local swirl or eddi spin in the fluid. Existence theories of traveling waves will be presented with proofs, at least with their ideas Stokes waves as an application of degree theoyr and global bifurcation theory, and solitary waves via a Nash-Moser implicit function theorem. I will discuss on a recent numerical simulation on the extremal rotational Stokes waves, new types of singular configuration attributed to the vorticity. I will talk about othe aspects of mathematical study on the water waves, the well-posedness, stability, etc.., if time permits" |
October 27, 2006, 330 PM at Science Center, Room 221 |
| GAUGE THEORY AND TOPOLOGY |
Katrin Wehrheim (MIT) |
Instanton Floer homology with Lagrangian boundary conditions - towards the Atiyah-Floer conjecture |
" |
October 27, 2006, 330 - 430 pm at Science Center Room 309 |
| SEMINAR ON DERIVED ALGEBRAIC GEOMETRY |
Jacob Lurie (HARVARD UNIVERSITY) |
Lecture VI |
" |
October 26, 2006, 300-500 PM at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Laurent Berger (IHES) |
Families of p-adic representations |
Abstract Fontaine has defined what it means for a p-adic Galois representation to be de Rham, semistable ,etc. Now let X be a space parameterizing Galois representations; what can we say about the set of x s such that V-x is de Rham, or semistable, etc? If we impose appropriate conditions, we get closed subspaces of X. This is joint work with Pierre Colmez" |
October 25, 2006, 300 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Paul Seidel (UNIVERSITY OF CHICAGO) |
Mirror symmetry and the topology of Lagrangian tori. |
" |
October 24, 2006, 430 - 530 pm at Science Center Room 507 |
| FACULTY COLLOQUIUM (BASIC NOTIONS) |
Ben Weinkove (HARVARD UNIVERSITY) |
Moment maps and geometry |
" |
October 23, 2006, 3 PM at Sci Center 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Vladimir Chernov (DARTMOUTH) |
|
" |
October 20, 2006, 330- 430 PM at Science Center 309 |
| SEMINAR ON DERIVED ALGEBRAIC GEOMETRY |
Jacob Lurie (HARVARD UNIVERSITY) |
Derived Schemes |
" |
October 19, 2006, 300-500 pm at Science Center, Room 507 |
| MATHEMATICS COLLOQUIUM |
Amie Wilkinson (NORTHWESTERN UNIVERSITY) |
Asymmetrical diffeomorphisms |
Which diffeomorphisms of a compact manifold M commute with no other diffeomorphiWhich diffeomorphisms of a compact manifold M commute with no other diffeomorphisms (except their own powers)? Smale asked if such highly asymmetrical diffeomorphisms are typical, in that they are dense in the Cr topology on the space of Cr diffeomorphisms Diffr(M). In this talk I will explain the recent (positive) solution to Smale s question for C1 symplectomorphisms and volume-preserving diffeomorphisms. I will also discuss progress on the general case. This is joint work with Christian Bonatti and Sylvain Crovisier" |
October 19, 2006, 430 at Science Center D |
| SEMINAR ON INCOMPRESSIBLE NAVIER-STOKES |
Tai-Peng Tsai (VISITING HARVARD UNIVERSITY) |
Seminar on incompressible Navier-Stokes equation |
This seminar will give an introduction to the current status of regularity of INS" |
October 18, 2006, 1200 - 200 pm at Science Center Room 232 |
| NUMBER THEORY SEMINAR |
David Helm (HARVARD UNIVERSITY) |
Towards a geometric Jacquet-Langlands correspondence for unitary Shimura varieties |
" |
October 18, 2006, 300 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM (BASIC NOTIONS) |
Peter Kronheimer (HARVARD UNIVERSITY) |
Three-manifolds, four-manifolds and Floer homology |
" |
October 16, 2006, 3 PM at Science Center 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Demetrios Christodoulou (ETH ZUERICH) |
The geometry of acoustical spacetime manifolds and the formation of shocks in fluids |
Abstract In this talk I shall present, in summary form, my recent monograph, whAbstract In this talk I shall present, in summary form, my recent monograph, which considers the relativistic Euler equations for the motion of a perfect fluid with an arbitrary equation of state. The initial data, given on a spacelike hyperplane in 4-dimensional Minkowski spacetime, are assumed to coincide with the data corresponding to a constant state outside a sphere. Under a suitable restriction on the size of the departure of the initial data from those of the constant state, certain theorems are established, which describe the maximal classical development of the initial data. In particular the theorems describe the geometry of the boundary of the domain of the maximal classical development and analyze the behavior of the solution at this boundary. A complete picture of shock formation in 3-dimensional fluids is in this way obtained" |
October 13, 2006, 330-430 at Science Center 309 |
| MIT / HARVARD ANALYSIS SEMINAR |
Enno Lenzmann (MIT) |
Pseudo-relativistic nonlinear Schr/ odinger equations |
" |
October 13, 2006, 1200 at Science Center, Room 530 |
| SEMINAR ON DERIVED ALGEBRAIC GEOMETRY |
Michael Hopkins (HARVARD UNIVERSITY) |
E-infinity ring spectra |
" |
October 12, 2006, 300 pm - 500 pm at Science Center Room 507 |
| MATHEMATICS COLLOQUIUM |
Demetrios Christodoulou (ETH ZURICH) |
The Formation of Shocks in 3-Dimensional Fluids |
" |
October 12, 2006, 1630 at Science Center Hall D |
| NUMBER THEORY SEMINAR |
Oliver Bultel (UNIVERSITY OF HEIDELBERG) |
Monodromy groups of abelian varieties of type U (n-1,1) |
We study Abelian varieties in characteristic p of which the ring of endomorphisms is the integers in a quadratic imaginary field in which p is split" |
October 11, 2006, 300 pm at Science Center Room 507 |
| RESEARCH LECTURES FOR NON-SPECIALISTS |
Curtis McMullen (HARVARD UNIVERSITY) |
The geometry of 3 manifolds |
" |
October 11, 2006, 8 PM at Science Center Lecture Hall D |
| DIFFERENTIAL GEOMETRY SEMINAR |
Valentino Tosatti (HARVARD UNIVERSITY) |
The Calabi flow with small initial energy |
" |
October 06, 2006, 430-530 at Science Center 232 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Ciprian Manolescu (COLUMBIA) |
A combinatorial description of knot Floer homology |
" |
October 6, 2006, 330-430 at Science Center 309 |
| DERIVED ALGEBRAIC GEOMETRY |
Jacob Lurie (HARVARD UNIVERSITY) |
Lecture III |
" |
October 6, 2006, 3-5PM at SciCenter 507 |
| NUMBER THEORY SERMINAR |
Matthias Schuett (HANNOVER UNIVERSITY) |
CM-newforms with rational coefficients |
We give a classification of CM-newforms with rational coefficients. This was formerly only known for weight 2, i.e. the classical CM elliptic curve case. The general proof uses the Groessencharacter, associated to a Hecke eigenform with CM by Ribet. The major application will consist in singular K3 surfaces over the rationals" |
October 03, 2006, 3 PM at 507 |
| FACULTY COLLOQUIUM (BASIC NOTIONS) |
Cliff Taubes (HARVARD UNIVERSITY) |
Does Dirac have a tin ear? |
" |
October 02, 2006, 3 PM at Science Center 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Ben Weinkove (HARVARD UNIVERSITY) |
The Calabi-Yau equation on almost-Kahler 4-manifolds |
" |
September 29, 2006, 330-430 at Science Center 309 |
| SEMINAR ON DERIVED ALGEBRAIC GEOMETRY |
Mike Hopkins (HARVARD UNIVERSITY) |
Classical Elliptic Cohomology |
" |
September 28, 2006, 3-5 PM at Science Center 507 |
| MATHEMATICS COLLOQUIUM |
Pierre Raphael (PRINCETON UNIVERSITY) |
Singularity formation for the nonlinear Schrodinger equation |
I will consider the focusing nonlinear Schrodinger equation i ut+ Delta u+u|u|p-1=0. This equation is a universal model for the propagation of waves in a nonlinear medium. From the mathematical point of view, it is an infinite dimensional Hamiltonian system with infinite speed of propagation. Of particular interest is the existence of finite time blow up solutions which is known since the 60 s, but the existence argument is purely obstructive and does not give any insight into the detailed description of the singularity formation. I will give an overview of the state of the art on this problem. In particular, I will present a series of recent results obtained in collaboration with Frank Merle which allow in some cases an explicit description of the singularity formation" |
September 28, 2006, 430 PM at Science Center Hall D |
| NUMBER THEORY SEMINAR |
Noam Elkies (HARVARD UNIVERSITY) |
[b-d, cd, bcd, 0, 0] |
These are the coefficients of the general elliptic curve E (in extended Weierstrass form) together with a point P=(0,0) such that P, 2P, 3P, and 4P are integral. This also yields an open set in the projective plane with coordinates (bcd) that birationally parametrizes the moduli space M of pairs (E,P) where E is an elliptic curve and P is any rational point on P. We use this model and similar ones to exhibit explicitly, for N up to about 16, the curves X_1(N) on M, and to study elliptic curves over C(T) or Q with a non-torsion point of low height and/or numerous integral multiples, such as those exhibited here and and here" |
September 27, 2006, 3 PM at 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Melanie Becker (TEXAS AM UNIVERSITY) |
Anomaly Cancellation and Smooth Non-Kahler Solutions in Heterotic String |
" |
September 26, 2006, 430 PM at Science Center 507 |
| DERIVED ALGEBRAIC GEOMETRY |
Jacob Lurie (HARVARD UNIVERSITY) |
A Talk on Derived Algebraic Geometry |
" |
September 21, 2006, 3-5PM at SciCenter 507 |
| SPECIAL LECTURE |
Joel Bellaiche (COLUMBIA UNIVERSITY) |
"An introduction to Arthur's conjectures" |
" |
May 25, 2006, 2:30-4:00pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Ariane Mezard (ECOLE NORMALE SUPéRIEURE, FRANCE) |
"Semi-stable representations of Gl2(Qp) and p-adic upper half plane" |
" |
May 24, 2006, 3:00pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Henri Darmon (MCGILL UNIVERSITY) |
"p-adic families of modular forms and the Gross-Kohnen-Zagier Theorem" |
" |
May 17, 2006, 3:00pm at Science Center, Room 507 |
| ANALYSIS SEMINAR |
Shih-Hsien Yu (CITY UNIVERSITY OF HONG KONG) |
"Boltzmann Green's function and its applications" |
" |
May 12, 2006, 11:00am at Science Center, Room 232 |
| SEMINAR ON TWISTED K-THEORY AND REPRESENTATIONS OF LOOP GROUPS |
Michael Hopkins (HARVARD UNIVERSITY) |
"Dirac Families" |
" |
May 11, 2006, 3-4:30pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
Martin Kolar (MASARYK UNIVERSITY, BRNO) |
"The local equivalence problem on Levi degenerate hypersurfaces" |
" |
May 10, 2006, 11:00am-12:00pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
Robert Coleman (UC BERKELEY) |
"Informal discussion about what we think we know, and what we want to know about the classical eigencurve" |
" |
May 05, 2006, 3:00pm at Science Center, Room 507 |
| SEMINAR ON TWISTED K-THEORY AND REPRESENTATIONS OF LOOP GROUPS |
Michael Hopkins (HARVARD UNIVERSITY) |
"Definition of Twisted K-theory" |
" |
May 04, 2006, 3-4:30pm at Science Center, Room 507 |
| HARVARD, BRANDEIS, M.I.T., NORTHEASTERN COLLOQUIUM AT HARVARD |
David Tartakoff (UNIVERSITY OF ILLINOIS AT CHICAGO) |
"(Analytic) regularity with high loss of derivatives, after Kohn" |
Abstract: The talk will summarize the regularity problem for solutions of the non-elliptic sums of squares of vector fields partial differential operators originating from several complex variables and present a simple new proof and extensions of Kohn s striking, even shocking recent example of hypoellipticity in the presence of large loss of derivatives." |
May 04, 2006, 4:30pm at Science Center, Lecture Hall D |
| BASIC NOTIONS SEMINAR |
Sebastian Casalaina-Martin (HARVARD UNIVERSITY) |
"Curves and Jacobians" |
ABSTRACT: Associated to a smooth algebraic curve of genus g, is a variety called the Jacobian. It is smooth, of dimension g, and moreover, can be given a group structure which identifies it with the group of line bundles of degree zero on the curve. For non-negative integers r and d, there are subvarieties of the Jacobian which correspond to line bundles on the curve, of degree d, whose space of global sections has dimension at least r+1. We will discuss the close connection between the geometry of these subvarieties and the geometry of the curve" |
May 01, 2006, 3:00pm at Science Center, Room 507 |
| SPECIAL LECTURE |
V.Vologodsky (UNIVERSITY OF CHICAGO) |
"Motivic sheaves over a curve[PDF]" |
" |
May 01, 2006, 4-5:00pm at Science Center, Room 232 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Yael Karshon (UNIVERSITY OF TORONTO) |
"Diffeology of orbifolds" |
Abstract: A modern approach to orbifolds is through Lie groupoids. A lower approach is to consider the underlying diffeology, i.e.,the underlying set X together with the information of which set-mapsfrom R^n to X are differentiable for each n. We show that, in the effective case, the diffeology determines the Lie groupoid up to Morita equivalence. Collaborators: Patrick Iglesias, Moshe Zadka, Masrour Zoghi" |
April 28, 2006, 3:15pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Samit Dasgupta (HARVARD UNIVERSITY) |
"Shintani zeta-functions and Gross-Stark units for totally real fields" |
Abstract: Let F be a totally real number field and let p be a finite prime of F, such that p splits completely in the finite abelian extension H of F. Stark has proposed a conjecture stating the existence of a p-unit in F with absolute values at the places above p specified in terms of the values at zero of the partial zeta functions associated to H/F. Gross proposed a refinement of Stark s conjecture which gives a conjectural formula for the image of Stark s unit in Fpx/E, where Fp denotes the completion of F at p and E denotes the topological closure of the group of totally positive units of F. We propose a further refinement of Gross conjecture by proposing a conjectural formula for the exact value of Stark s unit in Fpx. Our formula may be viewed as an explicit class field theory for F." |
April 26, 2006, 3:00pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
Richard Taylor (HARVARD UNIVERSITY) |
"Elliptic curves and L-functions" |
" |
April 24, 2006, 3:00pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Maryam Mirzakhani (HARVARD AND PRINCETON) |
"Simple geodesics and geometry of moduli spaces of curves" |
" |
April 21, 2006, 3:15-4:15pm at Science Center, Room 309 |
| HARVARD UNIVERSITY DUALITY SEMINAR |
Detlev Buchholz (UNIVERSITäT GöTTINGEN) |
"Integrable Models and Operator Algebras" |
Abstract: Recently, it has been possible to establish rigorously the existence of an abundance of 1+1-dimensional relativistic quantum field theories with factorizing scattering matrices by operator-algebraic means. This novel approach, which is complementary to the advanced methods of constructive quantum field theory, settles some longstanding questions in the context of integrable models (form-factor program) and sheds new light on the problem of constructing quantum field theories. In this talk, a survey is given on the basic ideas, results and perspectives of this approach" |
April 21, 2006, 11:45 am at Jefferson 453 |
| SEMINAR ON TWISTED K-THEORY AND REPRESENTATIONS OF LOOP GROUPS |
Dennis Gaitsgory (HARVARD UNIVERSITY) |
Twisted K-Theory and Representations of Loop groups |
" |
April 20, 2006, 3-4:30pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Jean-Marc Fontaine (UNIVERSITE PARIS-SUD ORSAY) |
"The special fiber of a crystalline representation" |
" |
April 19, 2006, 4:30-5:30pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Don Zagier (MAX-PLANCK-INSTITUT) |
"Mellin transforms, zeta values and the Casimir effect" |
" |
April 17, 2006, 3:00pm at Science Center, Room 507 |
| MIT/HARVARD ANALYSIS SEMINAR |
Simone Warzel (PRINCETON UNIVERSITY) |
"Level statistic on a tree" |
Abstract: The subject of this talk will be random Schrodinger operators on tree graphs. These operators are known to exhibit purely absolutely continuous spectrum and/or pure point spectrum depending on the energy and disorder regime. It is a widespread believe that for such operators the local fluctuations of the spectrum are related to the spectral type: whereas pure point spectrum should go along with Poisson statistics, purely absolutely continuous spectrum should produce a statistics with features similar to the random matrix case. We will examine this believe in the tree setting" |
April 14, 2006, 3:10-4:10pm at Science Center, Room 530 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Peter Teichner (UNIVERSITY OF CALIFORNIA AT BERKELEY) |
"Integral modular forms from super symmetric conformal field theories" |
" |
April 14, 2006, 3:15pm at Science Center, Room 309 |
| MIT/HARVARD ANALYSIS SEMINAR |
Gigliola Staffilani (MIT) |
"Symplectic non-squeezing for the KdV flow" |
Abstract: In this talk I will present a symplectic non-squeezing result for the Korteweg-de Vries (KdV) flow on the torus $\T$ obtained with Colliander, Keel, Takaoka and Tao. This result is similar to the one obtained for the NLS flow by Bourgain, and extends some work of Kuksin which initiated this line of investigation into non-squeezing results for infinite dimensional Hamiltonian systems. A major difficulty here is the lack of any sort of smoothing estimate which would allow us to easily approximate the infinite dimensional KdV flow by a finite-dimensional Hamiltonian flow. To resolve this problem we are forced to invert the Miura transform and work on the level of the modified KdV (mKdV) equation, for which smoothing estimates are available" |
April 14, 2006, 4:15pm at Science Center, Room 222 |
| SEMINAR ON TWISTED K-THEORY AND REPRESENTATIONS OF LOOP GROUPS |
Dennis Gaitsgory (HARVARD UNIVERSITY) |
"Representations of Loop Groups" |
" |
April 13, 2006, 3-4:30pm at Science Center, Room 507 |
| HARVARD, BRANDEIS, M.I.T., NORTHEASTERN COLLOQUIUM AT HARVARD |
Peter Teichner (UNIVERSITY OF CALIFORNIA, BERKELEY) |
"Generalized Cohomology via super symmetric Euclidean field theories" |
Abstract: We will survey some joint work in progress with Stephan Stolz. For a smooth manifold M, we define the space of all super symmetric d-dimensional Euclidean field theories over M. We show that after dividing out a concordance relation, the case d=0 gives de Rham cohomology and d=1 gives K-theory of M. Finally, we explain why the case d=2 might be related to the Hopkins-Miller-Lurie theory of topological modular forms" |
April 13, 2006, 4:30pm at Science Center, Lecture Hall D |
| FACULTY COLLOQUIUM |
Martin Nowak (HARVARD UNIVERSITY) |
"Five rules for the evolution of cooperation" |
" |
April 10, 2006, 3:00 pm at Science Center, Room 507 |
| MIT/HARVARD ANALYSIS SEMINAR |
Igor Rodnianski (PRINCETON UNIVERSITY) |
"Nonlinear wave equation and stability of Minkowski space II" |
" |
April 10, 2006, 1:15-2:15pm at Science Center, Room 232 |
| MIT/HARVARD ANALYSIS SEMINAR |
Natasa Pavlovic (PRINCETON UNIVERSITY) |
"On a periodic nonlinear Schrödinger equation" |
Abstract: In this talk we will present a joint work with Daniela De Silva, Gigliola Staffilani and Nikolaos Tzirakis on global well-posedness for the L2 critical Schrödinger equation with periodic boundary conditions in 1D. By combining an implementation of the method of almost conservation laws with number theoretic techniques we prove that the problem is globally well-posed in the Sobolev space Hs(T), for any s>4/9. Our 1D result matches the best known global well-posedness result for the corresponding problem on line" |
April 07, 2006, 4:15pm at MIT 2-142 |
| SPECIAL SEMESTER ON EIGENVARIETIES |
Richard Taylor (HARVARD UNIVERSITY) |
"Proving modularity without Ihara's lemma" |
" |
April 07, 2006, 3:00pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Richard Kenyon (UNIVERSITY OF BRITISH COLUMBIA) |
"Dimers and Amoebae" |
Abstract: This is joint work with Andrei Okounkov. We study perfect matchings (dimer coverings) of periodic planar graphs. Associated to a positive periodic weight function on the edges is an algebraic plane curve P(z,w)=0 whose amoeba defines the phase diagram for the underlying stat mech model" |
April 07, 2006, 3:15 pm at Science Center, Room 309 |
| MIT/HARVARD ANALYSIS SEMINAR |
Igor Rodnianski (PRINCETON UNIVERSITY) |
"Nonlinear wave equation and stability of Minkowski space I" |
This is the first of two special lectures on Einstein equation. The aim is to present a fairly detailed proof for the stability of Minkowski space." |
April 06, 2006, 2-3:30pm at Science Center, Room 411 |
| SPECIAL SEMESTER ON EIGENVARIETIES |
Richard Taylor (HARVARD UNIVERSITY) |
"Proving modularity without Ihara's lemma" |
" |
April 05, 2006, 1:00pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Olivier Wittenberg (ECOLE NORMALE SUPéRIEURE (FRANCE)) |
"Hasse principle for del Pezzo surfaces of degree 4" |
" |
April 05, 2006, 3:00pm at Science Center, Room 507 |
| SPECIAL SEMESTER ON EIGENVARIETIES |
Richard Taylor (HARVARD UNIVERSITY) |
"Proving modularity without Ihara's lemma" |
" |
April 4, 2006, 3:00pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
"Formal groups and cohomology theories" |
" |
April 03, 2006, 3:00 pm at Science Center, Room 507 |
| SEMINAR ON TWISTED K-THEORY AND REPRESENTATIONS OF LOOP GROUPS |
Michael Hopkins (HARVARD UNIVERSITY) |
|
" |
March 30, 2006, 3-4:30pm at Science Center, Room 507 |
| SEMINAR ON TWISTED K-THEORY AND REPRESENTATIONS OF LOOP GROUPS |
Michael Hopkins (HARVARD UNIVERSITY) |
|
" |
March 23, 2006, 3:00-4:00pm at Science Center, Room 507 |
| SPECIAL LECTURE |
Juerg Froehlich (ETH HOENGGERBERG, ZUERICH) |
"Nonequilibrium statistical mechanics and thermodynamics" |
Abstract: I review recent advances on how to derive the fundamental laws of thermodynamics from nonequilibrium quantum statistical mechanics. A discussion of basic concepts underlying thermodynamics, in particular of thermodynamic processes, is part of the story. I will emphasize the discussion of the 0th and the 2nd law of thermodynamics and the role of entropy production in calculating the degree of efficiency of heat engines" |
March 23, 2006, 3:00PM at Science Center, Lecture Hall E |
| NUMBER THEORY SEMINAR |
Teruyoshi Yoshida (HARVARD UNIVERSITY) |
"Hecke correspondences and semistable reduction of Shimura varieties" |
" |
March 22, 2006, 3:00pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR (ORGANIZED BY PROF. SHING-TUNG YAU) |
Rene Reinbacher (RUTGERS UNIVERSITY) |
"Bogomolov and Beyond" |
Abstract: In this talk we study stable holomorphic vector bundles on Calabi-Yau threefolds X. We use the attractor mechanism of IIB string theory to derive sufficient conditions for classes in H*(X) to correspond to Chern classes of stable bundles. We also propose some necessary conditions on these classes. In particular, we improve the original Bogomolov inequality" |
March 21, 2006, 4:30pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Seth Sullivant (HARVARD UNIVERSITY) |
"Groebner bases" |
Abstract: A Groebner basis for an ideal I in a polynomial ring is a special generating set which is useful for answering computational questions about I. Thus, the algorithm for computing Groebner bases of ideals is the main engine that drives computational commutative algebra software, like CoCoA, Singular, and Macaulay2. A geometric interpretation is that the computation of a Groebner bases takes a projective scheme and degenerates it to a monomial scheme. The resulting monomial scheme carries much of the same information as the original projective scheme, and the monomial case can be handled combinatorially. In my talk, I will try to explain these Groebner basics and hint how algebraic questions about Groebner bases can be useful in statistics" |
March 20, 2006, 3:00 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Hiraku Nakajima (KYOTO UNIVERSITY) |
"K-theoretic Donaldson invariants" |
" |
March 17, 2006, 3:15-4:15pm at Science Center, Room 309 |
| MIT/HARVARD ANALYSIS SEMINAR |
Alexander Barnett (DARTMOUTH COLLEGE) |
"Numerical study of the asymptotic rate of quantum ergodicity in chaotic billiards" |
Abstract: It is a long-standing question how eigenfunctions of the Laplacian (modes of a drum) behave asymptotically at large eigenvalue, for manifolds whose geodesic flow (Hamiltonian motion of a point particle) is hyperbolic. This field is called `quantum ergodicity or `quantum chaos . I will discuss known results and conjectures on the rate at which modes tend to become spatially uniform. I sketch the highly efficient and specialized methods invented to compute large numbers of modes of 2D Euclidean manifolds with Dirichlet boundary (ie, `billiards ), at mode numbers of order 10^6. These calculations provide, with unprecedented accuracy, evidence for the Quantum Unique Ergodicity conjecture of Rudnick-Sarnak, and for an ergodicity rate conjecture of Feingold-Peres involving the classical autocorrelation of the test function" |
March 17, 2006, 4:15 pm at MIT, Room 2-142 |
| SEVERAL COMPLEX VARIABLES SEMINAR |
Nessim Sibony (UNIVERSITY OF PARIS AT ORSAY) |
"Intersection of positive currents and applications to dynamics" |
" |
March 17, 2006, 1:00-2:00pm at Science Center, Room 232 |
| HARVARD, BRANDEIS, M.I.T., NORTHEASTERN COLLOQUIUM AT HARVARD |
Hiraku Nakajima (KYOTO UNIVERSITY) |
"Instanton counting and Donaldson invariants" |
Abstract : (based on joint work with L.Goettsche and K.Yoshioka) Nekrasov introduced a certain partition function, which can be regarded as the generating function of Donaldson invariants of $\mathbf R^4$ with the torus action. He conjectured that its leading coefficient is equal to the so-called Seiberg-Witten prepotential, which is defined via periods of elliptic curves. I will explain its solution and the relation to ordinary Donaldson invariants of 4-manifolds, especially to the wall-crossing formula" |
March 16, 2006, 4:30pm at Science Center, Lecture Hall D |
| GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR |
Yi Ni (CALTECH) |
Thurston norm minimizing Seifert surfaces |
Let K be a null-homologous knot in a closed 3-manifold Y, and F be a Seifert surface. One can cap off the boundary of F with a disk in the zero surgery on K to get a closed surface F_0. If we know that F is Thurston norm minimizing, we can ask whether F_0 is also Thurston norm minimizing. A classical theorem of Gabai says that the answer is Yes when Y is the 3-sphere. Gabai s theorem can be generalized to many other 3-manifolds using Heegaard Floer homology. In this talk, we will discuss a sufficient condition for F_0 to be Thurston norm minimizing" |
September 2019, 2000, 3:30 pm at Science Center 507 |
| NUMBER THEORY SEMINAR |
Robert Pollack (BOSTON UNIVERSITY) |
"Congruences, Iwasawa invariants and Kida's formula" |
" |
March 15, 2006, 3:00 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Bong Lian (BRANDEIS UNIVERSITY) |
"Chiral equivariant cohomology" |
" |
March 14, 2006, 4:30-5:30pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
Wilfried Schmid (HARVARD UNIVERSITY) |
"Automorphic distributions and L-functions" |
" |
March 13, 2006, 3:00pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Ilia Zharkov (HARVARD UNIVERSITY) |
"Integral affine structures" |
" |
March 10, 2006, 3:15-4:15pm at Science Center, Room 309 |
| MIT/HARVARD ANALYSIS SEMINAR |
Sylvia Serfaty (NYU) |
"Vortices in the Ginzburg-Landau model in the strongly repulsive limit" |
Abstract: I will present a series of rigorous results on the 2-dimensional Ginzburg-Landau model describing superconductors in an applied magnetic field, in the asymptotic regime of high-kappa (or strongly repulsive limit) where the vortices become point-like. The vortices are topological singularities: they are zeros of the order parameter carrying a nonzero degree. The results derive the values of critical fields for which vortices appear in energy-minimizers, an the (energetically) optimal numbers and repartitions of the vortices, obtained through the derivation of limiting problems. If time allows I will also present results on non-minimizing critical points. Most results are joint works with Etienne Sandier (Paris 12)" |
March 10, 2006, 4:15-5:15pm at MIT 2-142 |
| SEMINAR ON TWISTED K-THEORY AND REPRESENTATIONS OF LOOP GROUPS |
Michael Hopkins (HARVARD UNIVERSITY) |
|
" |
March 09, 2006, 3:00-4:30pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Yoichi Mieda (TOKYO UNIVERSITY, JAPAN) |
"On the action of the Weil group on the l-adic cohomology of rigid spaces over local fields" |
Abstract: In this talk, I give some fundamental results on the action of the Weil group on the compactly supported l-adic cohomology groups of rigid spaces over local fields. I will show that every eigenvalue of the action is a Weil number. Moreover I will prove the l-independence of the alternating sum of the traces of the action. The key of the proofs is the study of a generalization of the weight spectral sequence." |
March 08, 2006, 3:00pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR ( SPONSORED BY PROF. SHING-TUNG YAU) |
Jan Metzger (MAX PLANCK INSTITUTE) |
"Stable marginally trapped surfaces and dynamical horizons" |
" |
March 07, 2006, 4:15-5:15pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
Gerald Sacks (HARVARD UNIVERSITY) |
"Vaught's Conjecture" |
Abstract: Let T be a countable theory, and let M(T) be the set of countable models of T up to isomorphism. For example, T is the theory of algebraically closed fields, and a model of T is an algebraically closed field. Vaught s Conjecture says: if M(T) is uncountable, then M(T) has the same size as the set of real numbers" |
March 06, 2006, 3:00 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Jeff Viaclovsky (MIT) |
"Moduli spaces of anti-self-dual Riemannian metrics" |
" |
March 03, 2006, 3:15-4:15pm at Science Center, Room 309 |
| MIT/HARVARD ANALYSIS SEMINAR |
Jonathan Mattingly (DUKE UNIVERSITY) |
"Stochastic Navier Stokes: Spectral gaps and Ergodicity" |
I will discuss recent progress in understanding mixing and ergodicity in stochastically forced PDEs. I will use the 2D stochastic Navier Stokes equation as my primary example. I will concentrate on the case where the forcing is degenerate in that all of the degrees of freedom are not directly agitated stochastically. This hyopelliptic setting will require an infinite dimensional version of Hormander s sum of squares theorem. The discussion will include the use of ideas from Malliavin calculus and a replacement for the classical strong Feller property for Markov semi-group" |
March 03, 2006, 4:15pm at MIT 2-142 |
| NUMBER THEORY SEMINAR |
Avner Ash (BOSTON COLLEGE (VISITING HARVARD UNIVERSITY)) |
"p-adic deformations of arithmetic cohomology" |
" |
March 01, 2006, 3:00 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR (SPONSORED BY PROF. SHING-TUNG YAU) |
EDWARD GOLDSTEIN (BRANDEIS UNIVERSITY) |
"Volume minimization and estimates for isotropic submanifolds" |
Abstract: We ll begin by using integral geometry to exhibit global volume-minimizing properties for certain isotropic submanifolds in complex projective spaces. This will lead us to a problem of approximating holomorphic curves by isotropic surfaces- two area comparison results in this direction will be presented" |
February 28, 2006, 4:30-5:30pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Elizabeth Denne (HARVARD UNIVERSITY) |
"The Cauchy-Crofton Formula and Integral Geometry" |
" |
February 27, 2006, 3:00 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Igor Rodnianski (PRINCETON UNIVERSITY) |
"Kirchoff-Sobolev formula and applications to Yang-Mills and General Relativity" |
" |
February 24, 2006, 3:15-4:15pm at Science Center, Room 309 |
| MIT/HARVARD ANALYSIS SEMINAR |
Laszlo Erdoes (MUNICH) |
"Magnetic Lieb-Thirring inequalities" |
Abstract: The Pauli operator describes the energy of a nonrelativistic quantum particle with spin-1/2 in a magnetic field and an external potential. Bounds on the sum of the negative eigenvalues are called magnetic Lieb-Thirring (MLT) inequalities. The main feature of our estimate, compared to earlier results, is that in the large field regime it grows with the optimal (first) power of the strength of the magnetic field. As a byproduct of the method, we also obtain optimal upper bounds on the pointwise density of zero energy eigenfunctions of the Dirac operator. This is a joint work with J.P. Solovej" |
February 24, 2006, 4:15-5:15pm at Science Center, Room 222 |
| HARVARD, BRANDEIS, M.I.T., NORTHEASTERN COLLOQUIUM AT HARVARD |
Igor Rodnianski (PRINCETON UNIVERSITY) |
"On the Cauchy problem in General Relativity" |
Abstract: The talk will review some of the advances in the initial value problem in General Relativity covering: a breakdown criterion and connection with the Yang-Mills problem, new approach to stability of Minkowski space, and red-shift and radiation decay on a black hole background" |
February 23, 2006, 4:30pm (There will be tea at 4pm in the 4th floor Common Area) at Science Center, Hall D |
| NUMBER THEORY SEMINAR |
Alexander Stasinski (HARVARD UNIVERSITY) |
"Representations of reductive groups over finite rings and extended Deligne-Lusztig varieties" |
" |
February 22, 2006, 3:00 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR (ORGANIZED BY PROF. SHING-TUNG YAU) |
Andrei Todorov (UC SANTA CRUZ) |
"Regularized determinants of Calabi-Yau metrics" |
" |
February 21, 2006, 4:30pm at Science Center, Room 507 |
| MIT/HARVARD ANALYSIS SEMINAR |
Tom Hou (CALTECH) |
"The Interplay between Local Geometric Properties and the Global Regularity of the 3D Incompressible Euler Equations" |
Abstract: Whether the 3D incompressible Euler equation can develop a finite time singularity from smooth initial data has been an outstanding open problem. Here we review some existing computational and theoretical work on possible finite blow-up of the 3D Euler equation. We show that there is a sharp relationship between the geometric properties of the vortex filament and the maximum vortex stretching. By exploring this local geometric property of the vorticity field, we have obtained a global existence of the 3D incompressible Euler equations provided that the unit vorticity vector and the velocity field have certain mild regularity property in a very localized region containing the maximum vorticity. Further, we perform large scale computations of the 3D Euler equations to re-examine the alleged finite-time blowup of the two antiparallel vortex tubes, which has been considered as the most promising candidate for a finite-time blowup of the 3D Euler equations. Our numerical studies indicate that the maximum vorticity does not grow faster than double exponential in time. The velocity field and the enstrophy remain bounded throughout the computations. The vortex lines near the region of the maximum vorticity are relatively straight. This local geometric regularity of vortex lines seems to be responsible for the dynamic depletion of vortex stretching" |
February 17, 2006, 4:15 pm at Science Center, Room 222 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Marco Gualtieri (MIT) |
"Generalized complex manifolds in dimension four" |
Abstract: Generalized complex structures provide a unification of complex and symplectic geometry. In dimension 4 they can be viewed as complexified symplectic manifolds which are singular in a certain sense along loci in the manifold. Using this, I will describe a surgery which can be performed on symplectic 4-manifolds which can be used to construct new examples of generalized complex manifolds" |
February 17, 2006, 3:15pm-4:15pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Andre Reznikov (TEL-AVIV UNIVERSITY) |
"Rankin-Selberg type spectral identities and Gelfand pairs" |
Abstract: We discuss a simple method to construct Rankin-Selberg type spectral identities, including the classical identity and its anisotropic new analog. The method is based on the notion of Gelfand pairs. These identities could be used in order to obtain strong bounds on various periods of automorphic forms (including various sub-convexity bounds for special values of L-functions). Joint with J. Bernstein (Tel-Aviv)" |
February 15, 2006, 3:00 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
Dick Gross (HARVARD UNIVERSITY) |
"Arithmetic on elliptic curves: an update on Tate's Inventiones paper" |
" |
February 13, 2006, 3:00 pm at Science Center, Room 507 |
|
Michael Hopkins (HARVARD UNIVERSITTY) |
"SEMINAR ON TWISTED K-THEORY AND REPRESENTATIONS OF LOOP GROUPS" |
" |
February 13, 2006, 3:00pm at Science Center, Room 507 |
| MIT/HARVARD ANALYSIS SEMINAR |
Gang Zhou (TORONTO) |
"On Solitons Dynamics in Nonlinear Schr\"odinger Equations with potential." |
Nonlinear Schr\odinger equations with external potentials arise in condensed matter physics, nonlinear optics, plasma physics, theory of water waves and in other areas of physics and applied mathematics. For strong nonlinearities such equations have solitons trapped near minima of the potentials. We prove, under certain conditions on the potentials and initial conditions, that trapped solitons are asymptotic stable. The dynamics law of motion of the soliton is close to Newton s equation but with a dissipative term due to radiation of the energy to infinity" |
February 10, 2006, 4:15pm at Science Center, Room 222 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Dennis Gaitsgory (HARVARD UNIVERSITY) |
"A review of the geometric Langlands program" |
" |
February 10, 2006, 3:15-4:15 pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
David Helm (HARVARD UNIVERSITY) |
"Mazur's principle for certain U(2,1) Shimura varieties" |
" |
February 8, 2006, 3:00pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR/ SPONSORED BY PROF. SHING-TUNG YAU |
Gaoyong Zhang (POLYTECHNIC UNIVERSITY BROOKLYN, NY) |
"An L_p Affine Isoperimetric Inequality" |
" |
February 07, 2006, 4:30-5:30pm at Science Center, Room 507 |
| ALGEBRAIC GEOMETRY SEMINAR |
Curtis T. McMullen (HARVARD UNIVERSITY) |
"Dynamics on blowups of the projective plane" |
" |
February 07, 2006, 3:00 pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
Barry Mazur (HARVARD UNIVERSITY) |
"Functional Equations, signs, and their implications" |
" |
February 06, 2006, 3:00 pm at Science Center, Room 507 |
| MIT/HARVARD ANALYSIS SEMINAR |
Robert Seiringer (PRINCETON UNIVERSITY) |
"Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases" |
Abstract: We present a proof that the Gross-Pitaevskii (GP) equation correctly describes the ground state energy and corresponding one-particle density matrix of rotating, dilute, trapped Bose gases with repulsive two-body interactions. We also show that there is 100% Bose-Einstein condensation. While a proof that the GP equation correctly describes non-rotating or slowly rotating gases was known for some time, the rapidly rotating case was unclear mainly because the Bose (i.e., symmetric) ground state is not the lowest eigenstate of the Hamiltonian in this case. For the case of axially symmetric traps, our results show that the appearance of quantized vortices causes spontaneous symmetry breaking in the ground state. (Joint work with Elliott Lieb." |
February 03, 2006, 4:15 pm at Science Center, Room 222 |
| DIFFERENTIAL GEOMETRY SEMINAR |
JAKE SOLOMON (MIT) |
"Intersection Theory on the Moduli Space of Holomorphic Curves with Lagrangian Boundary Conditions" |
" |
December 20, 2005, 4:30-5:30pm at Science Center, Room 507 |
| MATHEMATICS EDUCATION SPEAKER SERIES SEMINAR |
Aaron Weinberg (ITHACA COLLEGE) |
Process-Object Frameworks and Mediating Metaphors |
Have you ever wondered why some students have a difficult time with even the most basic notions of calculus? One explanation involves Action-Process-Object-Schema (APOS) theory" |
December 19, 2005, 2 PM at SC 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Paul Seidel (UNIVERSITY OF CHICAGO) |
"Symplectic cohomology and Lefschetz fibrations" |
" |
December 16, 2005, 3:30pm at Science Center, Room 309 |
| DIFFERENTIAL GEOMETRY SEMINAR |
YE TIAN (MCGILL UNIVERSITY) |
"Rational points on modular abelian varieties" |
" |
December 16, 2005, 2:00-3:00pm at SCIENCE CENTER ROOM 507 |
| HARVARD, BRANDEIS, M.I.T., NORTHEASTERN COLLOQUIUM AT HARVARD |
Paul Seidel (UNIVERSITY OF CHICAGO) |
"The topology of Lagrangian submanifolds" |
Abstract: We will consider some questions about Lagrangian submanifolds of symplectic manifolds, restricting ourselves to a basic case, namely that of cotangent bundles. This was one of the original motivations for the introduction of cohomological (Floer theory) methods into symplectic topology, and a number of interesting partial results were obtained (Lalonde-Sikorav, Viterbo, Biran, among others). More recently, the area has received a new impetus from ideas of Donaldson and Fukaya-Smith, which bring us closer to understanding the big picture" |
December 15, 2005, 4:30pm at Science Center, Lecture Hall D |
| NUMBER THEORY SEMINAR |
Philippe Cassou-Nogues (BORDEAUX) |
"Galois module structure in Geometry" |
After recalling some classical results on the Galois module structure of rings of algebraic integers of number fields, we will explain how, in order to generalize them, we are led to study the Galois module structure of certain torsors associated with the rational points of abelian schemes. Finally, following, Ted Chinburg, we will introduce the notion of equivariant Euler characteristics of coherent sheaves and will give examples where their determination provides, in this geometric context, analogues of the results we started with. Numerous results of this talk have been obtained either by T. Chinburg, G. Pappas, and M.J. Taylor or are part of joint works with them." |
December 14, 2005, 3:00pm at Science Center, Room 507 |
| MATHEMATICS EDUCATION SEMINAR |
Igor Verner (TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY) |
Mathematics in Architecture Education: From Context Problems to Design Tasks |
Our study considers an applications-motivated mathematics curriculum for architecture colleges. At the first stage we developed a calculus course, based on the Realistic Mathematics Education approach. The course follow-up indicated the positive effect of integratingapplications on motivation, understanding, creativity and interest in mathematics. However we did not found that the architecture students considerably applied mathematical knowledge acquired in the course in their senior design projects. This situation motivated us to develop a Mathematical Aspects in Architectural Design (MAAD) course based on the Mathematics as a Service Subject approach. The MAAD course offers mathematical learning as part of hands-on practice in the architecture design studio. The course focuses on the analysis of different types of geometrical forms used in architectural design and consists of three parts: (1) Arranging regular shapes to cover the plain (tessellations), (2) Bending bars and flat plates to form curve lines and surfaces (deformations), (3) Intersecting solids (constructions). Each of the parts includes learning mathematical concepts, practice in solving mathematical problems in architecture, and a design project. The MAAD course follow-up showed that the students expressed curiosity and motivation to the project experience, and interest to deepen in mathematical subjects. The majority of the students practically applied their background mathematical knowledge and the new concepts learned in the course in their projects. The correlation between the project grades for design and mathematics showed the tight integration of the two subjects in the course" |
December 13, 2005, 3-4pm at Science Center, Room 705 |
| DIFFERENTIAL GEOMETRY SEMINAR |
CHIEN-HAO LIU (HARVARD UNIVERSITY) |
"Phase structures in superstring theory and transitions of Gromov-Witten invariants" |
" |
December 13, 2005, 4:30-5:30pm at SCIENCE CENTER ROOM 507 |
| QED SEMINAR |
J. Dimock (BUFFALO) |
"A renormalization group analysis of QED in 2+1 dimensions" |
" |
December 13, 2005, 1:00-2:30 pm at Science Center, Room 232 |
| FACULTY COLLOQUIUM |
Horng-Tzer Yau (HARVARD UNIVERSITY) |
"Some unsolved problems in quantum physics" |
" |
December 12, 2005, 3:00pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Rosa Sena-Dias (HARVARD UNIVERSITY) |
"Estimated transversality and rational maps" |
In his work on symplectic Lefschetz pencils, Donaldson introduced the notion of estimated transversality for a sequence of sections of a bundle. Together with asymptotic holomorphicity, it is the key ingredient allowing the construction of symplectic submanifols. Despite its importance in the area, estimated transversality has remained a mysterious property. In this talk our aim is to shed some light into this notion by studying it in the simplest possible case namely that of S 2. We state some new results about high degree rational maps on the 2-sphere that can be seen as consequences of Donaldson s existence theorem for pencils, and explain how one might go about answering a question of Donalson: what is the best estimate for transvesality that can be obtained? We also show how the methods applied to S 2 can be further generalized." |
December 09, 2005, 3:30-4:30pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
David Pollack (WESLEYAN UNIVERSITY) |
"Rigidity of p-adic cohomology classes for GL_3" |
Abstract: This is a report on joint work with Avner Ash and Glenn Stevens. Ash and Stevens have previously described p-adic analytic families of ordinary arithmetic cohomology classes for GL_n over Q, where the Hecke eigenvalues vary p-adic analytically as functions of the weight. In contrast to the GL_2 case, not all ordinary classes for GL_n deform in families. We will discuss a notion of p-adic rigidity for eigenclasses in the cohomology of GL_n, and give examples of non-selfdual cohomological cuspforms for GL_3 that are p-adically rigid" |
December 07, 2005, 3:00pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
ZHIQIN LU (UNIVERSITY OF CALIFORNIA IRVINE) |
"Weil-Petersson geometry on CY moduli" |
" |
December 06, 2005, 10:00-11:00am at Science Center, Room 530 |
| BASIC NOTIONS SEMINAR |
Veronique Godin (HARVARD UNIVERSITY) |
"String Topology (I)" A prequel to Dennis Sullivan's talk |
" |
December 05, 2005, 3:00pm at Science Center, Room 507 |
| GLOBAL METHODS IN CHROMATIC HOMOTOPY THEORY SEMINAR |
Tyler Lawson (MIT) |
"Topological Automorphic Forms II" |
Abstract: I will be reviewing and continuing Mark s talk from October. We will be discussing certain moduli problems of abelian varieties whose local deformation theory looks like the deformation theory of 1-dimensional p-divisible groups, and hence (by Jacob s talk) give rise to E_\infty ring spectra generalizing the spectrum of topological modular forms" |
December 02, 2005, 3:30pm at Science Center, Room 309a |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Ed Witten (IAS) |
"More on Twisted, N=4 Super Yang-Mills Theory" |
" |
December 02, 2005, 2:00-3:00pm at Science Center. Lecture Hall C |
| HARVARD, BRANDEIS, M.I.T., NORTHEASTERN COLLOQUIUM AT HARVARD |
Edward Witten (INSTITUTE FOR ADVANCE STUDY) |
"Gauge Theory and the Geometric Langlands Program" |
Abstract: A twisted version of N=4 supersymmetric Yang-Mills theory in four dimensions gives a natural framework for understanding the geometric Langlands program. Langlands duality arises from electric-magnetic duality of the gauge theory, with t Hooft operators playing the role of Hecke operators and D-modules arising from the noncommutativity of branes" |
December 01, 2005, 4:30pm at Science Center, Hall D |
| NUMBER THEORY SEMINAR |
Noam Elkies (HARVARD UNIVERSITY) |
"K3 and elliptic surfaces of high Q-rank" |
" |
November 30, 2005, 3:00pm at Science Center, Room 507 |
| ANALYSIS SEMINAR |
Wilhelm Schlag (UNIVERSITY OF CHICAGO) |
"On the focusing, energy critical, semi-linear wave equation in three dimensions" |
Abstract: We will describe recent joint work with Joachim Krieger on stable manifolds for this equation. They arise in the study of perturbations of certain stationary solutions. The latter are extremizers for the critical Sobolev imbedding in three dimensions (they minimize the Dirichlet energy with fixed L^6 norm). Since they have infinite L^2 mass, there has been some controversy in the physics literature as to their mobility under small perturbations (does it take infinite energy to move them?). We will comment on this and other issues, as for example the failure of modulation theory in this context" |
November 29, 2005, 2:30pm at Science Center, Room 232 |
| DIFFERENTIAL GEOMETRY SEMINAR |
STEVEN ROSENBERG (BOSTON UNIVERSITY) |
"Chern-Simons classes on loop spaces." |
" |
November 29, 2005, 4:30-5:30pm at Science Center, Room 507 |
| MATHEMATICS EDUCATION SPEAKER SERIES |
Igor Verner (TECHNION-ISRAEL INSTITUTE OF TECHNOLOGY) |
The effect of Integrating Applications in the Technion Calculus Course |
In this talk, I will present a Ph.D. study of Shuki Arashas under my supervision together with Prof. Avi Berman from the Technion Faculty of Mathematics. we conducted an education design experiment in which applications were integrated in the Multivariable Calculus course at the Technion. The purpose of our study was to epmphasize the connections between the mathematics course and the science and engeneering disciplines, and exmine the effect of applications on students understanding of calculus concepts, course achievements, and learning motivation. In the experiment, we extended the conventional curriculum by optional applictions motivatated tutroing sessions and tested several supplemental instruction frameworks. The follow-up inidicated the contribution of application tutoring sessions to understand calculus concepts and their significant positive effect on students achievements and motivation" |
November 29, 2005, 3PM at Science Center 705 |
| BASIC NOTIONS SEMINAR |
Thomas Lam (HARVARD UNIVERSITY) |
"Schubert polynomials for affine Grassmannians'' |
" |
November 28, 2005, 3:00pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Xi-Ping Zhu (ZHONGSHAN UNIVERSITY & CHINESE UNIVERSITY OF HONG KONG) |
"Complete noncompact Kahler manifolds with positive bisectional curvature" |
" |
November 22, 2005, 4:30-5:30pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
S.-T. Yau (HARVARD UNIVERSITY) |
"Mathematical problems in general relativity" |
" |
November 21, 2005, 3:00-4:00pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Michael Bush (UMASS AMHERST) |
"Mild pro-p groups and p-extensions with restricted ramification" |
Abstract: This talk will start with a survey of some work by J. Labute on mild pro-p groups. These groups have many nice properties and are of interest in number theory because they often arise as the Galois groups Gs(p) of maximal p-extensions of Q with ramification restricted to a finite set of primes S. In the latter part of the talk I will describe some ongoing joint work with Labute where we attempt to completely characterize those extensions of Q which are mild" |
November 16, 2005, 3:00pm at Science Center, Room 507 |
| ANALYSIS SEMINAR |
Christian Hainzl (UNIVERSITY OF ALABAMA AT BIRMINGHAM) |
"The mean-field approximation to Quantum Electrodynamics. The no-photon case" |
Abstract: Starting from a first-priciple QED Hamiltonian, in Coulomb gauge, neglecting photons, we show that, in a mean-field approximation, this Hamiltonian has a minimizer although it is a priori ill defined. We make sense out of it by means of an infinite volume limit. In the case of no external fields this corresponds to a correct filling of the Dirac sea by means of a minimization principle. Its energy is not finite but in cases of external fields and particles we can ask how does this vacuum respond and the physical quantities are then finite and can be described by an effective functional" |
November 15, 2005, 2:30-3:30pm at Science Center, Room 232 |
| BASIC NOTIONS SEMINAR |
Bob Strain (HARVARD UNIVERSITY) |
"Partial Differential Equations and Ludwig Boltzmann" |
" |
November 14, 2005, 3:00-4:00pm at Science Center, Room 507 |
| HARVARD, BRANDEIS, M.I.T., NORTHEASTERN COLLOQUIUM AT HARVARD |
Edward Bierstone (UNIVERSITY OF TORONTO) |
"Functoriality in resolution of singularities" |
Abstract: Algorithms for resolution of singularities in characteristic zero (by Bierstone-Milman, Villamayor and, more recently, Wlodarczyk and Kollar) are based on Hironaka s idea of reducing the problem to a simpler question of desingularization of an idealistic exponent or marked ideal. How can we determine whether two marked ideals undergo the same resolution process? From the point of view of this question of functoriality or equisingularity, I will compare algorithms and discuss results and open problems" |
November 10, 2005, 4:30pm at Science Center, Lecture Hall D |
| NUMBER THEORY SEMINAR |
Erez Lapid (JERUSALEM AND IAS) |
"The relative trace formula and its applications" |
Abstract: The relative trace formula is a tool invented by Jacquet in order to study period integrals of automorphic forms. Such period integrals are of interest because they are related to special values of L-functions, functoriality and arithmetic. I will discuss the setup and what is known about the relative trace formula (thanks to the hard work of many people, including Baruch,Jacquet,Mao,Offen,Rallis,Rogawski and myself) focusing on two examples. The first is periods over unitary groups. This includes the case of compact unitary groups, where the period amounts to a sum of point evaluations (over a genus of a fixed Hermitian form) of an automorphic form on an arithmetic quotient of the symmetric space of positive-definite Hermitian forms of rank n. The second example is a relative trace formula setup for the theta correspondence. This is useful in order to obtain precise versions of Waldspurger s result on Fourier coefficient of half-integral weight modular forms and its higher rank generalizations" |
November 09, 2005, 3:00pm at Science Center, Room 507 |
| ANALYSIS SEMINAR |
Fanghua Lin (COURANT INSTITUTE NEW YORK UNIVERSITY) |
"Segregations, Partitions and Maps into Singular Spaces" |
Abstract: Here we discuss asymptotic behavior of a class of strongly (interactive) coupled systems which are reduced from Nonlinear Schrodinger Systems or Reaction-Diffusion systems ehen the coupling constants go to infinite.We established the limits to be a class of optimal partition problems.The regularity of free boundaries in the problem would be our main concern.It is a joint work with Luis Caffarelli" |
November 08, 2005, 2:15pm at Science Center, Room 232 |
| DIFFERENTIAL GEOMETRY SEMINAR (ORGANIZED BY PROF. SHING-TUNG YAU) |
Bing Cheng (CORNELL UNIVERSITY) |
"Minimization with the Affine Normal Direction" |
" |
November 08, 2005, 4:30-6:00pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Jean-Pierre Serre (COLLEGE DE FRANCE) |
"Number of points mod m" |
" |
November 07, 2005, 3:00pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Frank Calegari (HARVARD UNIVERSITY) |
"Rational Homology Spheres and Automorphic Forms" |
Abstract: Let M be a compact connected orientable 3-manifold. A conjecture of Thurston predicts that whenever the fundamental group of M is infinite the manifold M admits a finite cover with non-trivial (rational) first homology. This conjecture implies geometrization for such M, but is unknown even for hyperbolic manifolds. Assuming M is hyperbolic, one possible approach to Thurston s conjecture is to show that _any_ ``sufficiently big (in some sense) manifold M must have non-trivial first homology. In joint work with Nathan Dunfield we show that for a certain natural definition of sufficiently big (large injectivity radius) this approach fails. Our construction uses the Riemann Hypothesis" |
November 04, 2005, 3:30pm at Science Center, Room 309 |
| DIFFERENTIAL GEOMETRY SEMINAR |
XI-PING ZHU (ZHONGSHAN UNIVERSITY & CHINESE UNIVERSITY OF HONG KONG) |
"RICCI FLOW" |
" |
November 03, 2005, 1.30 - 1.00 PM at SCIENCE CENTER room 530 |
| NUMBER THEORY SEMINAR |
Kiran Kedlaya (MIT) |
"Bounding Picard numbers of surfaces, or How to succeed in coding theory without really trying" |
" |
November 02, 2005, 3:00pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR (ORGANIZED BY PROF. SHING-TUNG YAU) |
William Meeks (UNIVERSITY OF MASSACHUSETTS-AMHERST) |
"The minimal lamination closure theorem, the local removable singularity theorem, the quadratic curvature decay theorem and the dynamics theorem for embedded minimal surfaces" |
" |
November 01, 2005, 4:30-6:00pm at Science Center, Room 507 |
| ANALYSIS SEMINAR |
Avraham Soffer (RUTGERS UNIVERSITY) |
"Dispersive decay, methods and applications" |
Abstract: Decay estimates of wave equations play an important role in scattering and spectral theory, and various new techniques have been developed in the last twenty years. I will describe some new approaches and results, of general nature" |
November 01, 2005, 1:00-2:30pm at Science Center, Room 232 |
| FACULTY COLLOQUIUM |
Yum-Tong Siu (HARVARD UNIVERSITY) |
"Multiplier ideals -- a new technique linking analysis and algebraic geometry" |
" |
October 31, 2005, 3:00pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Jenny Harrison (BERKELEY) |
"What is Stokes' theorem--from algebraic beginnings to geometric completions" |
" |
October 28, 2005, 3:30pm at Science Center, Room 309 |
| DIFFERENTIAL GEOMETRY SEMINAR |
XI-PING ZHU (ZHONGSHAN UNIVERSITY & CHINESE UNIVERSITY OF HONG KONG) |
"RICCI FLOW" |
" |
October 27, 2005, 11:30am-12:30pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
Ben Green (BRISTOL AND MIT) |
"Generalising the Hardy-Littlewood method for primes" |
Abstract: The Hardy-Littlewood method is a collection of tools in harmonic analysis which can be used to prove spectacular results in additive number theory. In 1937, for example, Vinogradov showed that all large odd numbers are the sum of three primes. Unfortunately, the method breaks down completely in certain situations of interest. Rather than solve a single linear equation in 3 primes, one might for example wish to solve two linear equations in 4 primes simultaneously (say if one was interested in arithmetic progressions of 4 primes). I will talk about some joint work with Terry Tao in which we have succeeded in partially generalising the H-L method to cover situations like this. In particular, I will sketch a proof of an asymptotic formula for the number of quadruples p_1 < p_2 < p_3 < p_4 < N of primes in arithmetic progression. The generalisation involves 2-step nilpotent Lie groups, and our motivation comes from ergodic theory. I will attempt to explain something of these connections" |
October 26, 2005, 3:00pm at Science Center, Room 507 |
| CLAY PUBLIC LECTURE |
Professor Hendrik W. Lenstra ((LEIDEN UNIVERSITY)) |
"Escher and the Droste Effect" |
The Print Gallery, a 1956 lithograph by the Dutch graphic artist M.C. Escher, features a stunning optical illusion -- a hidden Droste effect which produces an infinite series of self-reflections. On the basis of this discovery, a team of mathematicians at Leiden produced a series of hallucinating computer animations. These show, among others things, what happens inside the mysterious spot that Escher left blank in the middle of the lithograph. Hendrik W. Lenstra is active in number theory and algebra. He is best known for introducing advanced techniques in the area of number-theoretic algorithms which have important applications in the areas of cryptography and computer security. Open to the Public. Hosted by the Harvard Mathematics Department. For more information see www.claymath.org" |
October 25, 2005, 7:00pm at Science Center, Lecture Hall B |
| DIFFERENTIAL GEOMETRY SEMINAR (ORGANIZED BY PROF. SHING-TUNG YAU) |
Andreas Bjorn (HUMBOLDT UNIVERSITY-BERLIN) |
"Standard models from the heterotic string" |
" |
October 25, 2005, 4:30-6:00pm at Science Center, Room 507 |
| ANALYSIS SEMINAR |
Jacob Sterbenz (UCSD) |
"Long time decay for the wave equation on Schwarzschild space and non-linear scalar fields" |
" |
October 25, 2005, 2:30-3:30pm at Science Center, Room 232 |
| FACULTY COLLOQUIUM |
Dennis Gaitsgory (HARVARD UNIVERSITY) |
"Affine Kac-Moody algebras and their representations" |
This is a new series in which our senior faculty will give talks aimed at first year graduate students who want to get a feel for different areas of research" |
October 24, 2005, 3:00pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR (ORGANIZED BY PROF. SHING-TUNG YAU) |
Xi-Ping Zhu (CHINESE UNIVERSITY OF HONG KONG & SHONGSHAN UNIVERSITY) |
"Ricci Flow" |
" |
October 21, 2005, 2:00-3:00pm at Science Center, Room 530 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Jake Rasmussen (PRINCETON UNIVERSITY) |
"Stabilization in SL(N) knot homology" |
Early in 2004, Khovanov and Rozansky introduced a bigraded homology theory categorifying the sl(N) knot polynomial. I ll describe some conjectures (joint with N. Dunfield and S. Gukov) related the limiting behavior of this homology theory as N goes to infinity, and explain some of the computational evidence supporting them" |
October 21, 2005, 3:30pm at Science Center, Room 309 |
| HARVARD, BRANDEIS, M.I.T., NORTHEASTERN COLLOQUIUM AT HARVARD |
John Conway (PRINCETON UNIVERSITY) |
"15- and 290- Theorems" |
Abstract: These are theorems about universal quadratic forms. They answer the ollowing question: If a quadratic form represents 1,2,3,..., n, how large does n have to be so that we know it represents all positive integers. Schneeberger and I proved about ten years ago that the answer is 15 for positive definite forms with integral matrices. Very recently, Bhargava and Hanke proved that the answer is 290 for forms with integer values" |
October 20, 2005, 4:30 at Science Center, Lecture Hall D |
| NUMBER THEORY SEMINAR |
Dimitri Leemans (UNIVERSITE LIBRE DE BRUXELLES AND NORTHEASTERN UNIVERSITY) |
"The Suzuki simple groups Sz(q) seen as automorphism groups of some geometric structures" |
Using Jacques Tit s algorithm, a group G and some of its subgroups may be used to construct geometric structures on which G acts as an automorphism group. After introducing the basic notions of incidence geometries, we will focus on the infinite family of Suzuki simple groups Sz(q) (with q an odd power of 2). We will outline some classifications of incidence geometries and abstract polytopes on which these groups act as automorphism groups and show some number theory problems that arise while classifying these structures" |
October 19, 2005, 3:00pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR (ORGANIZED BY PROF. SHING-TUNG YAU) |
Pan Peng (HARVARD UNIVERSITY) |
"Ring structure in topological string partition function" |
" |
October 18, 2005, 4:30-6:00pm at Science Center, Room 507 |
| ANALYSIS SEMINAR |
Michael Loss (GEORGIAN TECH.) |
"A lower bound on the free energy of matter interacting with radiation" |
Abstract: The proof of the existence of the thermodynamic limit for matter was accomplished decades ago in the framework of non-relativistic quantum mechanics by Lieb and Leowitz. This result did not take account of interactions caused by magnetic fields, however, (the spin-spin interaction, in particular) or of the quantized nature of the electromagnetic field. Recent progress has made it possible to undertake such a proof in the context of non-relativistic QED. In this talk I will present one part of such a proof by giving a lower bound to the free energy that is proportional to the number of particles and which takes account of the fact that the field, unlike the particles, is never confined to a finite volume. This is joint work with Elliott Lieb" |
October 18, 2005, 2:30-3:30pm at Science Center, Room 232 |
| FACULTY COLLOQUIUM |
Joe Harris (HARVARD UNIVERSITY) |
"The Brill-Noether Theorem: representation theory for curves'' |
" |
October 17, 2005, 3:00pm at Science Center, Room 507 |
| GLOBAL METHODS IN CHROMATIC HOMOTOPY THEORY SEMINAR |
Jacob Lurie (HARVARD UNIVERSITY) |
"The Hopkins-Miller theorem for p-divisible groups" |
" |
October 14, 2005, 3:30pm at Science Center, Room 309a |
| DIFFERENTIAL GEOMETRY SEMINAR (ORGANIZED BY PROF. SHING-TUNG YAU) |
Mu-Tao Wang (COLUMBIA UNIVERSITY) |
"Positivily of Quasi-Local mass" |
" |
October 14, 2005, 4:30-6:00pm at Science Center, Room 530 |
| DIFFERENTIAL GEOMETRY SEMINAR (ORGANIZED BY PROF. SHING-TUNG YAU) |
Xi-Ping Zhu (CHINESE UNIVERSITY OF HONG KONG & SHONGSHAN UNIVERSITY) |
"Ricci Flow" |
" |
October 14, 2005, 1:00-2:00pm at Science Center, Room 530 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Michael Hutchings (UNIVERSITY OF CALIFORNIA, BERKELEY) |
"Embedded contact homology" |
" |
October 14, 2005, 3:30pm at Science Center, Room 309 |
| DIFFERENTIAL GEOMETRY SEMINAR (ORGANIZED BY PROF. SHING-TUNG YAU) |
Xi-Ping Zhu (CHINESE UNIVERSITY OF HONG KONG & SHONGSHAN UNIVERSITY) |
"Ricci Flow" |
" |
October 13, 2005, 11:30 am-1:00 pm at Science Center, Room 530 |
| NUMBER THEORY SEMINER |
Robert Pollack (BOSTON UNIVERSITY) |
``Overconvergent modular symbols, p-adic L-functions and Stark-Heegner points'' |
Abstract: In this talk, we will discuss a concrete approach to working with overconvergent modular symbols. This approach yields theoretical results such as the construction of a p-adic L-function attached to a critical slope modular form. Furthermore, it yields computational results such as a fast algorithm which computes p-adic L-functions (which can then be applied to compute Stark-Heegner points). This is a joint project with Glenn Stevens" |
October 12, 2005, 3:00pm at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
Joe Harris (HARVARD UNIVERSITY) |
"The Brill-Noether theorem: representation theory for curves" |
This is a new series in which our senior faculty will give talks aimed at first year graduate students who want to get a feel for different areas of research" |
October 07, 2005, 3:00pm at Science Center, Room 507 |
| GLOBAL METHODS IN CHROMATIC HOMOTOPY THEORY SEMINAR |
Doug Ravenel (UNIVERSITY OF ROCHESTER) |
"Applications of Artin-Schreier curves to stable homotopy theory" |
Abstract: This talk will be a self-contained continuation of the one I gave at MIT on 9/26. The slides for that talk (and two related preprints) are available online at http://www.math.rochester.edu/people/faculty/doug/preprints.html. They also show the material for this talk since time did not permit covering all of it last week. The main result is that the Jacobians of certain specific (Artin-Schreier) curves in characteristic p have formal 1-dimensional summands with large height. There is a three step program to use this result to construct higher chromatic analogs of the theory of topological modular forms. The first step was outlined in the MIT talk. This talk will concentrate on the second step, which has to do with finding a family of liftings of each curve to characteristic 0" |
October 07, 2005, 4:30pm at Science Center, Room 232 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Veronique Godin (HARVARD UNIVERSITY) |
"Homology of some mapping class groups and string topology" |
" |
October 07, 2005, 3:30pm at Science Center, Room 309 |
| DIFFERENTIAL GEOMETRY SEMINAR (ORGANIZED BY PROF. SHING-TUNG YAU" |
Xi-Ping Zhu (CHINESE UNIVERSITY OF HONG KONG & SHONGSHAN UNIVERSITY) |
"Ricci Flow" |
" |
October 06, 2005, 11:30am-1:00pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
Abhinav Kumar (HARVARD UNIVERSITY) |
"The densest lattice in twenty-four dimensions" |
" |
October 05, 2005, 3:00pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR (ORGANIZED BY PROF. SHING-TUNG YAU) |
CRISTINA SORMANI (CITY UNIVERSITY OF NEW YORK) |
"The covering spectrum and convergence of manifolds" |
" |
October 04, 2005, 4:30-6:00 at Science Center, Room 507 |
| FACULTY COLLOQUIUM |
Michael Hopkins (HARVARD UNIVERSITY) |
"Homotopy groups" |
This is a new series in which our senior faculty will give talks aimed at first year graduate students who want to get a feel for different areas of research" |
October 03, 2005, 3:00pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Horng-Tzer Yau (HARVARD UNIVERSITY) |
"Dynamics of Bose gas and well-posedness of the nonlinear Schrodinger equation in infinite dimensions" |
" |
September 30, 2005, 3:30-4:30pm at Science Center, Room 309 |
| DIFFERENTIAL GEOMETRY SEMINAR (ORGANIZED BY PROF. SHING-TUNG YAU) |
Xi-Ping Zhu (ZHONGSHAN UNIVERSITY & CHINESE UNIVERSITY OF HONG KONG) |
"Ricci Flow" |
" |
September 29, 2005, 11:30-12:30pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
Frank Calegari (HARVARD UNIVERSITY) |
"Towards an eigencurve over imaginary quadratic fields" |
Abstract: The usual construction of Eigenvarieties relies on the existence of associated Shimura varieties, which provide ample sources of Galois representations. For modular forms over an imaginary quadratic field this approach does not work. We propose a conjectural construction of an Eigencurve that will parameterize certain two dimensional continuous p-adic Galois representations over an imaginary quadratic field K. Perhaps surprisingly, this curve will not in general have the property that the classical points are Zariski dense. (with Barry Mazur)" |
September 28, 2005, 3:00pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
David Kazhdan (HEBREW UNIVERSITY OF JERUSALEM & HARVARD UNIVERSITY) |
"Integration over valued fields " ( a joint work with E. Hrushovski) |
Abstract: We show that the Grothendick group of bounded definable sets over a valued fields of the residue characteristic zero is [ almost] equal to the tensor product of the Grothendick group of the residue field and the Grothendick group of the value group. I ll discuss different applications of this isomorphism to analysis and algebraic geometry" |
September 27, 2005, 4:15pm at Science Center, Room 507 |
| QED WORKING SEMINAR |
Horng-Tzer Yau (HARVARD UNIVERSITY) |
Problems related to rigorous formulation of QED |
The aim of this seminar is to understand problems related to rigorous formulation of Quantum Electrodynamics. Although QED has excellent agreements with experiments, it exists only in perturbation theory and there is no rigorous mathematical foundation. An understanding of QED, furthermore, is needed for the study of more complicated quantum field theories. The first few meetings of this seminar will be a mini-course on second quantization and Dirac equation in the Euclidian space. After that, there will be presentations of some recent papers by various speakers. Graduate students are encouraged to attend and to meet with H. T. Yau for questions related to this seminar. More details of the seminar will be discussed in the first meeting." |
September 27, 2005, 11:30-1:00pm at Science Center, Room 530 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Ron Fintushel (MICHIGAN STATE UNIVERSITY) |
"4-manifolds with b+ = 1" |
" |
September 23, 2005, 2:00-3:00pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR ( ORGANIZED BY PROF. SHING-TUNG YAU) |
Xi-Ping Zhu (CHINESE UNIVERSITY OF HONG KONG & SHONGSHAN UNIVERSITY) |
"Ricci Flow" |
" |
September 23, 2005, 1:00-2:00pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
Steve Miller (HEBREW UNIVERSITY OF JERUSALEM, ISRAEL) |
"Expander graphs, GRH, and the elliptic curve discrete logarithm problem" |
Abstract: An important question in cryptography is how to generate elliptic curves over finite fields whose discrete logarithm problem is hard -- at least as hard as it is on other comparable curves. Using Hecke s theory of grossencharacter L-functions and assuming the Generalized Riemann Hypothesis (GRH) for them, we prove an equidistribution result for the difficulty of the discrete logarithm over elliptic curves defined over the same field and having the same number of points. The technique involves forming a graph of low degree isogenies connecting certain elliptic curves, and then showing that this graph is an expander graph. Low degree isogenies provide efficient reductions of the discrete logarithm problem on curves they connect, and expander graphs have the property that random walks mix rapidly. This provides a means to spread the difficulty of the discrete logarithm problem fairly uniformly over the family of curves in question. This is joint work with David Jao (a recent Harvard Math PhD) and Ramarathnam Venkatesan, of the Microsoft Research Cryptography and Anti-piracy group" |
September 21, 2005, 3:00 pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Jeng-Daw Yu (HARVARD UNIVERSITY) |
"A torelli type theorem for ordinary K3 surfaces over Fp" |
" |
September 20, 2005, 4:30pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Xi-Ping Zhu (ZHONGSHAN UINVERSITY & CHINESE UNIVERSITY OF HONG KONG) |
"Ricci Flow" |
" |
September 20, 2005, 1:00-2:00pm at Science Center, Room 232 |
| SPECIAL SEMINAR |
Tseno V. Tselkov (HARVARD UNIVERSITY) |
"Stark's Conjecture for Imaginary Quadratic Fields" |
Abstract: This is an expository paper presenting Stark s proof of his conjecture in the case of imaginary quadratic fields" |
May 09, 2005, 12:00pm at Science Center, Room 304 |
| NUMBER THEORY SEMINAR |
Chandrashekhar Khare (UNIVERSITY OF UTAH) |
"Mod p Galois representations" |
" |
May 04, 2005, 3:00-4:00pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Michael McQuillan (HARVARD UNIVERSITY) |
"La Joie des Champs" |
The very definition of Riemann surfaces, differential manifolds, analytic varieties, schemes, or whatever else your favourite geometric object may be has to be considered as wholly non-functorial with respect to the ideas. The appropriate, and basic notion, is stack, or rather better in Grothendieck s original French, `champs . It s essential to the understanding of the talk that the audience should know at least one example of a non-euclidean geometry, e.g., even spherical trigonometry would be fine. Knowing what Hausdorff/separated/T2 topological space means would also be very useful (even close to essential). As in all things the more you know, the more you re likely to understand, e.g., if you re familiar with so called `non-commutative geometry or you think that a `scheme which isn t quasi-projective is anything other than a pathology of commutative algebra you should definitely come to have your misconceptions corrected. An Anecdote: Stacks as a basic notion reminds me of an incident at a party: the visitor (a psychiatrist) was questioned by a mathematician for a bit as to what she did. Subsequently, she asked him what he did, and not unreasonably he asked, `Do you know what a Mobius strip is . Good try by the mathematician, but he got a negative answer, so he followed up with `Do you know what an etale pricinple homogeneous space is " |
May 02, 2005, 3:00-4:00pm at Science Center, Room 507 |
| SPECIAL LECTURE |
Shi-shyr Roan (INSTITUTE OF MATHEMATICS, ACADEMIA SINICA, TAIWAN) |
"Geometrical Characterization of Branching Indices of Affine A-D-E Diagrams" |
" |
April 29, 2005, 3:30pm at Science Center, Room 232 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Selman Akbulut (MICHIGAN STATE UNIVERSITY) |
"Aspects of 7-manifolds with G2 holonomy" |
" |
April 29, 2005, 3:30-4:30pm at Science Center, Room 309 |
| SYMPLECTIC GEOMETRY LEARNING SEMINAR |
Michael Usher (HARVARD UNIVERSITY) |
"What you can do with a Lefschetz pencil, II" |
" |
April 29, 2005, 12:00-1:00pm at Science Center, Room 232 |
| NUMBER THEORY SEMINAR |
Brian Conrad (UNIVERSITY OF MICHIGAN, VISITING CMI) |
"Canonical subgroups in p-adic families of abelian varieties" |
Abstract: Motivated by problems in the theory of p-adic modular forms, it is important to study how p-power torsion subgroups deform in p-adic families of abelian varieties. A very fundamental construction, first worked out by Lubin (and Katz in the relative case) for elliptic curves, is the so-called canonical subgroup. This was the foundation for Katz theory of classical p-adic modular forms, and recent generalizations by several mathematicians have generalized this theory to the higher-dimensional case. However, each of these constructions suffers from one of two restrictions that can be unpleasant in practice: good reduction for all fibers, or the specification of discrete parameters (such as the degree of a polarization, so as to work on a fixed moduli space of finite type). Reflection on the matter suggests that such restrictions are artifacts of the constructions and should not be necessary. I will explain an entirely different way to set up the higher-dimensional theory that avoids such restrictions, and is geometrically very natural (and consistent with other constructions). The essential tools that we use are the extremely pleasant topology and cohomology on Berkovich s theory of p-adic spaces, coupled with a theorem of Norman--Oort on the geometry of moduli spaces of abelian varieties in characteristic p (allowing p to divide the degree of a polarization). In the talk, we will treat Berkovich spaces like black magic" |
April 27, 2005, 3:00-4:00pm at Science Center, Room 507 |
| SPECIAL LECTURE |
Mihai Paun (STRASBOURG, FRANCE) |
"Generalization of a Theorem of Kobayashi-Ochiai" |
" |
April 22, 2005, 3:00 p.m. at Science Center Room 232 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Walter Neumann (COLUMBIA UNIVERSITY) |
"The Casson Invariant Conjecture" |
" |
April 22, 2005, 3:00-4:00pm at Science Center, Room 309 |
| SYMPLECTIC GEOMETRY LEARNING SEMINAR |
Michael Usher (HARVARD UNIVERSITY) |
"What you can do with a Lefschetz pencil, I" |
" |
April 22, 2005, 12:00-1:00pm at Science Center, Room 232 |
| NUMBER THEORY SEMINAR |
Florian Herzig (HARVARD UNIVERSITY) |
The weight in Serre's conjecture for Gl_3 |
Abstract: Following an idea of Taylor and Diamond in the Gl_2 case, I will discuss a conjectural relation between Serre weights for tamely ramified, odd three-dimensional mod p Galois representations and the decomposition of finite-dimensional characteristic 0 representations of Gl_3(F_p) in characteristic p. This yields an extension of the weight conjecture of Ash et al. in the tamely ramified case. I will mention a possible generalisation to Gl_n" |
April 20, 2005, 3:00-4:00pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Elizabeth Denne (HARVARD UNIVERSITY) |
"Introduction to Geometric Knot Theory" |
We all know how to tie some basic knots. How can we tell whether two knots are the same or different? What kind of geometric properties do knots have? How long a piece of rope do you need to tie a knot? This talk will give some answers to these surprisingly difficult questions. No knowledge of knot theory (aside from the ability to ties one s shoelaces) will be assumed" |
April 18, 2005, 3:00-4:00pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Zoltan Szabo (PRINCETON UNIVERSITY) |
"Exotic smooth structures on 4-manifolds with small Euler characteristics" |
" |
April 15, 2005, 3:30-4:30 at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Noam Elkies (HARVARD UNIVERSITY) |
Rank speculation |
Can the rank of an elliptic curve E over Q be arbitrarily large? We don t know the answer, and probably won t know for a long time. Lacking an answer, we can only speculate, extrapolating from known constructions of curves of high rank, and comparing with the status of analogous questions -- notably those concerning elliptic curves over other fields (such as C(T) and Q(T)) or having an N-torsion point for some fixed N>1. We report on the status of some of these questions and implications between them, and give a new argument suggesting that, for some finite (possibly zero) bound B, nonconstant elliptic curves over Q(T), none of whose specializations have rank >B over Q" |
April 13, 2005, 3:00-4:00pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Denis Auroux (MIT) |
"Near symplectic structures and Lefschetz pencils on smooth 4-manifolds" |
" |
April 08, 2005, 3:30-4:30pm at Science Center, Room 309 |
| NORTHEASTERN-BRANDEIS-MIT-HARVARD COLLOQUIUM |
Joan Birman (COLUMBIA UNIVERSITY) |
"Some open problems about mapping class groups of surfaces" |
There will be tea at 4pm in the 4th floor Common Are" |
April 07, 2005, 4:30pm at Science Center, Lecture Hall D |
| SPECIAL UNDERGRADUATE SEMINAR |
Joan Birman (COLUMBIA UNIVERSITY) |
"The Conjugacy Problem in the Braid Groups" |
Abstract: Braids, like the ones we weave in a person s hair, form a group. The group turns out to be infinite, and rich in structure. It pops up in many parts of mathematics, in various guises. After defining the braid groups, I plan to discuss a particularly interesting problem about braids: to decide whether, for arbitrary braids X and Y, there exists a braid Z with X = Z Y Z^{-1} The solution, due to Frank Garside, has been the subject of intensive work over many years. It has even lead to a class of groups (called" |
April 06, 2005, 2:00-3:00pm at Science Center, Room 221 |
| PANEL ON JOURNAL PUBLICATION |
Alan Bourque (Harvard University Libraries), Ann Kostant (Springer), Joan Birman (Math Sciences Publications and Columbia University), Edward Dunne (Ams), Benedict Gross (Dean of Harvard College and Leverett of Mathematics) will moderate () |
A Panel discussion on Journal publication issues relevant to Harvard |
In this era of Www, Google, ArXiv, TeX, and Pdf, we all have at our fingertips the best typesetting, distribution, and search mechanisms in the history of the world. The high prices charged by big publishing houses like Springer and Elsevier can no longer be justified by the same added values as in the past. Furthermore, these same high prices are forcing university libraries on shrinking budgets to downsize their journal subscriptions. In response, some mathematicians have started low-cost journals to show journal prices do not have to be as high as publishers claim. Every time we choose where to send our papers for publication, we knowingly or unknowingly take a stand in this debate. Prompted by Joan Birman s visit to give the colloquium, we will be having a panel discussion on these issues at Harvard. This is a rare occasion in the Boston area to hear all sides of the journal pricing debate as we will have representatives from large for-profit publishing ventures, nonprofit publishing ventures, professional organizations, and libraries. Consider yourself especially encouraged to attend if you know little or nothing about this topic" |
April 06, 2005, 4:15pm at Science Center, Room 507 |
| SYMPLETIC GEOMETRY LEARNING SEMINAR |
Tom Coates (HARVARD UNIVERSITY) |
"Examples of the quantization/Gromov-Witten correspondence" |
" |
March 25, 2005, 12:00-1:00pm at Science Center , Room 232 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Sergei Gukov (HARVARD UNIVERSITY) |
"Khovanov-Rozansky Homology and Topological Strings" |
" |
March 25, 2005, 3:30-4:30pm at Science Center ,Room 309 |
| NORTHEASTERN-BRANDEIS-MIT-HARVARD COLLOQUIUM |
Sergey Fomin (UNIVERSITY OF MICHIGAN) |
"Catalan combinatorics of arbitrary type" |
There will be tea at 4pm in the 4th floor Common Are" |
March 24, 2005, 4:30 at Science Center, Lecture Hall D |
| NUMBER THEORY SEMINAR |
Teruyoshi Yoshida (HARVARD UNIVERSITY) |
"Compatibility of local and global Langlands correspondence for Gln" (joint work with Richard Taylor) |
We show the compatibility in the title for the class of cuspidal automorphic representations of Gln over Cm fields studied in the book by Harris-Taylor. It had been proven except for the coincidence of the monodromy operator in that book; we determine the monodromy by looking at the weight spectral sequence for the Shimura variety with semistable reduction, corresponding to the Iwahori level structure. As a corollary we can deduce irreducibility of the attached n-dimensional global Galois representation in most cases" |
March 23, 2005, 3:00-4:00pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Hsian-Hua Tseng (UC BERKELEY) |
"Quantum riemann-roch theorem in orbifold gromov-witten theory" |
" |
March 22, 2005, 1:15pm at Science Center, Room 232 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Greg Landweber (UNIVERSITY OF OREGON) |
"Kirwan Surjectivity for K-theory" |
" |
March 18, 2005, 3:30-4:30 at Science Center, Room 309 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Felix Finster (UNIVERSITY OF REGENSBURG, GERMANY) |
"The long-time dynamics of scalar waves in the kerr geometry" |
" |
March 18, 2005, 9:00-10:00am at Science Center, Room 530 |
| NORTHEASTERN-BRANDEIS-MIT-HARVARD COLLOQUIUM |
Yasha Eliashberg (STANFORD UNIVERSITY) |
"Geometry of contact transformations: orderability vs. squeezing" |
There will be tea at 4pm in the 4th floor Common Area" |
March 17, 2005, 4:30pm at Science Center, Lecture Hall D |
| NUMBER THEORY SEMINAR |
Thomas Geisser (UNIVERSITY OF SOUTHERN CALIFORNIA) |
"Arithmetic cohomology and special values of zeta-functions" |
" |
March 16, 2005, 3:00-4:00pm at Science Center, Room 507 |
| SYMPLECTIC GEOMETRY LEARNING SEMINAR |
Tom Coates (HARVARD UNIVERSITY) |
"More about quantization and Gromov-Witten invariants" |
" |
March 11, 2005, 12:00-1:00pm at Science Center, Room 232 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Jason Cantarella (UNIVERSITY OF GEORGIA) |
"Tight knots in theory and computation" |
" |
March 11, 2005, 3:30-4:30pm at Science Center, Room 309 |
| THE TEACHING UNDERGRADUATE MATHEMATICS SEMINAR (TUMS) |
Angela Vierling-Claassen and Derek Bruff (HARVARD UNIVERSITY) |
"Understanding What Your Students Are Thinking" |
" |
March 11, 2005, 2:00-3:00pm at Science Center, Room 316 |
| NUMBER THEORY SEMINAR |
David Helm (HARVARD UNIVERSITY) |
"Geometric Jacquet-Langlands correspondences for unitary Shimura varieties" |
" |
March 09, 2005, 3:00-4:00pm at Science Center, Room 507 |
| SYMPLECTIC GEOMETRY LEARNING SEMINAR |
Tom Coates (HARVARD UNIVERSITY) |
"More about quantization and Gromov-Witten invariants" |
" |
March 04, 2005, 12:00-1:00pm at Science Center, Room 232 |
| THE TEACHING UNDERGRADUATE MATHEMATICS SEMINAR (TUMS) |
Matthew Leingang (HARVARD UNIVERSITY) |
"Seeking Points: A Case Study" |
" |
March 04, 2005, 1:30-3:00pm at Science Center, Room 316 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Frances Kirwan (OXFORD UNIVERSITY) |
"Moduli spaces of bundles over curves revisited" |
" |
March 04, 2005, 3:30-4:30pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Frank Calegari (HARVARD UNIVERSITY) |
"The modular degree of Elliptic Curves (joint with M.Emerton)" |
" |
March 02, 2005, 3:00-4:00pm at Science Center, Room 507 |
| THE BASIC NOTIONS SEMINAR |
Jon Hanke (DUKE UNIVERSITY) |
"Finiteness Theorems and Representing Numbers by Quadratic Forms" |
" |
February 28, 2005, 3:00-4:00pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Ciprian Manolescu (CLAY/PRINCETON UNIVERSITY) |
"Symplectic Floer theories and the Jones polynomial" |
" |
February 25, 2005, 3:30-4:30pm at Science Center, Room 309 |
| THE TEACHING UNDERGRADUATE MATHEMATICS SEMINAR |
Robin Gottlieb and Kathy Paur (HARVARD UNIVERSITY) |
"Managing an Interactive Classroom" |
" |
February 25, 2005, 2:00-3:00pm at Science Center, Room 316 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Vadim Kaloshin (MIT) |
"A non capture result in three body dynamics" |
" |
February 24, 2005, 3pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Wei-Dong Ruan (UNIVERSITY OF ILLINOIS-CHICAGO) |
"Homological mirror symmetry for weighted projective space through constructible sheaves" |
" |
February 22, 2005, 4:30pm - 5:30pm at Science Center, Room 507 |
| SYMPLECTIC GEOMETRY LEARNING SEMINAR |
Ezra Getzler (UNIVERSITY OF CHICAGO) |
"Open-closed Gromov--Witten theory" |
" |
February 18, 2005, 12:00-1:00 at Science Center, Room 232 |
| THE MATHEMATICS EDUCATION SPEAKER SERIES |
Tim Gutmann (UNIVERSITY OF NEW ENGLAND) |
"Research on the Professional Lives of Teaching Assistants: a Primer on the Status of Research in the Community and a Discussion of Research Questions and Issues" |
" |
February 18, 2005, 2:00-3:00pm at Science Center, Room 316 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Eaman Eftekhary (HARVARD UNIVERSITY) |
Heegaard Floer homology and gluing along torus boundaries |
" |
February 18, 2005, 3:30 - 4:30 Pm at Science Center, Room 309 |
| HARVARD, BRANDEIS, M.I.T., NORTHEASTERN COLLOQUIUM AT HARVARD |
Charles Fefferman (PRINCETON UNIVERSITY) |
"Whitney's extension problem" |
There will be tea at 4pm in the 4th floor Common Are" |
February 17, 2005, 4:00-6:00pm at Science Center Hall D |
| NUMBER THEORY SEMINAR |
Jordan Ellenberg (PRINCETON UNIVERSITY) |
Descent bounds for points of bounded height on varieties (joint work with A.Venkatesh) |
" |
February 16, 2005, 3:00 - 4:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Tom Coates (HARVARD UNIVERSITY) |
"The Gromov-Witten Theory of a point and KdV" |
" |
February 15, 2005, 4:30pm- 5:30pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Hee Jung Kim (BRANDEIS UNIVERSITY) |
Modifying Surfaces in 4-manifolds by Twist Spinning |
" |
February 11, 2005, 3:30 - 4:30 Pm at Science Center, Room 309 |
| SYMPLECTIC GEOMETRY LEARNING SEMINAR |
Tom Coates (HARVARD UNIVERISTY) |
"Quantization and Gromov-Witten Theory" |
" |
February 11, 2005, 12:00-1:00pm at Science Center, Room 232 |
| THE TEACHING UNDERGRADUATE MATHEMATICS SEMINAR (TUMS) |
Derek Bruff (HARVARD UNIVERSITY) |
"Caught on Tape: Clips of Teachers in Action" |
" |
February 11, 2005, 2-3pm at Science Center 222 |
| THE ELLIPTIC CURVES AND MODULAR FORMS SEMINAR |
Ronald VanLuijk (UC BERKELEY) |
K3 surfaces with Picard number one and infinitely many rational points |
" |
February 09, 2005, 1:00Pm - 2:00Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Jonathan Weitsman (UNIVERSITY OF CALIFORNIA-SANTA CRUZ) |
"Measures on Banach manifolds and supersymmetric quantum field theory" |
" |
February 08, 2005, 4:30pm - 5:30pm at Science Center, Room 507 |
| THE TEACHING UNDERGRADUATE MATHEMATICS SEMINAR |
Matthew Leingang and Derek Bruff (HARVARD UNIVERSITY) |
"Making Lessons Plans" |
" |
February 04, 2005, 2:00-3:00pm at Science Center, Room 222 |
| THE ELLIPTIC CURVES AND MODULAR FORMS SEMINAR |
Frank Calegari and William Stein (HARVARD UNIVERSITY) |
An Amazing Abelian Variety Af |
" |
December 15, 2004, 1:00Pm - 2:00Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Mark Reeder (BOSTON COLLEGE) |
Depth-zero supercuspidal L-packets for unramified groups |
" |
December 15, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| SPECIAL NUMBER THEORY AND EXCEPTIONAL GROUPS SEMINAR |
Sergei Krutelevich (UNIVERSITY OF OTTAWA) |
Higher composition laws, exceptional groups, and Jordan algebras |
" |
December 13, 2004, 2:00 - 3:00Pm at Science Center, Room 232 |
| SPECIAL SEMINAR |
Bruno DeOliveira (UNIVERSITY OF MIAMI, FLORIDA) |
Algebraic hyperbolicity of nodal hypersurfaces |
" |
December 10, 2004, 3:30 p.m. at Science Center, Room 411 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Bernard Julia (ECOLE NORMALE SUPERIOR) |
Some applications of non compact real Lie algebras (eventually generalized Kac-Moody-Borcherds algebras) to theoretical physics-- M-theory, superstrings, supergravities and gravity |
" |
December 10, 2004, 3:30Pm - 4:30Pm at Science Center, Room 309 |
| THE ELLIPTIC CURVES AND MODULAR FORMS SEMINAR |
William Stein (HARVARD UNIVERSITY) |
Computing p-Adic Heights Using Monsky-Washnitzer Cohomology |
" |
December 08, 2004, 1:00Pm - 2:00Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Samit Dasgupta (HARVARD UNIVERSITY) |
Stark--Heegner points on modular Jacobians |
" |
December 08, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
David Jerison (M.I.T.) |
Regularity of energy-minimizing free boundaries |
" |
December 06, 2004, 12:00Pm - 1:00Pm at Science Center, Room 221 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Rob Kusner (UNIVERSITY OF MASSACHUSETTS) |
Nondegeneracy and Moduli Spaces of Constant Mean Curvature Surfaces |
" |
December 03, 2004, 3:30 - 4:30 Pm at Science Center, Room 309 |
| THE ELLIPTIC CURVES AND MODULAR FORMS SEMINAR |
Noam Elkies (HARVARD UNIVERSITY) |
Elliptic curves with 3-adic Galois representation surjective mod 3 but not mod 9 |
" |
December 01, 2004, 1:00Pm - 2:00Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
William Stein (HARVARD UNIVERSITY) |
Data About Ranks of Elliptic Curves |
" |
December 01, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Simon Brendle (PRINCETON UNIVERSITY) |
Portofolio optimization under partial observation |
" |
November 29, 2004, 3:00 - 4:00 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Dick Gross (HARVARD UNIVERSITY) |
One symplectic root numbers, and their interpretations |
" |
November 17, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Paul Seidel (UNIVERSITY OF CHICAGO) |
Symplectic topology and contractible algebraic surfaces |
" |
November 12, 2004, 3:30 - 4:30 Pm at Science Center, Room 309 |
| THE ELLIPTIC CURVES AND MODULAR FORMS SEMINAR |
Frank Calegari (HARVARD UNIVERSITY) |
Irrationality of certain p-adic periods for small p |
" |
November 10, 2004, 1:00Pm - 2:00Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Tetsushi Ito (KYOTO) |
On the cohomology of varieties over local fields with maximal unipotent monodromy |
" |
November 10, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
Kevin Costello (IMPERIAL COLLEGE, LONDON) |
Topological conformal field theories from Calabi-Yau categories |
" |
November 10, 2004, 2:00 - 3:00Pm at Science Center, Room 530 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Sergei Gukov (HARVARD UNIVERSITY) |
Hitchin' S Functionals And Unification Of Topological Strings |
" |
November 09, 2004, 3:00Pm - 4:00Pm at Science Center, Room 221 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Stavros Garoufalidis (GEORGIA TECH) |
Holonomicity of the colored Jones function of a link in a homology sphere |
" |
November 05, 2004, 3:30 - 4:30 Pm at Science Center, Room 309 |
| HARVARD, BRANDEIS, M.I.T., NORTHEASTERN COLLOQUIUM |
Jean Bourgain (IAS) |
Sum-product theorems and exponential sum estimates |
" |
November 04, 2004, 4:30 Pm at Science Center, Lecture Hall D |
| NUMBER THEORY SEMINAR |
Marie-France Vigneras (PARIS) |
Some questions related to the p-adic Langlands program |
" |
November 03, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Rene Reinbacher (HARVARD UNIVERSITY) |
"Holomorphic Vector Bundles On Compact Calabi-Yau Threefolds With Non-Trivial Fundamental Group" |
" |
November 01, 2004, 12:00Pm - 1:00Pm at Science Center, Room 221 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Dror Bar-Natan (UNIVERSITY OF TORONTO) |
Trace Groups, Skein Modules and My Problems with Khovanov-Rozansky |
" |
October 29, 2004, 3:30 - 4:30 Pm at Science Center, Room 309 |
| HARVARD, BRANDEIS, M.I.T., NORTHEASTERN COLLOQUIUM |
Dror Bar-Natan (UNIVERSITY OF TORONTO) |
Khovanov Homology for Tangles and Cobordisms |
" |
October 28, 2004, 4:30 Pm at Science Center, Lecture Hall D |
| THE ELLIPTIC CURVES AND MODULAR FORMS SEMINAR |
Kevin Buzzard (IMPERIAL COLLEGE, LONDON) |
A Little Calculation with Hilbert Modular Forms |
" |
October 27, 2004, 1:00Pm - 2:00Pm at Science Center, Room 507 |
| DYNAMICS AND GEOMETRY SEMINAR |
Julio Rebelo (PUC-RIO) |
Dynamics of meromorphic vector fields and complex surfaces |
" |
October 27, 2004, 4:00 - 5:00 Pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
Toby Gee (IMPERIAL COLLEGE) |
Companion forms over totally real fields |
" |
October 27, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
James Sparks (HARVARD UNIVERSITY) |
On a new class of sasaki-einstein manifolds |
" |
October 25, 2004, 12:00Pm - 1:00Pm at Science Center, Room 221 |
| THE ELLIPTIC CURVES AND MODULAR FORMS SEMINAR |
Nathan Ryan (DARTMOUTH) |
Computing the Satake $p$-parameters of a Siegel Eigenform |
" |
October 21, 2004, 3:00 - 4:00 Pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
Laurent Fargues (PARIS) |
Realization of local Langlands correspondances in p-adic local moduli spaces |
" |
October 20, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Xiaofeng Sun (HARVARD UNIVERSITY) |
Canonical metrics on the moduli space of riemann surfaces |
" |
October 18, 2004, 12:00Pm - 1:00Pm at Science Center, Room 221 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
David Gay (UNIVERSITY OF QUEBEC, MONTREAL) |
Locally toric near-symplectic 4-manifolds |
" |
October 15, 2004, 3:30 - 4:30 Pm at Science Center, Room 309 |
| SPECIAL SEMINAR |
William Stein (HARVARD UNIVERSITY) |
A New Algorithm for Computing p-adic Cyclotomic Height Functions |
" |
October 15, 2004, 10:00Am - 11:00Am at Mit, Building 2, Room 2-136 |
| THE ELLIPTIC CURVES AND MODULAR FORMS SEMINAR |
William Stein (HARVARD UNIVERSITY) |
Computations About the Birch and Swinnerton-Dyer Conjecture for Modular Abelian Varieties Using Magma |
" |
October 13, 2004, 1:00Pm - 2:00Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Andrew Granville (MONTREAL) |
"An uncertainty principle in arithmetic" |
" |
October 13, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Tom Coates (HARVARD UNIVERSITY) |
Gromov--Witten theory and integrable systems |
" |
October 08, 2004, 3:30 - 4:30 Pm at Science Center, Room 309 |
| COMPUTING WITH MODULAR FORMS SEMINAR |
Noam Elkies (HARVARD UNIVERSITY) |
Two examples of using generating functions to compute with modular forms for $\Gamma(1)$ |
" |
October 07, 2004, 10:00Am - 11:30Am at Science Center, Room 116 |
| NUMBER THEORY SEMINAR |
Elena Mantovan (BERKELEY) |
Moduli spaces of Barsotti-Tate groups with relation to the local Langlands correspondences. |
" |
October 06, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| COMPUTING WITH MODULAR FORMS SEMINAR |
Robert Pollack (BOSTON UNIVERSITY) |
p-adic L-functions of elliptic curves |
" |
October 05, 2004, 10:00Am - 11:30Am at Science Center, Room 116 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Ben Weinkove (HARVARD UNIVERSITY) |
The J-Flow, the mabuchi energy and canonical metrics kahler geometry |
" |
October 04, 2004, 12:00Pm - 1:00Pm at Science Center, Room 221 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Peter Kronheimer (HARVARD UNIVERSITY) |
Donaldson invariants of 4-manifolds from Su(N) |
" |
October 01, 2004, 3:30 - 4:30 Pm at Science Center, Room 309 |
| THE ELLIPTIC CURVES AND MODULAR FORMS SEMINAR |
Frank Calegari (HARVARD UNIVERSITY) |
"Mod p representations on elliptic curves" |
" |
September 29, 2004, 1:00Pm - 2:00Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Curt McMullen (HARVARD UNIVERSITY) |
Minkowski's conjecture, well-rounded lattices and topological dimension |
" |
September 29, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Irene Minder and William Stein (HARVARD UNIVERSITY) |
The Mathematics Job Search |
" |
September 27, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Albert Chau (HARVARD UNIVERSITY) |
The Kahler-Ricci Flow And The Uniformization Of Complete Non-Compact Kahler Manifolds With Non-Negative Bisectional Curvature |
" |
September 27, 2004, 12:00Pm - 1:00Pm at Science Center, Room 221 |
| THE ELLIPTIC CURVES AND MODULAR FORMS SEMINAR |
Frank Calegari (HARVARD UNIVERSITY) |
Mod p representations on elliptic curves |
" |
September 27, 2004, 2:00 - 3:00Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Jean-Michel Bismut (UNIVERSITé PARIS-SUD) |
A deformation of Hodge theory |
" |
September 24, 2004, 1:00Pm - 2:00Pm at Science Center, Room 507 |
| COLLOQUIUM |
Michael Huber (UNIVERSITY OF TUEBINGEN, GERMANY) |
On Highly Symmetric Combinatorial Designs |
There will be tea at 4pm in the 4th floor Common Are" |
September 23, 2004, 4:30 Pm at Science Center, Lecture Hall A |
| MOTIVIC HOMOTOPY THEORY SEMINAR |
Michael Hopkins (HARVARD UNIVERSITY) |
Introduction to Morel's work on motivic homotopy groups |
Thrusday, September 30, 2004: No meetin" |
September 23, 2004, 3:00 - 5:00Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Frank Calegari (HARVARD UNIVERSITY) |
Eisenstein Deformation Rings |
" |
September 22, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| ALGEBRAIC GEOMETRY SEMINAR |
Joseph Landsberg (TEXAS AM AND HARVARD) |
Asymptotic directions on projective varieties and consequences |
" |
September 21, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| HARVARD, BRANDEIS, M.I.T., NORTHEASTERN COLLOQUIUM |
Claude LeBrun (SUNY STONY BROOK) |
"On the Curvature of 4-Manifolds" |
Abstract: A central problem in global differential geometry is to determine when a smooth compact n-manifold admits a metric which is as flat as possible. In this lecture, I will describe some recent results on the existence and non-existence of such optimal metrics on simply connected 4-manifolds. Interestingly, the difference between existence and non-existence turns out to delicately depend on one s choice of differentiable structure; it is not determined by the homeomorphism type alone" |
May 20, 2004, 4:30 Pm at Science Center D |
| NUMBER THEORY SEMINAR |
Chris Skinner (UNIVERSITY OF MICHIGAN) |
"Towards the main Conjecture for Modular Forms" |
" |
May 19, 2004, 3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Michael Brenner (HARVARD UNIVERSITY) |
"Surfaces of Constant Mean Curvature: Some Recent Developments" |
" |
May 11, 2004, 4:30 p.m. at Science Center, Room 507 |
| GEOMETRY SEMINAR |
Dragos Oprea (M.I.T.) |
"The Tautological Rings of the Stable Map Spaces" |
" |
May 10, 2004, 4:00 - 5:00 Pm at Science Center, Room 530 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Laura DeMarco (HARVARD UNIVERSITY) |
"Iteration at the Boundary of the Space of Rational Maps" |
" |
May 7, 2004, 3:30-5:00 Pm at Science Center, Room 309 |
| MODULAR FORMS SEMINAR |
Joan Lario (BARCELONA) |
Cm Elliptic Curves over Number Fields: Explicit examples of modular quotients |
" |
May 06, 2004, 3:07pm - 3:37pm at Sc 507 |
| HARVARD, BRANDEIS, M.I.T., NORTHEASTERN COLLOQUIUM |
Leon Ehrenpreis (TEMPLE UNIVERSITY) |
"Sharpening the Edge of the Wedge Theorem" |
Abstract: Denote by O+ and O- the positive and negative orthants in R^n. The wedges W+ and W- are the tubes over O+ and O-. The edge is the intersection of the wedges, which is the imaginary space. Let f+ and f- be functions which are holomorphic on W+ and W-. If f+ = f- on the edge then there is a function F which is holomorphic on all of C^n which extends f+and f-. We shall sharpen and extend this result in several directions: 1. Holomorphicity is defined by the Cauchy Riemann operator (d bar) which we shall replace by a general class of differential operators P(D). 2. Problems in the spirit of Bill Clinton: What is is ( for us is means =)? a. What is the weakest sense in which f+ = f- on the edge? (Problem of Norman Levinson) b. (Problem of Fefferman-Nirenberg-Paul Yang) Instead of Pf+ - = 0 we require only that Pf+ - vanish rapidly at the edge. c. (quasianalyticity problem) Instead of Pf+ - = 0 we give bounds on the (P^m)f+-." |
May 6, 2004, 4:00 - 6:00 Pm at Science Center, Hall D |
| NUMBER THEORY SEMINAR |
Grigor Grigorov (HARVARD UNIVERSITY) |
"An Adelic Version of Kato's Euler System" |
Abstract: I will explain how the system of elements constructed by Kato in K2 of modular curves can be viewed as an equivariant distribution on a suitable space of Schwartz functions. After that I will describe how one can construct explicitly another distribution which has values in the space of modular forms and how the two distributions are related. At the end I will explain how one can use that in the case of elliptic curves of analytic rank zero to get the full version of the Birch and Swinnerton-Dyer conjecture provided that some explicit linear combination of modular symbols does not vanish." |
May 5, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| GEOMETRY SEMINAR |
Curt McMullen (HARVARD UNIVERSITY) |
"Curves in Moduli Space: Spin and Discriminant" |
" |
May 5, 2004, 5:00 - 6:00 Pm at Science Center, Room 530 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Claire Voisin (INSTITUTE MATHEMATIQUE DE JUSSIEU - PARIS, FRANCE) |
"On the Homotopy Types of Kaehler and Projective Manifolds" |
Abstract: We construct compact Kaehler manifolds which do not have the homotopy type of a complex projective manifolds, and in particular do not deform to a projective manifolds. We construct such examples in any dimension at least equal to 4. We construct also simple connected, such examples starting from dimension 6." |
May 4, 2004, 4:30 Pm at Science Center, Room 507 |
| BASIC NOTIONS |
Marc Levine (NORTHEASTERN UNIVERSITY) |
"Motives" |
" |
May 03, 2004, 3-4pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Cumrun Vafa (HARVARD UNIVERSITY) |
"Quantum Foam and Topological Strings" |
" |
April 30, 2004, 3:30-5:00 Pm at Science Center, Room 309 |
| SPECIAL MATHEMATICS EDUCATION SEMINAR |
Maria Terrell (CORNELL UNIVERSITY) |
"Good Questions for Deep Learning of Mathematics" |
" |
April 29, 2004, 2:30 Pm at Derek Bok Center, Room 316 |
| GEOMETRY SEMINAR |
Akshay Vankatesh (M.I.T.) |
"Quantum Chaos on Locally Symmetric Spaces and Cartun-Invariant Measures" |
" |
April 28, 2004, 5:00 - 6:00 Pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
David Helm (HARVARD UNIVERSITY) |
"A Geometric Jacquet-Langlands Correspondence for U(2) Shimura Varieties" |
" |
April 28, 2004, 3:00Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Claire Voisin (INSTITUTE DE MATHEMATIQUE DE JUSSIEU) |
"Hodge Classes on Kaehler and Projective Manifolds" |
Abstract: We show using the Uhlenbeck-Yau theorem, that the Hodge conjecture cannot be extended in any way to the Kaehler case, since there are Kaehler compact manifolds m, with a non trivial Hodge class of degree 4 which is not in the subspace of h^4(M,Q) generated by the c2(F), where f runs through the set of coherent sheaves on m. we also show, using a theorem of Bando and Siu, that finite locally free resolutions do not necessarily exist for coherent sheaves on compact Kaehler manifolds." |
April 28, 2004, 4:00 - 5:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Jun Li (STANFORD UNIVERSITY) |
"Topological Vertex of Toric Calabi-Yau Manifolds" |
" |
April 27, 2004, 4:30 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Tom Coates (HARVARD UNIVERSITY) |
"Gromov--Witten Invariants" |
" |
April 26, 2004, 3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Jeff Viaclovsky (M.I.T.) |
"Moduli Spaces of Critical Riemannian Metrics on Four-Manifolds." |
" |
April 23, 2004, 3:30-5:00 Pm at Science Center, Room 309 |
| MODULAR SEMINAR |
Noam Elkies (HARVARD UNIVERSITY) |
"Explicit Shimura-Belyi Covers" |
" |
April 22, 2004, 3:00 Pm at Science Center, Room 507 |
| GEOMETRY SEMINAR |
Dylan Thurston (HARVARD UNIVERSITY) |
"Shadow Diagrams: Representing 4-Manifolds with 2-Complexes" |
" |
April 21, 2004, 5:00 - 6:00 Pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
Clifton Cunningham (UNIVERSITY OF CALGARY) |
"Some Remarks on Geometry, Orbital Integrals and Characters" |
Abstract: In the first part of this talk we describe recent work with Hales proving that (good) orbital integrals are motivic, in the sense of Denef-Loeser, and that the Fundamental Lemma over characteristic-p p-adic fields implies the Fundamental Lemma over characteristic-0 p-adic fields. In the second part of this talk we consider related issues for characters of p-adic groups as related to recent work with Aubert; specifically, we introduce `depth-zero character sheaves and use these to describe Waldspurger s basis for nilpotent distributions" |
April 21, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
H.T. Yau (STANFORD UNIVERSITY) |
"Quantum Brownian Motion and Random Schrodinger Equation" |
" |
April 20, 2004, 4:30 Pm at Science Center, Room 507 |
| MODULAR SEMINAR |
John Voight (UC BERKELEY) |
"Binary Quadratic Forms that Represent Almost the Same Primes" |
Abstract: The forms x^2+9y^2 and x^2+12y^2 represent the same set of prime numbers, namely, those primes p of the form p=12n+1. What other like pairs of forms exist? In this talk, we will exhibit all pairs of such forms that represent the same primes outside of a finite set" |
April 20, 2004, 2:00 3:00 Pm at Science Center, Room 507 |
| SPECIAL SEMINAR IN COMPLEX ANALYSIS |
John Erik Fornaess (UNIVERSITY OF MICHIGAN AT ANN ARBOR) |
"Harmonic Currents" |
Abstract: The talk is on recent joint work with Nessim Sibony. We discuss a couple of notions of energy for harmonic currents of bidegree (1,1). This allows us to define wedge products of currents. The underlying open problem is to understand compact subsets of projective space which are laminated by Riemann surfaces. A recent theorem of Y-T Siu states that these don t exist if the compact set is a smooth hypersurface." |
April 20, 2004, 4:00 - 5:00 Pm at Physics Department, Lyman Room 330 |
| BASIC NOTIONS SEMINAR |
John Voight (UC BERKELEY) |
"An Introduction to Algebraic Stacks" |
Abstract: A stack is a natural generalization of a scheme in the setting of moduli spaces, just as a scheme is a natural generalization of an algebraic variety in the setting of commutative rings. We will describe in a basic and motivated way the notion of a stack, with an eye towards moduli of elliptic curves" |
April 19, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Michael Thaddeus (COLUMBIA UNIVERSITY) |
"Stable Maps to a Loop Group" |
" |
April 16, 2004, 3:30-5:00 Pm at Science Center, Room 309 |
| ALGEBRAIC GEOMETRY SEMINAR |
Amit Khetan (UNIVERSITY OF MASSACHUSETTS AT AMHERST) |
"The Maximum Likelihood Degree" (Joint work with Fabrizio Catanese, Serkan Hoston, and Bernd Sturmfels) |
Abstract: Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We give formulas for the algebraic degree of the critical equations of this optimization problem. In the generic case, the maximum likelihood degree equals the top Chern class of a sheaf of differential 1-forms with logarithmic singularities. Working on a toric variety we can derive such formulas as the following: If f1, ..., fn are generic polynomials in two variables with Newton polygons P1, ..., Pn then the number of critical points of a generic product of powers of the fi is the sum of the areas of the Pi and the area of the Minkowski sum of the Pi" |
April 15, 2004, 3:00-4:00 Pm at Science Center, Room 530 |
| GEOMETRY SEMINAR |
Deepee Khosla (HARVARD UNIVERSITY) |
"The Enriques Conjecture" |
" |
April 14, 2004, 5:00 - 6:00 Pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
David Burns (KINGS' COLLEGE OF LONDON) |
"Aspects of Non-Commutative Iwasawa Theory" |
" |
April 14, 2004, 3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Conan Leung (UNIVERSITY OF MINNESOTA) |
"G-2 Geometry" |
" |
April 13, 2004, 4:30 Pm at Science Center, Room 507 |
| MATHEMATICAL PHYSICS SEMINAR |
Thomas Spencer (SCHOOL OF MATHEMATICS, INSTITUTE FOR ADVANCED STUDY) |
"Random Matrices and Hyperbolic Symmetry" |
Abstract: After reviewing some results and conjectures about statistical mechanics models with compact symmetry groups, we describe recent work with M. Zirnbauer on models with hyperbolic symmetry Su(1,1). In these models the" |
April 13, 2004, 4:30 Pm at Jefferson Laboratory, Room 453 |
| GEOMETRY SEMINAR |
Cumrun Vafa (HARVARD UNIVERSITY) |
"Geometric Physics" |
" |
April 12, 2004, 4:30 Pm at Science Center, Room 530 |
| BASIC NOTIONS SEMINAR |
Benedict Gross (HARVARD UNIVERSITY) |
'Parabolics and Parahorics' |
" |
April 12, 2004, 3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Sergei Gukov (HARVARD UNIVERSITY) |
"A Generalization of the Volume Conjecture" |
" |
April 9, 2004, 3:30 - 5:00 Pm at Science Center, Room 309 |
| ALGEBRAIC GEOMETRY SEMINAR |
Laura Matusevich (HARVARD UNIVERSITY) |
"Algebraic Geometry for Gkz Systems" |
Abstract: In the late 1980s, Gelfand, Graev, Kapranov and Zelevinsky introduced a class of systems of differential equations depending on parameters, now known as Gkz systems or A-hypergeometric systems. Solutions of these systems seem to appear naturally in algebraic geometry: as toric residues, as periods of certain families of Calabi-Yau varieties, as generating functions of intersection numbers of moduli spaces of curves. Recently Ezra Miller, Uli Walther and I gave a complete answer to the question of how the dimension of the solution space (called the rank) of a Gkz system behaves when the parameters vary. As it turns out, rank is upper semi-continuous. We can even describe explicitly the set of parameters for which rank is strictly bigger than the generic value, in terms of the local cohomology of an associated semigroup ring. The goal of this talk is to give an overview of the theory of hypergeometric ranks. No previous knowledge of Gkz systems will be assumed" |
April 8, 2004, 3:00-4:00 Pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
Alan Lauder (OXFORD UNIVERSITY) |
Rigid Cohomology and P-adic Point Counting |
" |
April 7, 2004, 2:00 Pm at Science Center, Room 507 |
| GEOMETRY SEMINAR |
Laura DeMarco (UNIVERSITY OF CHICAGO) |
Potential Theory and the Distribution of Algebraic Numbers |
" |
April 7, 2004, 5:00 - 6:00 Pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
Martin Weissman (BERKELEY) |
"D4 Modular Forms" |
" |
April 7, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Nicolas Monod (UNIVERSITY OF CHICAGO) |
"Superrigidity and Geometric Splitting" |
" |
April 6, 2004, 4:30 Pm at Science Center, Room 507 |
| GEOMETRY SEMINAR |
Nicolas Monod (UNIVERSITY OF CHICAGO) |
"Negative Curvature: from Geometric Group Theory to Non-Commutative Measure Theory" |
" |
April 5, 2004, 4:30 - 5:30 Pm at Science Center, Room 530 |
| BASIC NOTIONS SEMINAR |
Noam Elkies (HARVARD UNIVERSITY) |
"Hypergeometric Functions" |
Abstract: Find out why sum(m=0,n, binomial(n,m)*binomial(12*n+2,3*m)*8^m / binomial(4*n,m)) = 3^(6*n)" |
April 5, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| MODULAR SEMINAR |
Dimitar Jetchev (HARVARD UNIVERSITY) |
"My Senior Thesis about Visibility of Shafarevich-Tate Groups" |
" |
March 25, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| GEOMETRY SEMINAR |
Nicholas Ramsey (HARVARD UNIVERSITY) |
"Geometric Modular Forms" |
" |
March 24, 2004, 5:00 - 6:00 Pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
Matthias Flach (VISITING HARVARD) |
"On the Tamagawa Number Conjecture for Dirichlet L-functions" |
" |
March 24, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Melissa Liu (HARVARD UNIVERSITY) |
"A Mathematical Theory ot the Topological Vertex" |
" |
March 19, 2004, 3:30-5:00 Pm at Science Center, Room 309 |
| THE MODULAR SEMINAR |
Lassina Dembele (UNIVERSITY OF CALGARI AND BRANDEIS) |
"Quaternionic Modular Symbols and Computing Hilbert Modular Forms" |
Abstract: In this talk, we will present a new algorithm that can be used to compute Hilbert modular forms over totally real numbers. The implementation of the algorithm can be done in two ways. The first one borrows some ideas from the the classical notion of modular symbols, while the second one uses a modification of the classical definition of the Brandt matrices. We will illustrate our presentation with several examples" |
March 18, 2004, 3:00 Pm at Science Center, Room 507 |
| ALGEBRAIC GEOMETRY SEMINAR |
Charles Favre (UNIVERSITE PARIS 7) |
"Local Dynamics and Valuation Space" |
Abstract: We shall start with the following simple dynamical problem: how to compute the speed of convergence of points towards a super-attracting point in C^2 under the iteration of a holomorphic map f? Our strategy consists in studying the action of f on a suitable space of valuations V defined on the local ring C[[x,y]]. This space can be thought of as the total space of all blow-ups above the origin in C^2. A key to the understanding of the dynamics of f on V lies in the fact that this valuation space is a tree modeled on the real line. We shall discuss briefly these topics, and try to give some hints of further applications of these techniques" |
March 18, 2004, 3:00 - 4:00 Pm at Science Center Room 530 |
| GEOMETRY SEMINAR |
Allan Adams (HARVARD UNIVERSITY) |
"Strings, Loops, and Moduli Spaces" |
" |
March 17, 2004, 5:00 -6:00 Pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
Peter Sarnak (PRINCETON UNIVERSITY) |
"Classical Versus Quantum Fluctuations on the Modular Surface |
" |
March 17, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Yuli Rudyak (UNIVERSITY OF FLORIDA) |
"Category Weight and the Arnold Conjecture on Symplectic Fixed Points" |
" |
March 12, 2004, 3:30 - 5:00 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Marc Levine (NORTHEASTERN UNIVERSITY) |
"A Survey of Algebraic Cobordism" |
Abstract: We will discuss the construction of algebraic cobordism via the Morel-Voevodsky stable homotopy category, and our construction (with Fabien Morel) of a geometric version, as well as its main properties. We will also mention some on-going projects, such as relations with the stable moduli of curves" |
March 10, 2004, 3:00 Pm at Science Center, Room 507 |
| ALGEBRAIC GEOMETRY SEMINAR |
Mihnea Popa (HARVARD UNIVERSITY) |
Asymptotic Intersection Numbers and Restricted Volumes |
Abstract: I will describe work (partly in progress) on defining asymptotic intersection numbers of big (or pseudoeffective) line bundles on smooth projective varieties. Intuition is provided by intersecting with the positive part of a Zariski decomposition, in case it exists. The technical tool is a notion of volume for restrictions of linear series. One shows that the asymptotic intersection numbers and the restricted volumes define continuous functions of the big cone of the ambient variety, and obtains an interesting decomposition of this cone given by their zero-locus. This is joint work with Ein, Lazarsfeld, Mustata and Nakamaye" |
March 09, 2004, 3:00 Pm at Science Center, Room 507 |
| GEOMETRY SEMINAR |
Tom Coates (HARVARD UNIVERSITY) |
"Gromov-Witten Theory For Beginners" |
" |
March 08, 2004, 4:30 - 5:30 Pm at Science Center, Room 530 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Ron Fintushel (MICHIGAN STATE UNIVERSITY) |
"Invariants For Lagrangian Tori" |
" |
March 5, 2004, 3:30 - 5:00 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Akshay Venkatesh (M.I.T.) |
"Counting Number Fields by Discriminant" |
Abstract: An old conjecture states that the number of number fields with fixed degree and discriminant < X should grow linearly in X. Very little is known for large degree; I ll discuss some upper bounds. The key ingredient is translating the question to counting integral points on well-chosen varieties. This is joint work with J. Ellenberg. Time permitting; I ll discuss a recent result with H. Helfgott in the case of cubic fields. This also yields new upper bounds for the number of elliptic curves with specified conductor" |
March 3, 2004, 3:00 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Barry Mazur (HARVARD UNIVERSITY) |
"Differential Structures on Compact Manifolds and P-adic L-Function" |
" |
March 1, 2004, 3:00-4:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Peter Kronheimer (HARVARD UNIVERSITY) |
"Property P For Knots" |
" |
February 27, 2004, 3:30-5:30 Pm at Science Center Room, 309 |
| NUMBER THEORY SEMINAR |
Shou-Wu Zhang (COLUMBIA UNIVERSITY) |
"Rational Points on Hyper or Super Elliptic Curves" |
" |
February 25, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| GEOMETRY SEMINAR |
Matthew Bainbridge (HARVARD UNIVERSITY) |
"The Bass Note of a Riemannian Manifold" |
" |
February 25, 2004, 4:30 - 5:30 Pm at Science Center, Room 530 |
| GEOMETRY SEMINAR |
Izzet Coskun (HARVARD UNIVERSITY) |
"The Nef Cone Of The Moduli Space Of Curves And The F-Conjecture" |
" |
February 23, 2004, 4:30 - 5:30 Pm at Science Center, Room 530 |
| THE BASIC NOTIONS SEMINAR |
Yum-Tong Siu (HARVARD UNIVERSITY) |
Methods of $\bar\partial$ Estimates in Algebraic Geometry |
" |
February 23, 2004, 3:00pm at Sc 507 |
| GAUGE THEORY |
Shelly Harvey (MIT) |
"3-Manifold Invariants, Symplectic Structures, Deficiency of a Group, and Dash of Homology Cobordism" |
" |
February 20, 2004, 3:30-5:00 Pm at Science Center, Room 309 |
| SPECIAL SEMINAR |
Seth Sullivant (UC - BERKELEY) |
"What is Algebraic Statistics?" |
Abstract: The emerging field of algebraic statistics advocates the use of polynomial algebra as a tool for statistical analysis. The underlying principle is that many natural families of probability distributions on discrete random variables are algebraic varieties (the zero sets of a collection of polynomials). Knowing the polynomials which define these families of probability distributions can be useful for making statistical inferences and provides a different view point for some problems in probability theory. I will illustrate these ideas with some examples from the theory of graphical models and data security, phylogeny reconstruction, and the theory of conditionally specified models. No knowledge of polynomial algebra will be assumed" |
February 19, 2004, 2:00 - 3:00 Pm at Science Center, Room 507 |
| THE MODULAR SEMINAR |
Akshay Venkatesh (MIT) |
Arithmetic cases of quantum unique ergodicity |
I ll introduce and discuss the quantum unique ergodicity problem on locally symmetric spaces, which studies certain analytic properties of automorphic forms. Strikingly, it reflects a great deal of the geometry of the spaces. Most of the time I ll talk about the following concrete example: How and why would a holomorphic modular form concentrate at a point? (i.e., have an unusually large value at that point)? How does being a Hecke eigenform help prevent this phenomenon, and why is it easier for such a form to concentrate near a Cm point?" |
February 19, 2004, 3:00-4:00pm at Sc 507 |
| NUMBER THEORY SEMINAR |
Vladimir Berkovich (WEIZMANN INSTITUTE OF SCIENCE, ISRAEL) |
"Integration Of One-forms On P-adic Analytic Spaces" |
" |
February 18, 2004, 3:00 - 4:00 Pm at Science Center, Room 507 |
| GEOMETRY SEMINAR |
Melissa Liu (HARVARD UNIVERSITY) |
"Marino-Vafa Formula of One-Partition Hodge Integrals" |
" |
February 16, 2004, 4:30-5:30 Pm at Science Center, Room 530 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Michael Usher (M.I.T.) |
Gromov Invariants via Symplectic Lefschetz Fibrations |
" |
February 13, 2004, 3:30 at Science Center, Room 309 |
| MODULAR CURVES AND MODULAR FORMS |
William Stein (HARVARD UNIVERSITY) |
"A Foundation For Computing With Modular Abelian Varieties?" |
" |
February 12, 2004, 3:00-4:00 Pm at Science Center Room, 507 |
| NUMBER THEORY SEMINAR |
Teruyoshi Yoshida (HARVARD UNIVERSITY) |
"Non-abelian Lubin-Tate Theory and Deligne-Lusztig Theory for Gln" |
" |
February 11, 2004, 3:30 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Joachim Krieger (HARVARD UNIVERSITY) |
Global Regularity of Wave Maps |
" |
February 10, 2004, 1:30-3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
David Gay (UNIVERSITY OF QUEBEC, MONTREAL) |
"Constructing Symplectic Forms Which Vanish Along Circles" |
" |
February 06, 2004, 3:30 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Michael Harris (VISITING HARVARD; UNIVERSITY OF PARIS 7) |
Congruences Between Stable and Endoscopic Forms and Arithmetic Applications (Work in Progress) |
" |
February 04, 2004, 3:00 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Samit Dasgupta (BERKELEY) |
"Elliptic Units for Real Quadratic Fields" |
" |
January 14, 2004, 3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Garry Gibbons (UNIVERSITY OF CAMBRIDGE) |
"Bohm and other exotic Einstein Metrics and the stability of higher dimensional black holes" |
Seminar organized by Shing-Tung Ya" |
December 16, 2003, 1:30 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Curt McMullen (HARVARD UNIVERSITY) |
"Billiards and dynamics of Sl(2,R) over moduli space" |
" |
December 12, 2003, 3:30 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
William Stein (HARVARD) |
"Modular Degrees of Elliptic Curves of Prime Conductor" |
" |
December 10, 2003, 3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Satoshi Yamaguchi (HARVARD UNIVERSITY) |
"D-Branes in n=2 Landau-Ginzburg theory and Liouville theory |
" |
December 9, 2003, 1:30 pm at Science Center Rm 507 |
| COMPLEX GEOMETRY AND ANALYSIS SEMINAR |
Joseph J. Kohn (PRINCETON UNIVERSITY) |
"Hypoellipticity and loss of derivatives" |
" |
December 8, 2003, 11:00 am at Science Center, Rm 103b |
| BASIC NOTIONS SEMINAR |
Shlomo Sternberg (HARVARD UNIVERSITY) |
"The Euler-Maclaurin Formula in Higher Dimensions" |
" |
December 8, 2003, 3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Saso Strle (MCMASTER UNIVERSITY) |
"Cobordisms of rational homology spheres and 4-ball genus" |
" |
December 05, 2003, 3:30 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
M Kisin (CHICAGO) |
"Flat deformation rings, local models of Shimura varieties and modularity" |
" |
December 03, 2003, 3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Sergey Gukov (CLAY INSTITUTE) |
"Quantum geometry of hyperbolic 3-manifolds" |
" |
December 02, 2003, 1:30 P.M. at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Mihaela Iftime (UNIVERSITY OF MASSACHUSETTS) |
The gravitational field of a dust rotating cylinder |
" |
November 25, 2003, 1:30 p.m. at Harvard University, Science Center Room 507 |
| COLLOQUIUM |
Andrei Okounkov (PRINCETON UNIVERSITY) |
"Crystal shapes and algebraic curves" |
Abstract: This will be a nontechnical account of some recently found connections between certain random surface models and algebraic geometry, in particular, Gromov-Witten theory" |
November 20, 2003, 4:30 Pm at Science Centr, Hall D |
| NUMBER THEORY SEMINAR |
Wilfried Schmid (HARVARD) |
"An explicit proof of the Converse Theorem for Gl(3,Z), or: how many functional equations are necessary to characterize Gl(3,Z)-automorphy?" |
" |
November 19, 2003, 3:00 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Raoul Bott (HARVARD) |
"The Symbol of an Operator; a Reminiscence" |
" |
November 17, 2003, 3:00 Pm at Science Center, Room 507 |
| HARVARD, BRANDEIS, M.I.T., NORTHEASTERN COLLOQUIUM |
William Minicozzi (JOHNS HOPKINS UNIVERSITY) |
Double Spiral Staircases in Embedded Minimal Disks |
Abstract: The two classical examples of embedded minimal disks are the plane and the helicoid - the latter is a double spiral staircase. I will talk about joint work with Toby Colding which shows that these are the only possible local pictures and then uses this local structure to prove a global compactness theorem for embedded minimal disks" |
November 13, 2003, 4:30 p.m. at Harvard Univ., Science Center Hall D |
| NUMBER THEORY SEMINAR |
Gabrielle Nebe (ULM/HARVARD) |
"Ideal Lattices" |
" |
November 12, 2003, 3:00 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Jean-Pierre Serre (COLLEGE DE FRANCE) |
"Writing mathematics?" |
" |
November 10, 2003, 3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Victor Guillemin (MIT) |
"Signature Quantization" |
" |
November 07, 2003, 3:30 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Laurent Berger (HARVARD) |
De Rham representations and universal norms |
Abstract: If E is an elliptic curve and if (K_n)_n is the Z_p^* cyclotomic extension of K_0 = Q_p, we know what the projective limit of the E(Kn) for the trace maps looks like (the answer depends on whether E is supersingular or ordinary). One can reformulate this result in terms of the Tate module of E and Nekovar gave a conjectural description of the universal norms for any de Rham p-adic representation. I will explain how one can prove Nekovar s conjecture. Using the reciprocity formula of Cherbonnier-Colmez and the p-adic differential equation attached to a de Rham representation, one can reduce the conjecture to an application of Wronski s lemma" |
November 05, 2003, 3:00 Pm at Science Center, Room 507 |
| SEMINAR ON COMPLEX GEOMETRY AND ANALYSIS |
Yum-Tong Siu (HARVARD UNIVERSITY) |
Smooth Levi-flat submanifolds in compact Hermitian symmetric spaces (Continuation) |
" |
November 03, 2003, 4:15 p.m. at Harvard University, Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Stavros Garoufalidis (GEORGIA TECH) |
"The Jones polynomial and the signature of a knot" |
" |
October 31, 2003, 3:30 Pm at Science Center, room 309 |
| NUMBER THEORY SEMINAR |
Jean-Pierre Serre (COLLEGE DE FRANCE) |
"An application of l-adic cohomology to group theory" |
" |
October 29, 2003, 3:00-4:00 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
S.-T. Yau (HARVARD) |
"Geometry and Computer Graphics" |
" |
October 27, 2003, 3:00 Pm at Science Center, Room 507 |
| SEMINAR ON COMPLEX GEOMETRY AND ANALYSIS |
Yum-Tong Siu (HARVARD) |
"Smooth Levi-flat submanifolds in compact Hermitian symmetric spaces" |
" |
October 27, 2003, 4:15 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Andreea Nicoara (HARVARD) |
"Closed Range Considerations for the Tangential Cauchy-Riemann Operator on Weakly Pseudoconvex Cr Manifolds of Dimension Three." |
" |
October 24, 2003, 3:30 Pm at Science Center, Room 309 |
| MODULAR CURVES SEMINAR |
Frank Calegari (HARVARD) |
A counterexample to the Gouvea-Mazur conjecture |
Abstract: Gouvea and Mazur made a precise conjecture about slopes of modular forms. Weaker versions of this conjecture were established by Coleman and Wan. In this talk, I will exhibit examples contradicting the full conjecture as it currently stands. (Joint work with Kevin Buzzard." |
October 23, 2003, 3:00 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Fred Diamond (BRANDEIS) |
"Hilbert modular forms and mod p Galois representations" |
" |
October 22, 2003, 3:00-4:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Ilya Zharkov (HARVARD) |
"Kahler affine structures" |
" |
October 21, 2003, 1:30 Pm at Science Center, Room 507 |
| MODULAR CURVES SEMINAR |
Hui Zhu (HARVARD) |
Construction of Some Families of 2-Dimensional Crystalline Representations |
Abstract: Our work was inspired by a conjecture of Breuil on the modulo p reduction of 2-dimensional crystalline representations (especially of `higher weight ). In particular, if the representation arises from a modular form f, then his conjecture predicts what the residual Galois representation attached to f looks like for those f of higher weight k (i.e., k > p). In this talk, we describe how to explicitly construct families of 2-dimensional crystalline representations by ``constructing Wach modules, and then use these to give partial answers to the questions mentioned above" |
October 21, 2003, 3:00 Pm at Science Center, Room 507 |
| SEMINAR ON COMPLEX GEOMETRY AND ANALYSIS |
Jun-Muk Hwang (KOREA INSTITUTE FOR ADVANCED STUDY/HARVARD) |
"Multiplicities of pluri-anti-canonical divisors and degrees of Fano manifolds" |
" |
October 20, 2003, 4:15 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Lenny Ng (STANFORD) |
"Pseudoholomorphic curves and knot invariants" |
" |
October 17, 2003, 3:30 Pm at Science Center, Room 309 |
| MODULAR CURVES SEMINAR |
William Stein (HARVARD) |
The Arithmetic of J1(p) |
" |
October 16, 2003, 3:00 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Frank Calegari (HARVARD) |
"Ramification of Hecke Algebras" |
" |
October 15, 2003, 3:00-4:00 Pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY |
Kieran O'Grady (UNIVERSITA DEGLI STUDI DI ROMA "LA SAPIENZA") |
"Involutions and Linear Systems on Holomorphic Irreducible Manifolds" |
" |
October 14, 2003, 3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Vladimir Chernov (DARTMOUTH) |
"Vassiliev invariants of Legendrian, pseudo-Legendrian and framed knots in contact 3-manifolds" |
" |
October 10, 2003, 3:30 Pm at Science Center, Room 309 |
| JOINT COLLOQUIUM |
J.W. Cogdell (OKLAHOMA STATE UNIVERSITY) |
"Converse Theorems and Functoriality" |
Tea at 4:00 P" |
October 09, 2003, 4:30-5:30 at Science Center, Hall D |
| NUMBER THEORY SEMINAR |
David Helm (HARVARD) |
"A Geometric Jacquet-Langlands Correspondence" |
By the Jacquet-Langlands correspondence and Faltings isogeny theorem, it is known that the abelian variety $J_0^{Dpq}(N)$ (the Jacobian of a Shimura curve of discriminant $Dpq$ with $\Gamma_0(N)$ level structure) is isogenous to the $pq$-new subvariety of $J_0^D(pqN)$, whenever $p$ and $q$ are distinct primes not dividing $D$ or $N$. However, this approach is entirely nonconstructive, and gives no information at all about any particular isogeny between the two varieties. In this talk, we determine the kernels of all possible maps from one variety to the other up to support on a small finite set of maximal ideals of the Hecke algebra. We also examine consequences of this computation for the geometry of Jacobians of Shimura curves" |
October 08, 2003, 3:00-4:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINARS |
Eugenio Calabi () |
"Structures In Spaces Of Kahler Metrics" |
" |
October 07, 2003, 1:30 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Eugenio Calabi () |
"Structures in Spaces of Kahler Metrics" |
" |
October 07, 2003, 1:30 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Cliff Taubes (HARVARD) |
"Some Research Questions in Differential Topology". |
" |
October 06, 2003, 3:00 Pm at Science Center, Room 507 |
| COMPLEX GEOMETRY AND ANALYSIS SEMINAR |
Yum-Tong Siu (HARVARD) |
Closed Positive Currents and Nevanlinna Theory (Continuation) |
" |
October 06, 2003, 4:15 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Luo Wei (HARVARD) |
"J-holomorphic curves in symplectisation of the unit cotangent bundle of a Riemann surface with genus greater than 1". |
" |
October 03, 2003, 3:30-4:30 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Ehud De Shalit (HEBREW UNIVERSITY) |
"The monodromy-weight conjecture for p-adically uniformised varieties" |
" |
October 01, 2003, 3:00-4:00 Pm at Science Center, Room 507 |
| COMPLEX GEOMETRY AND ANALYSIS SEMINAR |
Yum-Tong Siu (HARVARD) |
Closed Positive Currents and Nevanlinna Theory |
" |
September 29, 2003, 4:15 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Irene Minder, Laura Matusevich, Danny Goroff (HARVARD) |
"Applying for an Academic Job in Mathematics". |
" |
September 29, 2003, 3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Denis Auroux (MIT) |
"Lefschetz fibrations in homological mirror symmetry." |
" |
September 26, 2003, 3:30-4:30 Pm at Science Center, Room 309 |
| MODULAR CURVES SEMINAR |
Jayce Getz (Harvard), Emma Smith (Mit) () |
"Systems of orthogonal polynomials arising from modular j-functions" |
" |
September 25, 2003, 3:00-4:00 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Benedict Gross (HARVARD) |
"On the local divisibility of Heegner points" |
" |
September 24, 2003, 3:00-4:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Bjorn Andreas(Harvard) () |
"Five Brane - Instanton Transitions On Calabi-Yau Threefolds" |
" |
September 23, 2003, 1:30 Pm at Science Center, Room 507 |
| COMPLEX GEOMETRY AND ANALYSIS SEMINAR |
Jeffrey McNeal (OHIO STATE UNIVERSITY) |
Compactness of the \bar\partial-Neumann problem |
On a smoothly bounded domain in Cn the compactness of \bar\partial-Neumann operator implies global regularity results on a solution to the Cauchy-Riemann equations. I will discuss conditions on a smoothly bounded domain, which involve the existence of certain plurisubharmonic functions, that imply the compactness of the \bar\partial -Neumann operator" |
September 22, 2003, 4:15 Pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
Tom Coates (HARVARD) |
"Quantization and Gromov-Witten Theory" |
" |
September 16, 2003, 3:00 Pm at Science Center, Room 507 |
| COMPLEX GEOMETRY AND ANALYSIS |
Jun-Muk Hwang (KOREA INSTITUTE FOR ADVANCED STUDY/VISITING HARVARD) |
"Rigidity of surjective holomorphic maps between projective varieties" |
" |
September 15, 2003, 3:00 Pm at Science Center, Room 507 |
| ALGEBRAIC GEOMETRY SEMINAR |
James McKernan (UNIVERSITY OF CALIFORNIA, SANTA BARBARA) |
"Boundedness of Fano varieties" |
Abstract: We prove that the family of all varieties of fixed dimension such that -K_X is ample and some fixed multiple of -K_X is Cartier are bounded, provided the singularities are reasonable" |
May 27, 2003, 3:00 Pm at Science Center, Room 507 |
| ALGEBRAIC GEOMETRY SEMINAR |
Lisa Jeffrey (UNIVERSITY OF TORONTO) |
Moduli spaces and symplectic geometry |
The moduli space M(n,d) of semistable holomorphic vector bundles of rank n and degree d (assumed coprime) is a smooth Kahler manifold. Generators of its cohomology ring have been known since the fundamental 1982 paper of Atiyah and Bott. In 1992 Witten gave formulas for the intersection numbers, which determine the relations in the cohomology ring. These formulas were proved mathematically in my joint work with Frances Kirwan. In this lecture we outline this argument" |
May 20, 2003, 3:00 Pm at Science Center, Room 507 |
| INFORMAL ALGEBRAIC GEOMETRY SEMINAR |
Lisa Jeffrey (UNIVERSITY OF TORONTO) |
"The residue formula and its applications" |
In joint work with F. Kirwan a formula was given for intersection pairings in reduced spaces $\mu^{-1}(p)/Stab(p) \subset K$, in terms of iterated residues. An alternate formula has been given by Guillemin and Kalkman; Kalkman showed the two formulas were equivalent. In this lecture we shall describe one recent application of the residue formula (joint work with R. Goldin and T. Holm). It is known that the image of the moment map of a Hamiltonian $T$-space is partitioned into chambers by the critical values of the moment map. If $T$ is a torus and $M$ a Hamiltonian $T$ space, then for all points $p \in Lie(T)$, one can define the Kirwan map kappap : H*T(M) -> H^*(Mp), where Mp = mu-1(p)/T is the reduced space associated to p. The kernel of kappap depends only on the chamber $C$ containing $p$. We have used the residue formula to exhibit a class which vanishes under $\kappa_p$ but not under $\kappa_q$ where $q$ is a point in a different chamber adjacent to $C$ " |
May 15, 2003, 3:00 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Oliver Bultel (UNIVERSITY OF HEIDELBERG) |
I-adic monodromy of abelian varieties in characteristic p |
" |
May 14, 2003, 3:00 Pm at Science Center, Room 507 |
| INFORMAL ALGEBRAIC GEOMETRY SEMINAR |
Lisa Jeffrey (UNIVERSITY OF TORONTO) |
"The kernel of the Kirwan map" |
" |
May 08, 2003, 3:00 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Nick Ramsey (HARVARD) |
Geometric Modular Forms of Half-Integral Weight |
Abstract: We propose a geometric formalism for half-integral weight modular forms that allows one to define these objects over very general rings. This is achieved by identifying these spaces with certain spaces of modular units. We ll discuss some basic properties (e.g. q-expansion principle) and define Hecke action. Time permitting, we ll discuss p-adic modular forms of half-integral weight and the p-adic U operator" |
May 07, 2003, 3:00 Pm at Science Center, Room 507 |
| ALGEBRAIC GEOMETRY SEMINAR |
Janos Kollar (PRINCETON UNIVERSITY) |
Rationally connected varieties over finite fields |
Abstract: Let X be a rationally connected variety over a finite field F. Given two F-points of X, is there a rational curve in X (defined over F) passing through these two points? The answer to this question (and its generalizations) solve some conjectures of Colliot-Th\ el\`ene on R-equivalence and on the Chow group of zero cycle" |
May 06, 2003, 3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOOLOGY SEMINAR |
Semyon Alesker (TEL AVIV UNIVERSITY) |
Non-commutative determinants and Monge-Ampere equations |
" |
May 02, 2003, 3:30 Pm at Science Center, Room 309 |
| JOINT COLLOQUIUM |
David Fisher (CUNY/LEHMAN COLLEGE) |
Non-linear representation theory of finitely generated groups |
Abstract: By a non-linear representation of a finitely generated group G, we mean an action of G on a smooth compact manifold M by volume preserving diffeomorphisms. In other words, a homomorphism from G into Diffomega(M). Ideally, one would like to classify non-linear representations, at least for large enough G and small enough M. I will survey a wide variety of results and techniques for approaching this problem, before concentrating on my recent joint work with Margulis. In this work, we consider the question of rigidity of non-linear representations of both higher rank lattices and, more generally, groups with property T of Kazhdan. We call a non-linear representation rigid if any perturbation is conjugate back to the original representation" |
May 01, 2003, 4:30-5:30 Pm at Science Center, Hall D |
| NUMBER THEORY SEMINAR |
Pete Clark (HARVARD) |
Rational Points on Atkin-Lehner Quotients of Shimura Curves |
" |
April 30, 2003, 3:00 Pm at Science center, Room 507 |
| MODULAR CURVES SEMINAR |
Akshay Venkatesh () |
"Counting Special Automorphic Forms" |
" |
April 29, 2003, 4:30 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Nathan Dunfield (HARVARD) |
Commensurability of fibered and non-fibered hyperbolic 3-manifolds |
" |
April 25, 2003, 3:30 Pm at Science Center, Room 309 |
| INFORMAL ALGEBRAIC GEOMETRY SEMINAR |
Izzet Coskun (HARVARD) |
"The enumerative geometry of Del Pezzo surfaces" |
Abstract: Using the example of Del Pezzo surfaces, I ll discuss how one might approach the enumerative geometry of surfaces in projective space" |
April 24, 2003, 3:00 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Yu-Ru Liu (HARVARD) |
Generalizations of the Turan and the Erdos-Kac Theorems |
" |
April 23, 2003, 3:00 Pm at Science Center, Room 507 |
| ALGEBRAIC GEOMETRY SEMINAR |
Michael Thaddeus (COLUMBIA UNIVERSITY) |
Stable Maps To A Loop Group |
Let $X$ be a compact complex manifold, $\Omega K$ the space of based loops on a compact Lie group. Atiyah pointed out that the space of based holomorphic maps $\phi: X \to \Omega K$ is finite-dimensional. When $X$ is a curve (say the projective line) this suggests the possibility of compactifying the space and evaluating Gromov-Witten invariants of the loop group. We explain how to do this. Surprisingly, the moduli space is not smooth, but it can be canonically deformed to a smooth space. We will outline a few simple applications, proving, for example, the associativity of the quantum cohomology" |
April 22, 2003, 3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Dror Bar-Natan (UNIVERSITY OF TORONTO) |
"Khovanov's homology for tangles and cobordisms". |
" |
April 18, 2003, 3:30 Pm at Science Center, Room 309 |
| INFORMAL ALGEBRAIC GEOMETRY SEMINAR |
Mihnea Popa (HARVARD) |
The geometry of moduli spaces of vector bundles on curves Ii |
" |
April 17, 2003, 3:00 Pm at Science Center, Hall E |
| NUMBER THEORY SEMINAR |
Pierrette Cassou-Nogues (UNIVERSITY OF BORDEAUX) |
The motivic Zeta function for quasi ordinary singularities. |
" |
April 16, 2003, 3:00-4:00 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Phillippe Cassou-Nogues (UNIV. OF BORDEAUX) |
Invariants of symmetric bundles |
" |
April 16, 2003, 4:30 - 5:30 Pm at Science Center, Room 507 |
| MODULAR CURVES SEMINAR |
Wilfried Schmid (HARVARD) |
"Automorphic distributions, L-functions, and functional equations" |
" |
April 15, 2003, 4:30 Pm at Science Center, Room 507 |
| INFORMAL ALGEBRAIC GEOMETRY |
Mihnea Popa (HARVARD) |
The geometry of moduli spaces of vector bundles on curves I |
Abstract: I am planning to give a two part survey on a number of results on generalized theta divisors on moduli spaces of vector bundles on curves. The main goal is to formulate effective results for linear series in the style of higher dimensional geometry" |
April 10, 2003, 3:00 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
David Jao (HARVARD) |
"Supersingular Primes for Points on Modular Curves" |
In 1987 Elkies showed that every elliptic curve defined over Q has infinitely many primes of supersingular reduction. In this talk, we extend this proof from X(1) to higher level modular curves X(p)/w and explain how the moduli interpretation in this context yields new supersingularity results for elliptic curves. We also indicate how the same techniques can be applied to Shimura modular curves to prove analogous results for higher dimensional abelian varietie" |
April 09, 2003, 3:00 Pm at Science Center, Room 507 |
| ALGEBRAIC GEOMETRY SEMINAR |
Jessica Young (MIT/HARVARD) |
"Hrushovski's proof of the Mordell Lang conjecture" |
" |
April 08, 2003, 3:00 pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Simon Brendle (PRINCETON UNIVERSITY) |
"A glueing theorem for the Ginzburg-Landau equations in higher dimensions". |
" |
April 04, 2003, 3:30 Pm at Science Center, Room 309 |
| INFORMAL ALGEBRAIC GEOMETRY SEMINAR |
Linda Chen (COLUMBIA UNIVERSITY) |
"Orbifold Chow ring of stacky toric varieties" |
" |
April 03, 2003, 3:00 Pm at Science Center, Room 507 |
| JOINT COLLOQUIUM |
Manjul Bhargava (PRINCETON/HARVARD) |
Gauss composition and generalizations |
Abstract: Gauss s law of composition of binary quadratic forms, laid down in his famous 1801 work Disquisitiones Arithmeticae , lies at the very foundations of modern algebraic number theory. The question arises: Do there exist similar composition laws on spaces of higher degree forms? We will show that the answer is yes, and that Gauss s law of composition is in fact only one in a family of at least 14 (!) such composition laws. We will define these 14 laws and describe their intimate connections with the exceptional Lie groups. Finally, we will present some analytic and number-theoretic applications, including the resolution of a fundamentally important case of the Cohen-Lenstra Martinet heuristics." |
April 03, 2003, 4:30-5:30 Pm at Science Center, Hall D |
| NUMBER THEORY SEMINAR |
Alexandru Popa (HARVARD) |
Central values of Rankin L-series over real quadratic fields |
Abstract: We consider the Rankin convolution L-series attached to a modular form f of weight 0 or 2 for Gl(2) over the rational numbers, and to a character of a real quadratic field. When the sign in the functional equation is +1, Waldspurger proved that the nonvanishing of the L-function at the center of the critical strip is related to the existence of a linear form on the space of automorphic forms belonging to the Jacquet-Langlands lift of the automorphic representation attached to f. Using automorphic representation techniques, we prove that the central value of the L-function can be recovered (up to an explicit constant) from the value of a specific linear form as above, evaluated at a special vector belonging to the Jacquet-Langlands lift of f. This extends and gives a new proof of the special value formulae of B. Gross and S. W. Shang in the imaginary field case" |
April 02, 2003, 3:00 pm at Science Center, Room 507 |
| SPECIAL MODULAR FORMS SEMINAR |
Frank Calegari, William Stein (HARVARD) |
About algebraic numbers and p-adic modular forms |
Frank Calegari will give one (or two) 15 minute practice talk(s) this Tuesday (April 1) at 4:30pm in Science Center 507. This is in preparation for his talk to The Friends. One of his talks might be about algebraic numbers, and they other might be about p-adic modular forms. After Frank s talk(s) William Stein will give a 30 minute talk about the modular forms database." |
April 01, 2003, 4:30 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Zoltan Szabo (PRINCETON UNIVERSITY) |
'Knot Floer homology' |
" |
March 21, 2003, 3:30 Pm at Science Center, Room 309 |
| JOINT MATHEMATICS COLLOQUIUM |
Rahul Pandharipande (PRINCETON UNIVERSITY) |
Gromov-Witten theory for target curves |
Abstract: Gromov-Witten theory concerns integrals over the moduli space of maps from Riemann surfaces to target varieties. I will present a complete description of the theory for 1-dimensional targets with connections to representation theory and integrable hierarchies. The talk represents joint work with A. Okounko" |
March 20, 2003, 4:30 Pm at Science Center, Hall D |
| NUMBER THEORY SEMINAR |
Catherine O'Neil (MIT) |
"Explicit 3-descent on elliptic curves" |
" |
March 19, 2003, 3:00 Pm at Science Center, Room 507 |
| MODUALAR CURVES SEMINAR |
Jonathan Hanke (PRINCETON UNIVERSITY) |
Representing numbers by (ternary) quadratic forms |
Abstract:This talk will describe the main features and results of the analytic approach for understanding which integers $m$ are represented by a positive definite quadratic form $Q$ in $n$ variables. These results can be interpreted in terms of features of the theta function associated to $Q$, which is a modular form of weight $n/2$. When $n$ is odd the situation is particularly interesting as the theta function is a modular form of half-integral weight. I will give an overview of the main ideas and theorems used to describe the numbers represented by $Q$ from a modular persrective, and then describe some recent results about the representation behavior of ternary forms. These results can be phrased in terms of a local-global principle for quadratic forms, and are related to certain features special to modular forms of half-integral weight" |
March 18, 2003, 4:30 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Jonathan Weitsman (UNIVERSITY OF CALIFORNIA, SANTA CRUZ) |
'The topology of Hamiltonian Loop Group Spaces' |
" |
March 14, 2003, 3:30 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Manjul Bhargava (PRINCETON UNIVERSITY/HARVARD) |
"The parametrization of quadratic, cubic, quartic, and quintic rings" |
Abstract: It is well-known that orders in quadratic number fields are uniquely determined by their discriminants. However, this is not true for orders in higher degree fields. How can one classify the orders in number fields of higher degree? We will show that a natural solution exists in terms of the integer orbits in certain special group representations. The method we use applies to rings of ranks n = 2, 3, 4, and 5, and the resulting theory turns out to have a close resemblance to the classical development of the solutions to the n-tic equation (even when n=5...!). On the other hand, the resulting theory is also intimately related to the sequence of Lie groups A1, G2, F4 E8. If time permits, I ll try and discuss some of these remarkable connections" |
March 12, 2003, 3:00 Pm at Science Center, Room 507 |
| MODULAR CURVES SEMINAR |
Romyar Sharifi (HARVARD) |
"Massey Products and Ideal Class Groups". |
Abstract: I will define Massey products as operations in Galois cohomology starting with the simplest example, cup products. I will be most interested in the Galois cohomology of the maximal extension of a number field K unramified outside a set of primes S with coefficients in roots of unity. I will give a formula for certain Massey products, and then I will show how this formula implies a relationship between the structure of the class group of a Kummer extension L of K unramified outside S and of the class group of K itself. In particular, under certain mild assumptions, a precise version of the following statement will hold: the k-th graded quotient in the augmentation filtration of the class group of L is isomorphic to the class group of K modulo the image of (k+1)-fold Massey products" |
March 11, 2003, 4:30 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Hubert Bray (MIT) |
"Proof of the Poincare Conjecture for 3-Manifolds with Yamabe Invariant Greater Than Rp^3" |
" |
March 07, 2003, 3:30 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Martin Weissman (HARVARD) |
"The Fourier-Jacobi Map and Applications" |
First, I will discuss the Fourier-Jacobi expansion of Siegel modular forms, and the relation to L-functions for Sp(4). Then I will discuss applications of a ``Fourier-Jacobi map to representations of groups of type A, D, and E (simply-laced groups). Motivated by work of Howe on ``singular modular forms for the symplectic group, I will discuss small representations of groups and applications via dual reductive pairs to functoriality" |
March 05, 2003, 3:00 Pm at Science Center, Room 507 |
| ALGEBRAIC-GEOMETRY SEMINAR |
Robert Friedman (COLUMBIA UNIVERSITY) |
"Regular elements and principal bundles" |
Abstract: Kostant and Steinberg constructed sections of the adjoint quotient morphism for a simple Lie algebra or a simple and simply connected algebraic group with values in the Zariski open subset of all regular elements. This talk will discuss the uniqueness of these sections, suitably interpreted, and describe the connections with principal bundles on curves of arithmetic genus one and elliptic curves as well as applications to representation theory" |
March 04, 2003, 3:00 Pm at Science Center, Room 507 |
| MODULAR CURVES SEMINAR |
William Stein (HARVARD) |
"Writing Theta Series in Terms of Cuspidal Eigenforms" (or "What's Brewing in Meccah right now."). |
Abstract: Lagrange proved that every positive integer is the sum of four squares. How many other quadratic forms in four variables represent every positive integer? Manjul Bharghava is currently attempting to give an ultimate generalization of Lagrange s theorem by giving a complete list of all forms that represent all integers. To quote Manjul: The goal is to classify all forms that represent all integers. I ve reduced this classification to understanding these 6560 forms [or ~900, since I can take care of most of the 6560 forms of smallish level using arithmetic methods], but these forms are essentially unrelated to each other and so must be dealt with individually. Now to get the desired upper bound on the set of numbers that might not be represented by the form, one computes a certain product of local factors, which Jon Hanke has written code to do, and which takes about a half hour on the biggest forms, which is very reasonable. The other thing one needs is the sum of the absolute values of the eigenform coefficients of the cuspidal part of the theta series. The ratio of these two quantities tells us how far one needs to check in order to prove that the form represents all integers. My talk will be about how I m using modular symbols, Magma, and Octave to compute the sum of the absolute values of the eigenform coefficients of the cuspidal part of the theta series in a reasonable amount of time. Jon Hanke will talk March 18, probably about his part of the computation, and hopefully Manjul will tie everything together later in the semester" |
March 04, 2003, 4:30 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Amer Iqbal (HARVARD) |
"Counting Curves in Local Hirzebruch Surfaces". |
" |
February 28, 2003, 3:30 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Preda Mihailescu (ETH-ZURICH) |
"Zooming into Catalan's conjecture" |
We give a historically backed up introduction to the study and solution of Catalan s conjecture -- which consists in the statement that the only consecutive rational integer strict powers are 8 and 9. In the first part of the talk, we will give a historical overview of the various approaches -- and respective results -- to the study of Catalan s conjecture. In the second part, the zooming in will consist in an increasingly technical, magnifying focus on the central consequences of the presumed existence of unknown solutions to Catalan s equation. The way these consequences lead to a contradiction should become clear or at least plausible to the audience (depending upon time,technical prerequisites ... and, maybe, chemistry of the moment)" |
February 26, 2003, 3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Yi-Jen Lee (PRINCETON UNIVERSITY) |
"Noncontractible periodic orbits, Gromov invariants, and Floer-theoretic torsions". |
" |
February 21, 2003, 3:30 Pm at Science Center, Room 309 |
| JOINT COLLOQUIUM |
Hiraku Nakajima (KYOTO UNIVERSITY) |
"Quiver varieties and quantum toroidal algebras" |
Abstract: Consider quiver varieties for an affine quiver. They are moduli spaces of instantons on the Ale space. Their equivariant $K$ groups have structures of representations of the quantum toroidal algebra, a $q$--analog of the loop algebra of the affine Lie algebra ($2$--toroidal algebra). This is generalization of my construction for quiver varieties for a finite quiver. I discuss some open problems" |
February 20, 2003, 4:30-5:30 Pm at Science Center, Hall D |
| NUMBER THEORY SEMINAR |
Vladimir Berkovich (WEIZMANN INSTITUTE OF SCIENCE) |
"Integration of one-forms on $p$-adic analytic spaces" |
" |
February 19, 2003, 3:00 Pm at Scinece Center, Room 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Ravi Vakil () |
"Vanishing of Chow (or cohomology) classes on the moduli space of curves" |
" |
February 18, 2003, 3:00-4:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Michael Hopkins (MIT/HARVARD) |
"Twisted K-theory and the cubic Dirac operator" |
" |
February 14, 2003, 3:30 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Noam D.Elkies (HARVARD) |
"Yet more nonlinear codes from modular curves" |
" |
February 12, 2003, 3:00 Pm at Science Center, Room 507 |
| MODULAR CURVES SEMINAR |
Ben Howard (HARVARD) |
"Anticyclotomic Iwasawa theory of Cm elliptic curves". |
Abstract: We study the growth of the Selmer group of a Cm elliptic curve $E$ in the anticyclotomic Zp-extension of the Cm field, where $p$ is a prime of good, ordinary reduction for $E$. When the complex $L$-function of $E$ vanishes to even order, the two variable main conjecture of Rubin implies that the Pontryagin dual of the $p$-power Selmer group over the anticyclotomic extension is a torsion Iwasawa module. When the order of vanishing is odd, work of Greenberg shows that it is not a torsion module. The goal of the talk is to show that in the case of odd order of vanishing the dual of the Selmer group has rank exactly one as an Iwasawa module, and to relate the torsion submodule to Katz s $p$-adic $L$-function." |
February 11, 2003, 4:30 Pm at Science Center, Room 507 |
| MODULAR CURVES SEMINAR |
Ben Howard (HARVARD) |
"Anticyclotomic Iwasawa theory of Cm elliptic curves" |
Abstract: We study the growth of the Selmer group of a Cm elliptic curve $E$ in the anticyclotomic Zp-extension of the Cm field, where $p$ is a prime of good, ordinary reduction for $E$. When the complex $L$-function of $E$ vanishes to even order, the two variable main conjecture of Rubin implies that the Pontryagin dual of the $p$-power Selmer group over the anticyclotomic extension is a torsion Iwasawa module. When the order of vanishing is odd, work of Greenberg shows that it is not a torsion module. The goal of the talk is to show that in the case of odd order of vanishing the dual of the Selmer group has rank exactly one as an Iwasawa module, and to relate the torsion submodule to Katz s $p$-adic $L$-function." |
February 08, 2003, 4:30 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOOGY SEMINAR |
Weiyang Qiu (HARVARD) |
Special Lagrangian Submanifolds with Boundary and Lagrangian Free Boundary Problem. |
" |
February 07, 2003, 3:30 Pm at Science Center, Room 309 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
Curt McMullen (HARVARD) |
"Billiards and Curves on Hilbert Modular Surfaces" |
" |
February 04, 2003, 3:00 Pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
David Kazhdan (HARVARD) |
"Representations of Groups over two dimensional fields" |
" |
January 31, 2003, 1:00-2:00 Pm at Science Center, Room 507 |
| MODULAR CURVES SEMINAR |
Edray Goins (CALTECH) |
"Deformations of Galois Computations: An Adventure in Galois Cohomology" |
Abstract: One can show that, in certain cases, a p-adic Galois representation is modular via an ``$R= \mathbb T$ argument; this is the basis of ideas outlined by Andrew Wiles and Richard Taylor. This talk will give an overview of what this means by discussing Barry Mazur s concept of the Universal Deformation Ring. We will (1) review the connection of deformations of Galois representations with Galois cohomology, (2) present a definition of local conditions of a Galois representation which generalizes the usual definition in weight 2, and (3) give a formula for the dimension of the universal deformation ring in certain cases by working through some explicit computations" |
January 21, 2003, 4:30-5:30 Pm at Science Center, Room 507 |
| MODULAR CURVES SEMINAR |
David Savitt () |
"Strongly divisible lattices and (almost) explicit Galois deformation rings" |
His talk will be about how Breuil s work on integral p-adic Hodge theory (strongly divisible lattices) may be used to compute certain deformation rings of potentially semistable Galois representations, and about some expected consequences for the modularity of such representations" |
January 15, 2003, 3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Chong-Qing Cheng (NANJING UNIVERSITY - VISITING HARVARD UNIVERSITY) |
Variational construction of diffusion orbits in 4-d symplectic maps |
Organized by Shing-Tung Ya" |
December 17, 2002, 1:30Pm at 507 Science Center |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Jake Rasmussen (HARVARD) |
"Floer homology for knot complements" |
" |
December 13, 2002, 3:30 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Robbert Dijkgraaf (UNIVERSITY OF AMSTERDAM) |
Random Matrices and Calabi - Yau Manifolds |
Organized by Shing-Tung Ya" |
December 12, 2002, 1:00Pm at 507 Science Center |
| JOINT MATHEMATICS COLLOQUIUM |
Tom Hales (UNIVERSITY OF PITTSBURGH) |
Characters, motives, and a bit of logic |
" |
December 12, 2002, 4:30 Pm at Science Center, Hall D |
| NUMBER THEORY SEMINAR |
Prof. Mazur (HARVARD) |
"Rational connectivity, rational sections and rational points" |
" |
December 11, 2002, 3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Lawrence Man Hou Ein (UNIVERSITY OF ILLINOIS AT CHICAGO - VISITING HARVARD UNIVERSITY) |
Multiplier ideals and local algebraic geometry |
" |
December 10, 2002, 1:30Pm at Science Center room 507 |
| MODULAR CURVES AND MODULAR FORMS SEMINAR |
Marty Wiessman (HARVARD) |
"Modular forms over Quadratic Imaginary Fields" |
Abstract: In the first half of the talk, I ll discuss classical modular forms over a quadratic imaginary field K and conjectures of Cremona. This will include the conjectural variant of Taniyama-Shimura connecting these modular forms with elliptic curves and abelian varieties. In the second half of the talk, I ll discuss a different sort of modular form over K which seems closely connected to that of Cremona, and which seems more closely tied to arithmetic" |
December 10, 2002, 4:30 Pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
Victor Rotger (UNIVERSITAT POLITECNICA DE CATALUNYA) |
"Shimura Curves Embedded in Igusa's Threefold" |
" |
December 10, 2002, 3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Albert Chau (HARVARD) |
"Stability for the Kahler Ricci flow on non-compact manifolds" |
" |
December 06, 2002, 3:30 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Michael Hopkins (MIT/HARVARD) |
"The Atkin operator in algebraic topology" |
Abstract: Recently the Atkin U operator has shown up as a topologically defined logarithm for topological modular forms. In this talk I plan to describe how this comes about, and its significance in algebraic topology. This talk will be accessible to a general audience" |
December 04, 2002, 3:00 Pm at Science Center, Room 507 |
| MODULAR CURVES SEMINAR |
Toby Gee () |
"Companion Forms" |
" |
December 03, 2002, 4:30 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Dennis Gaitsgory (UNIVERSITY OF CHICAGO) |
"The geometric Langlands program" |
" |
December 02, 2002, 3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Hubert Bray (MASSACHUSETTS INSTITUTE OF TECHNOLOGY) |
To be announced soon. |
" |
November 26, 2002, 1:30Pm at Science Center room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
Tomohide Terasoma () |
"Algebracicity of Cyclotomic Weil Hodge Cycles" |
" |
November 26, 2002, 3:00 Pm at Science Center, Room 507 |
| MODULAR CURVES SEMINAR |
Graham Herrick () |
A Conjectural Formula for Slopes of Classical Eigenforms |
" |
November 26, 2002, 4:30-5:30 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Sijue Wu (UNIVERISTY OF MARYLAND/HARVARD) |
On the motion of the interface between two fluids |
" |
November 25, 2002, 3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Danny Ruberman (BRANDEIS) |
'Casson's invariant in dimensions 3 and 4'. |
" |
November 22, 2002, 3:30 Pm at Science Center, Room 309 |
| COLLOQUIUM |
Dan Boneh (STANFORD UNIVERSITY) |
New Tools in Cryptography From Algebraic Geometry |
" |
November 21, 2002, 4:30 Pm at Science Center, Hall D |
| NUMBER THEOORY SEMINAR |
Frank Calegari (HARVARD) |
"The Hecke Algebra has Large Index" |
Abstract: Let $\rho$ be a mod $p$ modular Galois representation. What does the set of (modular) crystalline representations look like inside the space of all deformations of $\rho$? Recent conjectures of Mazur and Buzzard suggest some surprising answers. I shall discuss these conjectures, as well as a conjecture of Coleman and a deceptively simple looking conjecture of Serre. I will try and provide evidence for some of these conjectures, and show how this evidence can be used to extend a theorem of Jochnowitz, answering a question of Serre. This is joint work with Matthew Emerton" |
November 20, 2002, 3:00 Pm at Science Center, Room 507 |
| MODULAR CURVES SEMINAR |
Peter Clark (HARVARD) |
Tate-Tate-Tate Stuff: A Survey of the Period-Index Problem |
" |
November 19, 2002, 4:30-5:30 Pm at Science Center, Room 507 |
| DIIFFERENTIAL GEOMETRY SEMINAR |
Nikolai Nadirashvili (THE UNIVERSITY OF CHICAGO) |
The local embedding problem for surfaces |
Organized by Shing-Tung Ya" |
November 19, 2002, 3:00Pm at 507 Science Center |
| DIFFERENTIAL GEOMETRY SEMINAR |
Alberto Bressan (SISSA) |
Some open problems in the theory of conservation laws. |
Organized by Shing-Tung Ya" |
November 19, 2002, 1:30Pm at Science Center room 507 |
| BASIC NOTIONS SEMINAR |
Shing-Tung Yau (HARVARD UNIVERSITY) |
The Spectrum of a Riemann Surface |
" |
November 18, 2002, 3-4 Pm at Science Center 507 |
| SPECIAL GAUGE THEORY AND TOPOLOGY SEMINAR |
Ib Madsen () |
'The cohomology of the stable mapping class group:Mumford's conjecture'. |
" |
November 15, 2002, 1:00-2:00 Pm at Science Center, Room 110 |
| NUMBER THEORY SEMINAR |
Mihran Papikian (UNIVERSITY OF MICHIGAN) |
"Optimal elliptic curves and their j-invariants." |
Abstract: We study the non-separable degrees of the j-invariants of one dimensional quotients of Drinfeld Jacobians with connected kernel, and give an asymptotic bound on the non-separable degree in terms of the size of the conductor. In some situations we are able to prove that it equals 1. The main technical tool used is Grothendieck s monodromy pairing and its rigid analytic realization. Using the same techniques we also prove the analogue of the degree conjecture over function fields" |
November 13, 2002, 3:00 Pm at Scinece Center, Room 507 |
| MODULAR CURVES SEMINAR |
Juping Wang () |
'Singular Automorphic Forms" |
" |
November 12, 2002, 4:30 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Jiun-Cheng Chen (HARVARD UNIVERSITY) |
Moduli Space, Derived Categories And The Minimal Model Program |
" |
November 12, 2002, 1:30Pm at Hu - Science Center room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
Christopher Hacon (UNIVERSITY OF UTAH) |
"Characterization of Abelian Varieties" |
" |
November 12, 2002, 3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Stavros Garoufalidis (GEORGIA TECH) |
M-theory and 3-dimensional topology |
" |
November 08, 2002, 3:30 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Richard Hain (DUKE/HARVARD) |
"Galois actions on fundamental groups of curves and the cycle C-C-" |
" |
November 06, 2002, 3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Eliot Brenner (YALE UNIVERSITY) |
Complex Affine Crystallographic Groups: results towards a classification in low dimensions. |
" |
November 05, 2002, 1:30Pm at Science Center room 507 |
| BASIC NOTIONS SEMINAR |
Benedikt Gross (HARVARD) |
Class fields and Drinfeld modules |
" |
November 04, 2002, 3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Conan Leung (UNIVERSITY OF MINNESOTA) |
G2 Geometry [Riemannian Geometry over normed algebras] |
" |
November 01, 2002, 3:30 Pm at Science Center, Room 309 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
Johan DeJong (MIT) |
"Cubic Fourfolds and Spaces of Rational Curves" |
" |
October 29, 2002, 3:00 Pm at Science Center, Room 507 |
| MODULAR CURVES SEMINAR |
William Stein (HARVARD) |
"Observations About the Arithmetic of Quotients of J1(p)" |
" |
October 29, 2002, 4:30 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Richard Hain (DUKE UNIVERSITY - VISITING HARVARD UNIVERSITY) |
Cohomology of moduli spaces of curves and abelian varieties in low genus |
In this talk I will discuss the problem of computing the cohomology of moduli spaces of curves of principally polarized abelian varieties in low genus. This will include a survey of what is known, useful techniques (algebraic and analytic geometry, topology, group cohomology, stratified Morse theory) and current obstacles" |
October 29, 2002, 1:30Pm at Hu - Science Center room 507 |
| BASIC NOTIONS SEMINAR |
Noam D. Elkies (HARVARD) |
Np, P, and primality: Prologue to "Primes is in P" |
" |
October 28, 2002, 3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Stas Smirnov (KTH, STOCKHOLM) |
"Critical lattice models and conformal invariance". |
" |
October 25, 2002, 3:30 Pm at Science Center, Room 309 |
| JOINT MATHEMATICS COLLOQUIUM |
Richard Schwartz (UNIVERSITY OF MARYLAND) |
Complex hyperbolic geometry, triangle groups, and spherical Cr structures on hyperbolic manifolds |
Tea at 4:00 pm in the Math Loung" |
October 24, 2002, 4:30 Pm at Science Center, Hall D |
| NUMBER THEORY SEMINAR |
Kevin Buzzard (HARVARD/IMPERIAL COLLEGE) |
"Eigencurves for definite quaternion algebras" |
" |
October 23, 2002, 3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Horng-Tzer Yau (COURANT INSTITUTE OF MATHEMATICAL SCIENCES) |
"Quantum dynamics of many-body systems and nonlinear Schrodigner" |
" |
October 22, 2002, 1:30Pm at Science Center, Room 507 |
| MODULAR CURVES SEMINAR |
Kevin Buzzard (HARVARD) |
"Computing Weight One Modular Forms" |
" |
October 22, 2002, 4:30 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Joseph Harris (HARVARD UNIVERSITY) |
Are Cubics Rational? |
" |
October 21, 2002, 3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Michael Hutchings (BERKELEY) |
"Rounding corners of polygons and the embedded contact homology of T^3" |
" |
October 18, 2002, 3:30 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Pierre Colmez (INSTITUT DE MATHEMATIQUES DE JUSSIEU) |
"On families of p-adic galois representions" |
" |
October 16, 2002, 3:00 Pm at Science Center, Room 507 |
| ALGEBRAIC GEOMETRY SEMINAR |
Richard Hain (HARVARD/DUKE) |
The cycle C-C-, positivity of normal functions, and Moriwaki's inequality |
" |
October 15, 2002, 3:00-4:00 Pm at Science Center, Room 507 |
| MODULAR CURVES SEMINAR |
Frank Calegari (HARVARD) |
"Hodge-Tate Stuff" |
" |
October 15, 2002, 4:30-5:30 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Dylan Thurston (HARVARD) |
"How efficiently do 3-manifolds bound 4-manifolds?" |
" |
October 11, 2002, 3:30 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Ben Howard (HARVARD) |
"Iwasawa theory of Heegner points" |
Abstract: Let E be an elliptic curve over Q, let K be an imaginary quadratic field satisfying the Heegner hypothesis that all primes dividing the conductor of E are split, and let Kinf be the anticyclotomic Zp extension of K. We discuss results in the direction of Perrin-Riou s Iwasawa Main Conjecture, which relates the Selmer group of E over Kinf to Heegner points. Making use of the recent work of Zhang, we also discuss generalizations in which the Heegner hypothesis is weakened, and in which K is replaced by a Cm field and E is replaced by an abelian variety of Gl2 type defined over the maximal real subfiel" |
October 09, 2002, 3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Yann Rollin (MIT) |
"Seiberg-Witten equations and Einstein rigidity of the complex hyperbolic plane." |
" |
October 04, 2002, 3:30-5:00 Pm at Science Center, Room 309 |
| NUMBER THEEORY SEMINAR |
Alexander Braverman (HARVARD) |
"Geometric Langlands correspondence for $\calD$-modules in prime characteristic" |
" |
October 02, 2002, 3:00 Pm at Science Center, Room 507 |
| MODULAR CURVES SEMINAR |
Bill McGraw (MADISON) |
"Modular Form Congruences and Selmer Groups " |
Abstract: A famous question of Hida asks whether or not congruences between integral weight modular forms descend, via the Shimura correspondence, to congruences between half integral weight forms. For example, Serre shows that the every modular form in M2(p) is congruent to a form in Mp+1(1). We prove a general result which describes the corresponding picture in the half-integral weight case. We then discuss implications for the congruences between the algebraic parts of special values of $L$-functions as well as the `visibility of elements in Selmer groups" |
October 01, 2002, 4:30-5:30 Pm at Science Center, Room 507 |
| ALGEBRAIC GEOMETRY SEMINAR |
Joao Santos (MIT) |
"Blowups of surfaces and moduli of framed vector bundles" |
" |
October 01, 2002, 3:00 Pm at Science Center, Room 507 |
| SPECIAL NUMBER THEORY SEMINAR |
Richard Borcherds (UNIVERSITY OF CALIFORNIA, BERKELEY) |
"The Gross-Kohnen-Zagier Theorem". |
" |
September 27, 2002, 2:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Raoul Bott (HARVARD) |
"Musings" |
" |
September 27, 2002, 3:30-4:30 Pm at Science Center, Room 309 |
| JOINT MATHEMATICS COLLOQUIUM |
Richard Borcherds (UNIVERSITY OF CALIFORNIA, BERKELEY) |
"Renormalization" |
Tea is from 4:00 to 4:3" |
September 26, 2002, 4:30-5:30 Pm at Science Center, Hall D |
| MODULAR CURVES AND MODULAR FORMS SEMINAR |
William Stein (HARVARD) |
"Discriminants of Hecke Algebras" |
" |
September 24, 2002, 4:30-5:30 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Mark Dickinson (UNIVERSITY OF MICHIGAN AT ANN ARBOR) |
"Non-Gorenstein Hecke algebras and the Taylor-Wiles method" |
" |
September 18, 2002, 3:00 Pm at Science Center, Room 507 |
| ALGEBRAIC GEOMETRY SEMINAR |
Mircea Mustata (CLAY MATHEMATICS INSTITUTE AND HARVARD) |
"Log discrepancies, jet schemes and inversion of adjunction" |
" |
September 17, 2002, 3:00 Pm at Science Center, Room 507 |
| THE MODULAR CURVES SEMINAR |
Brian Conrad () |
"J1(p) has connected fibers" |
" |
September 17, 2002, 4:30-5:30 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Ding Xiaqi (ACADEMIA SINICA) |
"Weak Functions and Related Problems" |
" |
May 31, 2002, 1:30 Pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
Barry Mazur (HARVARD) |
"Informal Lecture on the Anticyclotomic Arithmetic of Elliptic Curves" |
" |
May 21, 2002, 2:00-3:00 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Matthew Emerton (NORTHWESTERN UNIVERSITY) |
"p-adic automorphic representations" |
" |
May 15, 2002, 3:00-4:00 Pm at Science Center, Room 507 |
| MODULAR CURVES SEMINAR |
Romyar Sharifi (HARVARD UNIVERSITY) |
"Periods of cusp forms and the Galois Lie algebra" |
Abstract: I will define the stable derivation algebra and explain its relation with the Galois Lie algebra of the projective line minus three points, and I will discuss the depth filtration on these Lie algebras. I will then give a simple combinatorial proof of the relationship between periods of cusp forms on Sl2(Z) and relations in the stable derivation algebra modulo depth three. This gives a very elementary approach to a portion of the story Goncharov explained in fundamental gps. seminars of previous weeks. I may also discuss relations with the pairing studied by McCallum and I" |
May 13, 2002, 2:00 Pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
Martin Nowak (IAS) |
"From qvasispecies to universal grammar" |
" |
May 09, 2002, 11:00-12:00 Am at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Noam Elkies (HARVARD) |
"Points of low canonical height on elliptic curves and surfaces" |
" |
May 08, 2002, 3:00-4:00 Pm at Science Center, Room 507 |
| MODULAR CURVES SEMINAR |
Erez Lapid (OHIO STATE) |
'L-functions and root numbers at the center of symmetry ' |
Abstract: It is unknown whether L(1/2,chi) >= 0 for quadratic Dirichlet characters. (It is an immediate consequence of Grh.) Using Eisenstein series we show that L(1/2,pi) >= 0 for self-dual cuspidal representations of Gl(n) of symplectic type. This is joint work with Steve Rallis. The same technique is also used to show that, under some technical assumptions, the root number of orthogonal representations is 1 (an automorphic analogue of a result of Frohlich-Queryut)" |
May 06, 2002, 2:00 Pm at Science Center, Room 507 |
| JDG 2002 PRESENTS FIFTH CONFERENCE ON GEOMETRY AND TOPOLOGY |
M.Atiyah, R.Bryant, L.Caffarelli, J.Cheeger, P.Daskalopoulos, X.de la Ossa, J.P.Demailly, G.Huisken, J.Li, G.Margulis, W.Meeks, A.Nahmod, Ch.Taylor, C.L.Terng, E.Viehweg, L.S.Young (SPEAKERS FROM VARIOUS INSTITUTIONS) |
Details can be found on the conference webpage. |
For details check the conference web page." |
May 03-05, 2002, Friday 1:00pm-5:30pm Saturday 9:00am-5:30pm Sunday 9:00am-4:15pm at Science Center, Lecture Hall C |
| SEVERAL COMPLEX VARIABLES |
Y-T Siu (HARVARD) |
Series of lectures by Yum-Tong Siu |
" |
May 02, 2002, 2:15Pm at Science Center, Room 507 |
| INFORMAL ALGEBRAIC GEOMETRY SEMINAR |
Eduardo Esteves () |
Limit linear series and Weierstrass points (conclusion) |
" |
May 02, 2002, 3:30 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Elena Mantovan (HARVARD) |
"On certain unitary Shimura varieties." |
" |
May 01, 2002, 3:00-4:00 Pm at Science Center, Room 507 |
| EXTRA NUMBER THEORY SEMINAR |
Vinayak Vatsal () |
"Heegner Points" |
" |
May 01, 2002, 2:00-3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Kawamata Yujiro (UNIVERSITY OF TOKYO) |
Minimal Models and Derived Categories |
" |
April 30, 2002, 1:30 P.M. at Science center, Room 507 |
| BASIC NOTIONS SEMINAR |
Fernando Rodriguez Villegas (UNIVERSITY OF TEXAS/HARVARD) |
"Apery's proof of the irrationality of zeta(3)" |
" |
April 29, 2002, 3:00-4:00 Pm at Science Center, Room 507 |
| SEVERAL COMPLEX VARIBLES SEMINAR |
Irwin Kra (SUNY AT STONY BROOK) |
'Constructions of abelian differentials of the third kind on some symmetric Riemann surfaces (Some pretty examples in search of a theory)' |
" |
April 26, 2002, 2:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Eun Soo Lee (MIT) |
'The support of the Khovanov's invariants for alternating links.' |
" |
April 26, 2002, 3:30 Pm at Science Center, Room 309 |
| SEVERAL COMPLEX VARIBLES SEMINAR |
Yum-Tong Siu (HARVARD) |
Series of lectures by Y-T Siu |
" |
April 25, 2002, 3:30 Pm at Science Center, Room 507 |
| COLLOQUIUM |
Kenneth Ribet (UNIVERSITY OF CALIFORNIA, BERKELEY) |
"The geometry of a Langlands correspondence" |
Abstract: Twenty years ago, Kahzdan and Mazur suggested the possibility of a geometric interpretation of a relationship among Hecke operators that Eichler and Shimizu had proved using the Selberg trace formula. In this question, there are two distinguished prime numbers and two algebraic curves. A surprise is that the reduction of one curve modulo the first prime is related to the reduction of the other curve modulo the second prime. This unexpected twist, which surfaced in a positive way as a tool in level-lowering for Galois representations, seems to convey the unwelcome news that there is no simple relation between the Jacobians of the two curves. Nonetheless, a recent construction of David Helm of Berkeley shows how one might construct an abelian variety isomorphic to one Jacobian in terms of the arithmetic of the other" |
April 25, 2002, 4:30-5:30 Pm at Science Center, Halol D |
| THE GALOIS AND FUNDAMENTAL GROUPS SEMINAR |
A.B. Goncharov (BROWN UNIVERSITY) |
The multiple zeta motives and geometry of modular varieties Ii |
" |
April 24, 2002, 2:00 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Fred Diamond (BRANDEIS UNIVERSITY) |
"Nuclear families of Hilbert modular forms" |
" |
April 24, 2002, 3:00 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Vladimir Berkovich (WEIZMANN INSTITUTE) |
"p-adic analytic and piecewise linear spaces'' |
" |
April 24, 2002, 4:30-5:30 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Emma Carberry (MIT) |
On the Existence of Minimal Tori in S^3 of Arbitrary Spectral Genus |
" |
April 23, 2002, 1:30 Pm at Science Center, room 507 |
| BASIC NOTIONS SEMINAR |
Shing-Tung Yau (HARVARD) |
Construction of Some Symplectic Manifolds |
" |
April 22, 2002, 3:00-4:00 Pm at Science Center, Room 507 |
| SEVERAL COMPLEX VARIABLES SEMINAR |
Yum-Tong Siu (HARVARD) |
Series of Lectures by Yum-Tong Siu (Continuation) |
Yum-Tong Siu will give a series of lectures on the solutions of the following two conjectures: 1. The plurigenera of a compact projective algebraic manifold (not necessarily of general type) are invariant under holomorphic deformation. The proof uses transcendental methods which up to this point still cannot be translated into a purely algebro-geometric proof. Moreover, the conjecture of the deformational invariance of the plurigenera for compact Kaehler manifolds is still open. Techniques toward the solution of the conjecture for the Kaehler case will be presented. 2. A generic hypersurface of sufficiently high degree in the complex projective space is hyperbolic, in the sense that there is no nonconstant holomorphic map from the Euclidean complex line into it" |
April 18, 2002, 2:15 Pm at Science Center, Room 507 |
| GALOIS AND FUNDAMENTAL GROUPS SEMINAR |
A.B. Goncharov (BROWN UNIVERSITY) |
The multiple zeta motives and geometry of modular varieties |
" |
April 17, 2002, 2:00-3:00 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
John Coates (CAMBRIDGE UNIVERSITY) |
"Iwasawa algebras and arithmetic". |
" |
April 17, 2002, 3:00 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Vinayak Vatsal (UNIVERSITY OF BRITISH COLUMBIA) |
Unramified covers of X0(N) |
" |
April 17, 2002, 4:30 p.m. at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Steven Rosenberg (BOSTON UNIVERSITY) |
Ricci and Scalar Curvature in Infinite Dimensions |
" |
April 16, 2002, 1:30 P.M. at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Michael Thaddeus (COLUMBIA UNIVERSITY) |
"Stable Maps to a Loop Group" |
" |
April 16, 2002, 3:30 - 5:00 Pm at Science Center, Room 309 |
| MODULAR FORMS AND MODULAR FORMS SEMINAR |
Peter Green (HARVARD) |
"Local Langlands mod p" |
" |
April 15, 2002, 2:00-3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Gang Tian (MIT) |
"Genus 2 Lefschetz fibrations". |
" |
April 12, 2002, 3:30 Pm at Science Center, Room 309 |
| INFORMAL ALGEBRAIC GEOMETRY SEMINAR |
Eduardo Esteves () |
Limit linear series and Weierstrass points |
" |
April 11, 2002, 3:30 Pm at Science Center, Room 507 |
| JOINT MATHEMATICS COLLOQUIUM |
Gopal Prasad (UNIVERSITY OF MICHIGAN) |
Towards classification of admissible representations of reductive p-adic groups via their restriction to compact-open subgroups |
" |
April 11, 2002, 4:30-5:30 Pm at Science Center, Hall D |
| NUMBER THEORY SEMINAR |
Solomon Friedberg (BOSTON COLLEGE) |
Double Dirichlet Series and the Nonvanishing of Quadratic Twists of the Adjoint Square L-Function |
" |
April 10, 2002, 3:00 p.m. at Science Center 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Daniel Pollack (UNIVERSITY OF WASHINGTON/MIT) |
New Solutions of the Einstein Constraint Equations in General Relativity |
" |
April 09, 2002, 1:30 Pm at Science Center, Room 507 |
| MODULAR CURVES AND MODULAR FORMS SEMINAR |
Mak Trifkovic (HARVARD) |
"Nuts and Bolts" |
" |
April 08, 2002, 2:00-3:00 Pm at Science Center, Room 507 |
| SEVERAL COMPLEX VARIABLES SEMINAR |
Mihai Paun (UNIVERSITY OF SRASBOURG) |
"Characterization of the Kahler cone" |
" |
April 05, 2002, 2:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Vu The Khoi (BRANDEIS) |
"Cut-and-paste method for computing the Seifert volume" |
" |
April 05, 2002, 3:30 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Tetsushi Ito (UNIVERSITY OF TOKYO) |
"Weight-monodromy conjecture for certain threefolds in mixed characteristic" |
The weight-monodromy conjecture claims the coincidence of the shifted weight filtration and the monodromy filtration on etale cohomology of a proper smooth variety over a local field. Although it is proved in some cases, the case of dimension > 2 in mixed characteristic has been an important open problem in arithmetic geometry. In this talk, I will give a proof of the weight-monodromy conjecture for certain threefolds by using the weight spectral sequenceof Rapoport-Zink and the Hodge index theorem. I will also indicate some possible applications to Shimura varieties and the Langlands correspondences" |
April 03, 2002, 3:00-4:00 Pm at Science Center, Room 507 |
| GALOIS AND FUNDAMENTAL GROUPS SEMINAR |
Alexander Goncharov (BROWN UNIVERSITY) |
"Multiple zeta-motives and configuration spaces M{0,n}" |
" |
April 03, 2002, 2:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Philip Candelas (OXFORD UNIVERSITY) |
"Arithmetic of Calabi-Yau Manifolds" |
" |
April 02, 2002, 1:30 P.M. at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Matt Baker (HARVARD) |
"Linear recurrence sequences, p-adic analysis, and Diophantine equations" |
" |
April 01, 2002, 3:00-4:00 Pm at Science Center, Room 507 |
| MODULAR CURVES AND MODULAR FORMS SEMINAR |
Pete Clark (HARVARD) |
"p-adic uniformization of Shimura curves" |
" |
April 01, 2002, 2:00-3:00 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Frans Oort (UTRECHT UNIVERSITY AND MIT) |
"Families of p-divisible groups" |
" |
March 20, 2002, 3:00 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
William Stein (HARVARD) |
"Charting the Land of Elliptic Curves" |
Abstract: I will discuss some reasons why elliptic curves over the rational numbers are so interesting, then discuss Swinnerton-Dyer s early tables of elliptic curves from Antwerp Iv and Cremona s systematic extension of those tables. In a different direction, I ll talk about Brumer and McGuinness s table of curves of prime conductor, and about a recent push by the author and Mark Watkins to extend that table to composite conductor. Finally, I ll talk about extending Swinnerton-Dyer s tables to abelian varieties (higher dimensional analogues of elliptic curves)" |
March 20, 2002, 2:00-3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Shing-Tung Yau (HARVARD) |
"Mass Gap for Schrodinger Operator" |
" |
March 19, 2002, 1:30 Pm at Science Center, Room 507 |
| MODULAR CURVES AND MODULAR FORMS SEMINAR |
Teruyoshi Yoshida (TOKYO) |
"Class field theory for curves over local fields and X0(p) over Qp" |
Abstract : There is a class field theory of higher dimensional arithmetic schemes (or varieties over local/global fields) developed by Bloch/Parshin/Kato/S.Saito and others. I will briefly introduce these theories and some of my results concerning varieties over local fields. As a particular application, I compute the abelian fundamental group classifying (geometrically connected) abelian étale coverings of X0(p)/Qp, which are related to the global result of Mazur in the Eisenstein ideal paper" |
March 18, 2002, 2:00-3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Yi-Jen Lee (PRINCETON) |
"Reidemeister torsion in symplectic Floer theory and counting pseudo-holomorphic tori". |
" |
March 15, 2002, 3:30 Pm at Science Center, Room 309 |
| JOINT MATHEMATICS COLLOQUIUM |
Bill Meeks (UMASS, AMHERST) |
"The classical theory of minimal surfaces: a study of the classical examples and their uniqueness." |
" |
March 14, 2002, 4:30-5:30 Pm at Science Center, Hall D |
| INFORMAL ALGEBRAIC GEOMETRY SEMINAR |
Joseph Harris (HARVARD) |
"Introduction to rationally connected varieties" |
Notes: After a two-week hiatus, the informal algebraic geometry seminar will resume with a series of talks on rationally connected varieties. We ll start by reviewing basic properties of these varieties, then give proofs of the recent theorem on existence of sections in one-parameter families of rationally connected varieties and its converse. We will return to the topic of multiplier ideals later in the semester" |
March 14, 2002, 3:30-4:30 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Gabriele Nebe (UNIVERSITAT ULM) |
"Clifford groups and Barnes Wall lattices" |
" |
March 13, 2002, 3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Jonathan Weitsman (HARVARD) |
Morse Theory and the Topology of Hamiltonian Loop Group Spaces |
" |
March 12, 2002, 1:30 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Gabrielle Nebe (ULM UNIVERSITY) |
"Lattices and spherical designs" |
" |
March 11, 2002, 3:00-4:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Paul Seidel (IAS) |
"Floer cohomology in dimensions n and n+1." |
" |
March 08, 2002, 3:30 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Matt Papanikolas (BROWN UNIVERSITY) |
"Algebraic independence over function fields" |
Abstract: We will discuss recent progress in the transcendence theory of periods of Drinfeld modules. In particular, we will focus on modules with complex multiplication and applications to special values of the function field Gamma function. Joint work with Greg Anderson and Dale Brownawell" |
March 06, 2002, 3:00-4:00 Pm at Science Center, Room 507 |
| GALOIS AND FUNDAMENTAL GROUPS SEMINAR |
Romyar Sharifi (HARVARD) |
Generators of a Lie algebra associated to the projective line minus three points |
I will define and exhibit nontriviality of the Soule elements in the pro-l Lie algebra associated to the action of Galois on the projective line minus three points. These elements generate this Lie algebra over the l-adic numbers. I shall sketch the proof of this fact that was given by Hain and Matsumoto" |
March 06, 2002, 2:00-3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Mu-Tao Wang (COLUMBIA UNIVERSITY) |
"Mean Curvature Flow in Higher Codimension" |
" |
March 05, 2002, 1:30 Pm at Science Center, Room 507 |
| MODULAR CURVES AND MODULAR FORMS SEMINAR |
Chris Mihelich () |
"The Order at 2 of the Odd Partition Function" |
" |
March 04, 2002, 2:00-3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Is Singer (MIT) |
"Chiral anomalies and determinant line bundles" |
" |
March 01, 2002, 3:30 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Loic Merel (UNIVERSITY OF PARIS 7) |
"For a fistful of L-values." |
" |
February 27, 2002, 3:00-4:00 Pm at Science Center, Room 507 |
| GALOIS AND FUNDAMENTAL GROUPS SEMINAR |
Romyar Sharifi (HARVARD) |
"Lie algebras associated to Galois actions" |
I will consider the representation of the absolute Galois group of a number field in the outer automorphism group of a pro-l fundamental group of a curve and will describe the weight filtration on the corresponding pro-l mapping class group through which one can associate a Lie algebra over the l-adic integers. I will focus on two cases: an elliptic curve with one point removed and the projective line minus three points, especially the latter. I will discuss results on the nontriviality of elements in these Lie algebras" |
February 27, 2002, 2:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Shinobu Hosono (TOKYO UNIVERSITY) |
"Fourier-Mukai Partners and Mirror Symmetry of K3 Surfaces" |
" |
February 26, 2002, 1:30 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Noam Elkies (HARVARD) |
"The 27 lines on a cubic surface" |
" |
February 25, 2002, 3:00 Pm at Science Center, Room 507 |
| THE MODULAR CURVES LUNCH/SEMINAR |
Marty Weissman (HARVARD UNIVERSITY) |
Fourier Coefficients for Gl(3) Automorphic Forms |
" |
February 25, 2002, 2:00-3:00 at Sci 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Sue Tolman (MIT AND UNIVERSITY OF ILLINOIS) |
"Topological properties of Hamiltonian torus actions" |
" |
February 22, 2002, 3:30 Pm at Science Center, Room 309 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Stephen S.T. Yau (UNIVERSITY OF ILLINOIS AT CHICAGO) |
"Complex Plateau Problem in C^3" |
" |
February 22, 2002, 4:30 Pm at Science Center, Room 507 |
| JOINT MATHEMATICS COLLOQUIUM |
Loic Merel (UNIVERSITY OF PARIS 7) |
"Class number formulas" |
Tea at 4:00 Pm in the Math Lounge, 4 floor. Abstract: There is a longstanding interest among number theorists for values at th integers of the Riemann zeta function (and its generalizations called L-functions). The first important discoveries are possibly Euler s formulas (\zeta(2)=\pi^2/6, etc) and Dirichlet s class number formula. Since then many L-functions attached to various arithmetic-geometric objects (representations of Galois groups, Dirichlet characters, elliptic curves, modular forms,etc.) have been identified. I ll partially explain how the concept has been unified. Bloch and Kato, after the work of many other people, proposed a formula predicting the values at integers of L-functions that extends many conjectures proposed before (by Artin, Beilinson, Birch, Deligne, Stark, Swinnerton-Dyer, etc.). Their prediction has been confirmed in a few of the most primitive cases. I will not fully discuss the conjecture; instead, based on examples, I will explain a sense in which the formula of Bloch and Kato is not yet satisfactory. I will also suggest a way that leads slightly beyond the conjecture of Bloch and Kato" |
February 21, 2002, 4:30-5:30 Pm at Science Center, Hall D |
| INFORMAL ALGEBRAIC GEOMETRY SEMINAR |
Mihnea Popa (HARVARD) |
"Multiplier Ideals and Applications" |
" |
February 21, 2002, 3:30-4:30 Pm at Science Center, Room 507 |
| THE NUMBER THEORY SEMINAR |
Matt Baker (HARVARD) |
"Canonical heights over abelian extensions" |
Abstract:Let A be an abelian variety defined over a number field K, and let Kab denote the maximal abelian extension of K. We conjecture that there exists a constant C>0 (depending on A and K) such that if $P \in A(K^{ab})$ is non-torsion, then the canonical height of P is at least C. We will sketch a proof of this conjecture when A is an elliptic curve satisfying some additional hypotheses. We will also discuss some possible generalizations of the conjecture" |
February 20, 2002, 3:00-4:00 Pm at Science Center, Room 507 |
| GALOIS AND FUNDAMENTAL GROUPS SEMINAR |
Pete Clark (HARVARD) |
"More Geometric Galois Theory" |
" |
February 20, 2002, 2:00-3:00 Pm at Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
Gavril Farkas (UNIVERSITY OF MICHIGAN) |
"Stable bundles, difference varieties, and divisors on moduli spaces of pointed curves" |
Abstract:We do global calculations on moduli spaces of pointed curves to compute the graded Betti numbers of general sets of points on any nonhyperelliptic canonically embedded curve C. It turns out that these results have surprising connections with moduli spaces of stable vector bundles on curves and geometric divisors on moduli spaces of pointed curves. Among other things we prove that for any canonically embedded curve C, all exterior powers of the universal quotient on C have a theta divisor which is identified with a difference variety in the Jacobian of C. These vector bundles are of great interest since Green s Conjecture on syzygies of canonical curves boils down to computing the dimensions of their spaces of sections. This is joint work with M. Mustata and M. Popa" |
February 19, 2002, 3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
William Benter (QUANTRIX) |
Development of a Mathematical Model for Successful Horse Race Wagering |
Abstract: The talk will describe the elements necessary for the development of a state-of-the-art computerized horse race wagering system. An explanation will be given of the pari-mutuel wagering system along with an overview of the predicament faced by the would-be successful horse race gambler. The estimation of logit and probit models for deriving horse win probability estimates from fundamental data will be discussed, followed by a description of the application of optimal betting formulae to horse race wagering. The speaker will share his insights gained from over a decade of practical implementation of such a system, and report on the results that have been achieved" |
February 19, 2002, 4:30 Pm at Science Center, Lecture Hall A |
| DIFFERENTIAL GEOMETRY SEMINAR |
Dan Stroock (MIT) |
A Mathematician's Version of the Original Paper of Black and Scholes |
Abstract: There is a disturbing gap in Black and Scholes s paper which introduced their financial model for pricing options. In most textbooks on the subject, the author either circumvents this gap by using a different model to arrive at the same conclusion as Black and Scholes or the author follows Black and Scholes and ignores the gap. Recently, Ioanid Rosu and I figured out a way to patch the original Black and Scholes argument. Our patch requires an elementary but intriguing piece of analysis" |
February 19, 2002, 1:30 Pm at Science Center, Room 507 |
| MODULAR CURVES AND MODUAR FORMS SEMINAR |
Ken Ono () |
"Weierstrass points on X0(p) and modular forms" |
Abstract. As usual, let j(z) denote the usual modular invariant. Here we study the values j(Q) mod p for Weierstrass points Q on X0(p). The main result, which follows from elementary considerations regarding modular forms modulo p, is a congruence between these values and supersingular j-invariants" |
February 18, 2002, 2:00-3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Danny Calegari (HARVARD) |
"Bounded cochains on 3-manifolds" |
" |
February 15, 2002, 3:30 Pm at Science Center, Room 309 |
| INFORMAL ALGEBRAIC GEOMETRY SEMINAR |
Mihnea Popa (HARVARD) |
"Multiplier Ideals and Applications" |
" |
February 14, 2002, 3:30-4:30 Pm at Science Center, Room 507 |
| GALOIS ACTIONS ON FUNDAMENTAL GROUPS |
Romyar Sharifi (HARVARD) |
Galois actions on pro-l fundamental groups |
I will construct the Lie algebras associated to the outer action of Galois on the pro-l fundamental groups of curves and discuss some of their basic properties" |
February 13, 2002, 2:00-3:00 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Mak Trifkovic (HARVARD) |
"\mu-Invariants of Elliptic Curves over Q" |
" |
February 13, 2002, 3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Xiao Wei Wang (HARVARD) |
"Balanced Point, Bergmann Kernel and Stability of Vector Bundle" |
" |
February 12, 2002, 1:30 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Fernando Rodriguez Villegas (UNIVERSITY OF TEXAS) |
12 Lattice polygons, a modular form, and a puzzle. |
" |
February 11, 2002, 3:00-4:00 Pm at Science Center, Room 507 |
| INFORMAL ALGEBRAIC GEOMETRY SEMINAR |
Mihnea Popa (HARVARD) |
"Multiplier Ideals" |
The informal algebraic geometry seminar will meet on Thursdays. Talks may span several weeks; the goal is to provide a setting where speakers and listeners are given the time to develop ideas and to absorb them" |
February 07, 2002, 3:30-4:30 Pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
Romyar Sharifi (HARVARD) |
'Galois actions on fundamental groups' |
I will discuss results which relate to the action of Galois on algebraic fundamental groups of curves, especially the projective line minus three points. In particular, I will consider the structure of a Lie algebra arising from a filtration of the absolute Galois group induced by the lower central series of the pro-l fundamental group. (This talk is meant to be an introduction to and partial overview of topics likely to be discussed in the Galois and Fundamental Groups seminar in future weeks." |
February 06, 2002, 3:00 Pm at Science Center, Room 507 |
| ALGEBRAIC GEOMETRY SEMINAR |
Amnon Yekutieli (BEN GURION UNIVERSITY, ISRAEL) |
"Perverse sheaves and dualizing complexes over noncommutative ringed schemes" |
Abstract: In this talk I will discuss an attempt at Grothendieck Duality on noncommutative spaces. Since in the case of affine noncommutative spaces (i.e. rings) Grothendieck Duality is pretty well understood, and on the other hand we don t even know what is a noncommutative space in general, we consider an intermediate case: a noncommutative space Y that s an affine fibration over a commutative scheme X. That s a fancy way to say that Y=(X,A) where A is a sheaf of quasi coherent noncommutative rings on X. We call (X,A) a quasi coherent ringed scheme. As usual in such circumstances, we encounter the problem of gluing. On each affine open set U in X we have a rigid dualizing complex for A|U from the ring construction, and these are compatible on intersections. But how to glue these complexes globally? One should note that Cousin complexes, the solution devised by Grothendieck for gluing dualizing complexes, will not work in the noncommutative world due to well knownobstructions. Instead we choose to use perverse sheaves. This is a gluing methodinvented by Bernstein-Beilinson-Deligne-Gabber in the context of geometry of singular spaces. We discovered that the Auslander condition of dualizing complexes over noncommutative rings (a very algebraic property) is exactly what is needed to define perverse modules over a noncommutative ring. And furthermore using a few nicefeatures of the theory, we can also extend the definition from rings to noncommutative ringed schemes. Finally it turns out that rigid dualizing complexes are themselves perverse sheaves of bimodules (namely on the product X^2), so we can glue the local pieces together.I will explain what are dualizing complexes and what they are good for(concentrating on the noncommutative side). Then I ll discuss perverse sheaves, the Auslander condition and how they interact. I ll finish by sketching our construction. The work is joint with J.J. Zhang (Seattle)" |
February 05, 2002, 3:00-4:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Oliver Schnuerer (HARVARD UNIVRESITY) |
The Second Boundary Value Problem for Flow Equations |
" |
February 05, 2002, 1:30pm at Math Department, Room 507 |
| MODULAR CURVES LUNCH/SEMINAR |
William Stein (HARVARD) |
Visible Evidence for the Birch and Swinnerton-Dyer Conjecture for Rank 0 Modular Abelian Varieties |
" |
February 04, 2002, 2:00-3:00 at Sci 507 |
| BASIC NOTIONS SEMINAR |
Noam Elkies (HARVARD) |
"The ubiquitous discrete subgroups of So(3,R)" |
" |
February 04, 2002, 3:00-4:00 Pm at Science Center, Room 507 |
| GALOIS AND FUNDAMENTAL GROUPS SEMINAR |
Romyar Sharifi (HARVARD) |
Galois actions on Fundamental Groups |
Abstract: I will describe some basic results concerning the (outer) actionbof the absolute Galois group of a number field on the algebraic and pro-p fundamental groups of a curve defined over that number field. My focus will be primarily on the case of the projective line minus the points at 0,1 and infinity" |
January 31, 2002, 2:00-3:00 Pm at Science Center, Room 507 |
| SPECIAL NUMBER THEORY SEMINAR |
Laurent Berger (BRANDEIS) |
'p-adic representations and differential equations' |
I will explain how to associate objects of a differential natureto a p-adic representation. Using recent results of Andre (or Mebkhout or Kedlaya) on the structure of p-adic differential equations, these constructions allow us to give a proof of Fontaine s monodromy conjecture:every de Rham p-adic representation is potentially semi-stable" |
January 23, 2002, 3:00-4:00 Pm at Science Center, Room 507 |
| SPECIAL BASIC NOTIONS SEMINAR |
Tim Gowers (CAMBRIDGE UNIVERSITY) |
"Szemeredi's theorem for arithmetic progressions of length four" |
" |
January 22, 2002, 2:00-3:00 Pm at Science Center, Room 507 |
| JOINT MATHEMATICS COLLOQUIUM |
Steve Gersten (UNIVERSITY OF UTAH) |
'Isoperimetric functions of nilpotent groups' |
There will be a tea at 4:00 Pm in the 4th floor Common Are" |
December 13, 2001, 4:30 Pm at Science Center, Hall D |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Brendan Hassett (RICE) |
"Variation of moduli spaces and the minimal model program" |
" |
December 11, 2001, 3:00 Pm at Science Center, Room 507 |
| MODULAR CURVES AND MODULAR FORMS SEMINAR |
Matt Baker (HARVARD) |
"Something Moderately Cool: Elliptic curves, the Abc conjecture,and points of small canonical height" |
Abstract: We will begin by discussing the connection between the Abc conjecture and Szpiro s conjectural relationship between the conductor and discriminant of an elliptic curve. Then we will discuss a conjecture of Lang which predicts, in particular, that among all elliptic curves E over Q and all rational points P in E(Q), there is a point of smallest nonzero canonical height. After giving some computational examples due to William Stein, we will then discuss a theorem of Hindry and Silverman which implies that Lang s conjecture is implied by Szpiro s (and hence by the Abc) conjecture" |
December 10, 2001, 2:00-3:00 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Fan Chung () |
Guessing Secrets --- from Erdos to Internet Algorithms |
" |
December 10, 2001, 3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Denis Auroux (MIT) |
'Fundamental groups of plane curve complements and symplectic invariants' |
" |
December 07, 2001, 3:30 Pm at Science Center, Room 309 |
| SEMINAR ON EDUCATION IN THE MATHEMATICAL SCIENCES |
Jane Gorman (EDUCATION DEVELOPMENT CENTER, INC) |
Japanese Lesson Study: Polishing the Stone. |
College and School faculty interested in forming lesson study groups are especially encouraged to attend these seminars" |
December 5, 2001, 4:00 Pm at 317 Science Center |
| NUMBER THEORY SEMINAR |
Edray Goins (CALIFORNIA ISTITUTE OF TECHNOLOGY) |
"Icosahedral Q-Curves." |
" |
December 05, 2001, 3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Suhyoung Choi (SEOUL UNIVERSITY) |
Flat Real Projective and Affine Structures on Two and Three Manifolds |
" |
December 04, 2001, 1:30pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
William Stein (HARVARD) |
'Welcome to the Magma Computer Algebra System' |
" |
December 03, 2001, 3:00 Pm at Science Center, Room 507 |
| MODULAR CURVES AND MODULAR FORMS SEMINAR |
Jayce Getz () |
'Partition identities and a theorem of Zagier' |
" |
December 03, 2001, 2:00-3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Aleksey Zinger (MIT) |
"Enumeration of Genus-Two Curves with a Fixed Complex Structure in Low-Dimensional Projective Spaces" |
" |
November 30, 2001, 3:30 Pm at Science Center, Room 309 |
| HARVARD SEMINAR ON EDUCATION IN MATHEMATICAL SCIENCES |
Michael Martin (BOSTON COLLEGE AND TIMSS CO-DIRECTOR) |
Using Timss Mathematics and Science Results to Inform Educational Policty |
College and school faculty interested in forming lesson study groups are especially encouraged to attend these seminars." |
November 28, 2001, 4:00 at 317 Science Center |
| NUMBER THEORY SEMINAR |
Manjul Bhargava (PRINCETON) |
"Higher Composition Laws" |
" |
November 28, 2001, 3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Fan Chung Graham (UC - SAN DIEGO) |
Discrete Green's functions and the hitting times |
" |
November 27, 2001, 1:30pm at Science Center Room 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Curt McMullen (HARVARD) |
"Dynamics on K3 surfaces" |
" |
November 27, 2001, 3:00 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Noam D. Elkies (HARVARD) |
"Differential Galois theory" |
*** Note Special Time And Place **" |
November 26, 2001, 2 Pm at Sever Hall, Room 213 |
| MODULAR CURVES AND MODULAR FORMS SEMINAR |
Cristophe Cornut (HARVARD) |
'Heegner points" |
" |
November 26, 2001, 2:00-3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Mihalis Dafermos (MIT) |
Some Recent Progress on the Strong Cosmic CensorshipConjecture in General Relativity |
" |
November 20, 2001, 1:30 P.M at Science Center Room 507 |
| MODULAR CURVES AND MODULAR FORMS SEMINAR |
Benedict Gross (HARVARD) |
'Heegner points in the context of representation theory' |
" |
November 19, 2001, 2:00-3:00 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Tatiana Toro (UNIVERSITY OF WASHINGTON) |
"Quasisymmetric embeddings of R^n" |
" |
November 19, 2001, 3:00-4:00 Pm at Science Center, Room 507 |
| CURRENT DEVELOPEMENTS IN MATHEMATICS CONFERENCE |
Daniel Freed, Gunar Carlsson, Elliott Lieb, Shou-Wu Zhang, Wing Wong (DIFFERENT INSTITUTIONS) |
See seperate program |
" |
November 16-17, 2001, Friday 2:00pm, Saturday 8:30am at Harvard University, Science Center Lecture Hall "C" |
| JOINT MATHEMATICS COLLOQUIUM |
Richard Kenyon (UNIVERSITE PARIS-SUD) |
'Random maps from Z^2 to Z' |
Tea is from 4:00-4:30Pm in the 4th floor of Common Area. Abstract: We study a particular family of random maps from Z^2 to Z, arising from lozenge tilings of the plane. If we fix a finite domain U in Z^2 and a set of boundary values for the map, what can be said about the typical behavior of the map in the interior of U? For the present model we will show how, for nice boundary values, the scaling limit (limit when the lattice spacing tends to zero) gives a simple conformally invariant random object, the massless free field. We also discuss the conjecture that, for more general boundary values, the limiting object is still the massless free field for a nonstandard conformal structure arising from solving a certain Beltrami equation in U." |
November 15, 2001, 4:30 Pm at Science Center, Hall D |
| SEMINAR ON EDUCATION IN THE MATHEMATICAL SCIENCES |
Daniel Chazan (MICHIGAN STATE UNIVERSITY) |
Identifying Values and Commitments in a time of reform: Video as an Expressive Medium in Mathematics Education. |
College and School faculty interested in forming lesson study groups are especially encouraged to attend these seminars" |
November 14, 2001, 4:00 Pm at 317 Science Center |
| NUMBER THEORY SEMINAR |
Liang-Chung Hsia (NATIONAL CENTRAL UNIVERSITY, TAIWAN) |
"On the reduction of a non-torsion point of a Drinfeld module" |
" |
November 14, 2001, 3:00 Pm at Science center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Leonid Koralov (PRINCETON UNIVERSITY) |
Random Perturbations of 2-dimensional Hamiltonian Flows |
" |
November 13, 2001, 1:30 P.M. at Science Center Room 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Keiji Oguiso (UNIVERSITY OF TOKYO) |
"Automorphism groups in a family of K3 surfaces" |
" |
November 13, 2001, 3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Paul Kirk (UNIVERSITY OF INDIANA) |
'A cut and paste formula for the eta invariant and a non-additivity formula for the signature defect' |
" |
November 09, 2001, 3:30-5:00 Pm at Science Center, Room 309 |
| SEMINAR ON EDUCATION IN THE MATHEMATICAL SCIENCES |
Michal Yerushalmy (HAIFA UNIVERSITY) |
Developing Mathematical Intuition in Teaching and Learning: Video as a Tool for Research and Professional Development |
College and School faculty interested in forming lesson study groups are especially encouraged to attend these seminars" |
November 07, 2001, 4:00 Pm at 317 Science Center |
| NUMBER THEORY SEMINAR |
Frank Calegari (UNIVERSITY OF CALIFORNIA AT BERKELEY) |
'Semistable Abelian Varieties of small conductor' |
Fontaine proved in 1985 that there do not exist any Abelian varieties over Z. Jacobians of the modular curves X0(pn) (non-zero for sufficiently large n) provide examples of Abelian varieties over Z[1/p] for each p. If, however, we restrict our attention to semistable Abelian varieties, then combining Fontaine s theorem, recent papers of Brumer-Kramer and of Schoof, and some new ideas and results, we prove the following: There exists a semistable Abelian variety over Z[1/n] with n squarefree if and only if n is not in the set: {1,2,3,5,6,7,10,13}" |
November 07, 2001, 3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Sijue Wu (UNIVERSITY OF MARYLAND) |
On the motion of waterwaves with and without a variable bottom |
" |
November 06, 2001, 1:30 P.M at Science Center Room 507 |
| SERIES OF LECTURES BY PROF. A.CATTANEO |
Alberto Cattaneo (INSTITUT FUR MATHEMATIK, ZURICH) |
'The Bv formalism, topological theories and deformation quantization' |
" |
November 06, 2001, 5:00Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Sijue Wu (UNIVERSITY OF MARYLAND AT COLLEGE PARK) |
'Mathematical Analysis of Vortex Sheets' |
" |
November 05, 2001, 3:00-4:00 Pm at Science Center, Room 507 |
| MODULAR CURVES AND MODULAR FORMS |
Frank Calegari () |
'Aspects of the Eigencurve' |
I shall discuss some recent conjectures of Kevin Buzzard concerning classical modular forms and the Gouvea-Mazur conjecture. Using some very naive techniques, Kevin and I have proved a special case of these conjectures. I shall try and describe the flavour of these calculations, as well as discussing other intriguing phenomena that arise." |
November 05, 2001, 2:00-3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Nathan Dunfield (HARVARD) |
'Transfering Virtual Haken Via Dehn Filling' |
" |
November 02, 2001, 3:30 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Matthew Baker (HARVARD) |
'Modular parametrizations for curves of genus at least two' |
" |
October 31, 2001, 3:00 Pm at Science Center, Room 507 |
| SEMINAR ON EDUCATION IN THE MATHEMATICAL SCIENCES |
Daniel Goroff (HARVARD UNIVERSITY) |
Lessons and Non-Lessons Concerning Japanese Mathematics Education- The case of the Famous Third International Study Tapes |
College and School faculty interested in forming lesson study groups are especially encouraged to attend these seminars" |
October 31, 2001, Wednesday, 4:00 Pm at 317 Science Center |
| BASIC NOTIONS SEMINAR |
Joseph Harris (HARVARD) |
'Rationally connected varieties' |
" |
October 29, 2001, 3:00 Pm at Science Center, Room 507 |
| MODULAR CURVES AND MODULAR FORMS SEMINAR |
Edray Goins (MSRI) |
'Finding a modualr form associated with a Psl(2,7)-extension' |
" |
October 29, 2001, 2:00-3:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Melissa Liu (HARVARD) |
'Moduli of J-holomorphic Curves with Lagrangian Boundary Conditions' |
" |
October 26, 2001, 3:30-5:00 Pm at Science Center, Room 309 |
| JOINT MATHEMATICS COLLOQUIUM |
David Mumford (BROWN UNIVERSITY) |
Mathematics and vision |
There will be a tea at 4:00 Pm in the 4th floor Common Are" |
October 25, 2001, 4:30-5:30 Pm at Science Center, Hall D |
| NUMBER THEORY SEMINAR |
Curt McMullen (HARVARD) |
'Coxeter groups, Salem numbers and the Hilbert metric' |
" |
October 24, 2001, 3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Tatiana Toro (HARVARD UNIVERSITY) |
Free boundary regularity for the Poisson kernel below the continuous threshold |
" |
October 23, 2001, 1:30pm at Science Center Room 507 |
| SERIES OF LECTURES BY PROF. A.CATTANEO |
Alberto Cattaneo (INSTITUT FUR MATHEMATIK, ZURICH) |
'The Bv formalism, topological theories and deformation quantization' |
Lecture " |
October 23, 2001, 5:00Pm at Science Center, Room 507 |
| MODULAR CURVES AND MODULAR FORMS SEMINAR |
Fernando Rodriguez-Villegas (UNIVERSITY OF TEXAS) |
"Hypergeometric weight 4 forms" |
" |
October 22, 2001, 2:00-3:00 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMIANR |
Benedict Gross (HARVARD) |
'Salem numbers and orthogonal groups' |
" |
October 22, 2001, 3:00-4:00 Pm at Science Center, Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Conan Leung (UNIVERSITY OF MINNESOTA) |
'Lagrangian submanifolds in hyperkahler manifolds, Legendre transform and Plucker formula'. |
" |
October 19, 2001, 3:30-5:00 Pm at Science Center, Room 309 |
| SERIES OF LECTURES BY PROF. A.CATTANEO |
Alberto Cattaneo (INSTITUT FUR MATHEMATIK, ZURICH) |
"The Bv formalism, topological theories and deformation quantization" |
" |
October 18, 2001, 5:00 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Kiran Kedlaya (UNIVERSITY OF CALIFORNIA AT BERKELEY) |
'Computing zeta functions using Monsky-Washnitzer cohomology' |
" |
October 17, 2001, 3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Tom Graber (HARVARD UNIVERSITY) |
Open-String Gromov-Witten Invariants |
" |
October 16, 2001, 1:30pm at Science Center Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
Johan DeJong (MIT) |
'Period-Index Problem for Surfaces' |
" |
October 16, 2001, 3:00 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Don Zagier (MAX PLANCK INSTITUT FUER MATHEMATIK, BONN) |
'Counting graphs' |
" |
October 15, 2001, 3:00 Pm at Science Center, Room 507 |
| MODULAR CURVES SEMINAR |
Pete Clark (HARVARD) |
Searching for Quaternionic Modular Forms |
" |
October 15, 2001, 2:00-3:00 at Science Center 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Mikhail Khovanov (UC DAVIS) |
'A cohomology theory of links" |
" |
October 12, 2001, 3:30-5:00 Pm at Science Center, Room 309 |
| SERIES OF LECTURES BY PROF. A.CATTANEO |
Alberto Cattaneo (INSTITUT FUR MATHEMATIK, ZURICH) |
"The Bv formalism, topological theories and deformation quantization" |
Lecture 1. Usually the seminar will take place on Tuesdays, 5:00-7:00 Pm, at Science Center, Room 50" |
October 11, 2001, 5:00 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Romyar Sharifi () |
'Relations in and between pro-p Galois groups and a Lie algebra associated to the projective line minus three points' |
" |
October 10, 2001, 3:00 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Fernando Rodriguez Villegas (HARVARD UNIVERSITY) |
Calabi-Yau manifolds over finite fields |
Science Center Room 50" |
October 09, 2001, 1:30pm at |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Daniel Ruberman (BRANDEIS) |
Positive scalar curvature and diffeomorphisms of 4-manifolds. |
" |
October 05, 2001, 3:30-5:00 Pm at Science Center, Room 309 |
| NUMBER THEORY SEMINAR |
Helna Verrill (HANNOVER UNIVERSITY, GERMANY) |
Lattices of modular symbols for Gamma 0(N) with weight k > 2 |
" |
October 03, 2001, 3:00 Pm at Science Center, Room 507 |
| HARVARD/MIT ALGEBRAIC GEOMETRY SEMINAR |
Mihnea Popa (HARVARD) |
'Regularity on abelian varieties' |
Abstract: I will introduce the notion of \emph{Mukai regularity} for coherent sheaves on abelian varieties, defined via conditions on the supports of cohomologies of Fourier-Mukai transform complexes. In a very special form, depending on the choice of a polarization, this resembles and in fact strenghtens the classical notion of Castelnuovo-Mumford regularity. The techniques are in part a generalization of an approach of Mumford-Kempf-Lazarsfeld made possible by the use of Mukai s theory. I will then explain how this can be applied to a variety of questions related to abelian varieties and more general irregular varieties, ranging from the appearance of new interesting invariants for line bundles, to effective results on linear series and defining equations and to a study of special classes of vector bundles. This is joint work with G.Pareschi." |
October 02, 2001, 3:00-4:30 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Sergei Gukov (HARVARD UNIVERSITY, PHYSICS DEPARTMENT) |
Manifolds of G2 Holonomy, Dynamical Systems, and Quantum Field Theory |
" |
October 02, 2001, 1:30pm at Science Center, room 507 |
| MODULAR CURVES MODULAR FORMS SEMINAR |
William Stein (HARVARD) |
'Nonvanishing Twists and Visible Shafarevich-Tate Groups' |
" |
October 01, 2001, 2:00-3:00 Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Daniel Allcock (HARVARD) |
'Hyperbolic Reflection Groups' |
" |
October 01, 2001, 3:00-4:00 Pm at Science Center, Room 507 |
| JOINT COLLOQUIUM |
Fernando Rodriguez-Villegas (UNIVERSITY OF TEXAS) |
"Periods, L-functions, and Knots" |
There will be a tea in the 4th floor Common Are" |
September 28, 2001, 4:00-5:00 Pm at Science Center, Hall D |
| DIFFERENTIAL GEOMETRY SEMINAR |
Vadim Kaloshin (AIM AND MIT) |
"Dynamics of an oil spill" |
" |
September 25, 2001, 1:30pm at Science Center Room 507 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Alberto Cattaneo (UNIVERSITY OF ZURICH) |
'A field theoretic interpretation of the Chas-Sullivan bracket'. |
" |
September 21, 2001, 3:30-5:00 Pm at Science Center, Room 309 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR |
Lorenzo Ramero (INSTITUT DE MATHEMATIQUES DE JUSSIEU) |
"Almost Purity and P-adic Analytic Geometry" |
" |
September 18, 2001, 3:00Pm at Science Center, Room 507 |
| BASIC NOTIONS SEMINAR |
Noam D. Elkies (HARVARD) |
"Six Ways of Looking at Aut(S6)' |
" |
September 17, 2001, 3:00-4:00 Pm at Science Center, Room 507 |
| MODULAR CURVES AND MODULAR FORMS |
William Stein (HARVARD) |
"Intro to Magma for Number Theorists" |
" |
September 17, 2001, 2:00-3:00 Pm at Science Center, Room 507 |
| NUMBER THEORY SEMINAR |
Matthew Emerton (UNIVERSITY OF CHICAGO) |
On the p-adic interpolation of systems of Hecke eigenvalues and Galois representations |
" |
May 23, 2001, 3-4 pm at Science Center, Room 507 |
| SPECIAL GAUGE THEORY AND TOPOLOGY SEMINAR |
Peter Teichner (UCSD) |
"Feynman diagrams and grope cobordism" |
Abstract:I am planning to convince the audience that gropes are very simple geometric objects, combinatorially parameterized by Feynman diagrams, and that they form an important link between the topology of 3- and 4-dimensional manifolds" |
May 07, 2001, 12:30 Pm at Science Center, Room 507 |
| GEOMETRIZATION SEMINAR |
John Holt (HARVARD) |
"Season Final: Completion of the proof in the fibered case" |
" |
May 04, 2001, 1:00 Pm at Science Center, Room 530 |
| COLLOQUIUM |
Avi Wigderson (IAS, PRINCETON & HEBREW UNIVERSITY) |
"Some Insights of Computational Complexity Theory |
* There will be a tea at 4:00 Pm in the 4th floor Common Area. Absract: Computational complexity theory has been one of the most exciting fields of scientific research over the last few decades. This research studies the power of feasible computation, and is guided by a few clear and focused questions, deeply motivated on scientific, practical and philosophical grounds, like the P vs Np problem, and the questions on the power of rendomized and quantum computation.While these problems are far from resolved, Complexity Theory was able to offer fresh rigorous definitions to some central notions which naturally (or less so) arise from these questions, and unveil many rich and beautiful connections between them. In this general survey, I would like to probe some of the unique features and insights of the complexity theory viewpoint. This will be done by considering how (and why) notions which intrigued people for centuries or even millenia (like Knowledge, Randomness, Cryptography, Learning, Proof, and naturally, Computation), reveal new dimensions, and are suprisingly linked together, when viewed from our special Computational Complexity glasses." |
May 03, 2001, 4:30-5:30 Pm at Science Center, Hall D |
| NUMBER THEORY SEMINAR |
Dennis Gaitsgory (HARVARD) |
"Geometric Langlands for Gl(n)" |
* There will be a tea at 4:00 Pm in the 4th floor Common Area" |
May 02, 2001, Part I: 3:00-4:00 Pm, Part Ii: 4:30-5:30 Pm at Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR |
William Meeks (UNIVERSITY OF MASSACHUSSETTS-AMHERST) |
"The Uniqueness of the Helicoid and the Asymptotic Geometry of Properly Embedded Minimal Surfaces of Finite Topology" |
" |
May 01, 2001, 1:30 Pm at Science Center, Room 507 |
| HARVARD SEMINAR ON EDUCATION IN MATHEMATICAL SCIENCES |
Jack Bookman (DUKE UNIVERSITY) |
Understanding How Students Learn Using Web-Based Modules." |
Participants are encouraged to gather in the seminar room between 1:00 and 1:30 and are welcome to bring their lunch. Desserts and drinks will be provided." |
May 01, 2001, 1:30-2:30 at 317 Science Center |
| BASIC NOTIONS SEMINAR |
Tom Braden (HARVARD) |
"Hodge Theory for Polytopes" |
" |
April 30, 2001, 3:00-4:00 Pm at Science Center, Room 507 |
| SERIES OF LECTURES BY PROF. I.CHEREDNIK |
Ivan Cherednik (UNC CHAPEL HILL) |
"Double Affine Hecke Algebra & Fourier Transform" |
Lecture 9 And The Last. We will switch from the q-transform in the noncompact (Jackson) case to roots of unity and generalized Verlinde algebras. Status: Elementary" |
April 30, 2001, 3:30 Pm at Science Center, Room 338 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Richard Wentworth (JOHN HOPKINS UNIVERSITY) |
"Mapping class groups and rigidity" |
" |
April 27, 2001, 3:30-5:00 Pm at Science Center, Room 309 |
| GEOMETRIZATION SEMINAR |
John Holt (HARVARD) |
"The Double Limit Thm, Part Ii" |
" |
April 27, 2001, 1:00 Pm at Science Center, Room 112 |
| NUMBER THEORY SEMINAR |
Gordon Savin (UTAH/ HARVARD) |
"Functoriality of Theta Lifting for Generic Discrete Series" |
" |
April 25, 2001, 3:00-4:00 Pm at Science Center, Room 507 |
| SPECIAL SEMINAR |
Stanislav Smirnov (KTH, STOCKHOLM & CALTECH, PASADENA) |
"Critical percolation in the plane is conformally invariant" |
Abstract: We will discuss critical site percolation on triangular lattice in the plane. We will prove conformally invariant Cardy s formula (conformal field theory prediction for the probabilities of crossings) and construct the (conformally invariant) continuum scaling limit" |
April 24, 2001, 3:00-4:00 Pm at Science Center, Room 507 |
| SERIES OF LECTURES BY DYLAN THURSTON |
Dylan Thurston (HARVARD) |
"Jacobi Diagrams Iii: Finite Type Invariants" |
" |
April 24, 2001, 4:30 Pm at Science Center, Room 530 |
| HARVARD SEMINAR ON EDUCATION IN MATHEMATICAL SCIENCES |
John D. Emerson and Frederick Hosteller (MIDDLEBURY COLLEGE RSP. HARVARD UNIVERSITY) |
Students can Help Improve College Teaching: A metastudy of student ratings of courses |
Participants are encouraged to gather in the seminar room between 1:00 and 1:30 and are welcome to bring their lunch. Desserts and drinks will be provided." |
April 24, 2001, 1:30-2:30 at 317 Science Center |
| SERIES OF LECTURES BY PROF. I.CHEREDNIK |
Ivan Cherednik (UNC CHAPEL HILL) |
"Double Affine Hecke Algebra & Fourier Transform" |
Lecture 8.The self-duality of the q-Harish-Chandra transformand the Plancherel formulas will be discussed including the consideration of the p-adic limit.Status: Elementary, Continues Lecture 7" |
April 23, 2001, 4:30-6:30 Pm at Science Center, Room 112 |
| BASIC NOTIONS SEMINAR |
Eric Sommers (HARVARD) |
"Nilpotent Elements in Simple Lie Algebras" |
" |
April 23, 2001, 3:00-4:00 Pm at Science Center, Room 507 |
| SERIES OF LECTURES BY DAVID GABAI AND VALENTIN POENARU |
Valentin Poenaru (UNIVERSITE PARIS SUD) |
Lecture 4. "Discussion" |
" |
April 20, 2001, 11:00 Am at Science Center, Room 101b |
| GEOMETRIZATION SEMINAR |
John Holt () |
"The Double Limit Theorem" (part 1) |
" |
April 20, 2001, 1:00 Pm at Science Center, Room 530 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
David Gabai (CALTECH) |
'The Smale conjecture for hyperbolic 3-manifolds' |
" |
April 20, 2001, 3:30-5:00 Pm at Science Center, Room 309 |
| SERIES OF LECTURES BY DAVID GABAI AND VALENTIN POENARU |
Valentin Poenaru (UNIVESITE PARIS SUD) |
Lecture 3. |
" |
April 19, 2001, 2:30 Pm at Science Center,Room 103b |
| SERIES OF LECTURES BY DAVID GABAI AND VALENTIN POENARU |
David Gabai (CALTECH) |
Lecture 2. "The equivariant representation Theorem for M3 after V.Poenaru" |
" |
April 19, 2001, 1:30 Pm at Science Center, Room 101b |
| SERIES OF LECTURES BY DAVID GABAI AND VALENTIN POENARU |
David Gabai (CALTECH) |
Lecture1. |
" |
April 18, 2001, 1:00 Pm at Science Center, Room 310 |
| NUMBER THEORY SEMINAR |
Heisuke Hironaka (YAMAGUCHI UNIVERSITY) |
On resolution of singularities in positive characteristics |
" |
April 18, 2001, 3:00-4:00 Pm at Science Center, Room 507 |
| HARVARD SEMINAR ON EDUCATION IN MATHEMATICAL SCIENCES |
Paul Blanchard and Haynes Miller (BU RSP MIT) |
Teaching and Learning about Differential Equations: A Panel. |
Participants are encouraged to gather in the seminar room between 1:00 and 1:30 and are welcome to bring their lunch. Desserts and drinks will be provided." |
April 17, 2001, 1:30-2:30 at 317 Science Center |
| SPECIAL SEMINAR |
Dylan Thurston (HARVARD) |
Lecture 2 : "Knot invariants by counting configurations |
The linking number of a two-component link is the simplest example ofa knot invariant constructed by counting configurations. In this talkwe will generalize the construction of the linking number as much aspossible, constructing a knot invariant with values in the space of Jacobi diagrams with a distinguished cycle. This construction canmost naturally be seen as a degree of a certain map betweenconfiguration spaces" |
April 17, 2001, 3:00 Pm at 65 Mt Auburn St |
| DIFFERENTIAL GEOMETRY SEMINAR |
Daniel Allcock (HARVARD UNIVERSITY) |
Reflection Groups on the Cayley Hyperbolic Plane |
" |
April 17, 2001, 1:30pm at Science Center, Room 507 |
| SERIES OF LECTURES BY PROF. I.CHEREDNIK |
Ivan Cherednik (UNC CHAPEL HILL) |
"Double Affine Hecke Algebra & Fourier Transform" |
Lecture 7.Using the nonsymmetric polynomials from the previouslecture and the automorphisms of Daha, closely connectedwith topology of elliptic curves, we will prove the self-duality of the q-Harish-Chandra transform.Status: Elementary, Somewhat involves Lecture 5,6" |
April 16, 2001, 4:30-6:30 Pm at Science Center, Room 112 |
| GEOMETRIZATION SEMINAR |
Nathan Dunfield (HARVARD) |
"3-manifolds which fiber over the circle" |
" |
April 13, 2001, 1:00-2:00 Pm at Science Center, Room 530 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Ciprian Manolescu (HARVARD) |
"Seiberg-Witten-Floer stable homotopy type of three-manifolds" |
" |
April 13, 2001, 3:30-5:00 Pm at Science Center, Room 309 |
| COLLOQUIUM |
Eduard Looijenga (UTRECHT UNIVERSITY) |
"Arrangements and moduli spaces" |
Abstract. An arrangement in a projective space is a finite collection of hyperplanes of that space. This notion has a natural extension to the case of a torus embedding or an abelian variety. And also to the case of the Baily-Borel compactification of an arithmetic quotient of complex ball or of a type IV domain. There is a uniform way of modifying such a variety in terms of the given arrangement, which in the case of the three coordinate lines in the projective plane boils down to the standard Cremona transformation. Surprisingly many Git quotients that have an interpretation as a moduli space of varieties for which a Torelli theorem holds can so be obtained (in one of these settings). For instance, this applies to the moduli spaces of quartic curves, sextic curves, quartic surfaces, Enriques surfaces, rational elliptic surfaces. There are also interesting examples in singularity theory." |
April 12, 2001, 4:30-5:30 Pm at Science Center, Hall D (there will be a tea at 4:00Pm in the 4th floor Common Area) |
| NUMBER THEORY SEMINAR |
David Savitt (HARVARD) |
"Modularity of some potentially Barsotti-Tate Galois representations" |
" |
April 11, 2001, 3:00-4:00 Pm at Science Center, Room 507 |
| JACOBI DIAGRAMS AND FINITE-TYPE INVARIANTS |
Dylan Thurston (HARVARD) |
The Universal Lie Algebra |
The space of Jacobi diagrams is the vector space generated by vertex-oriented trivalent graphs modulo a certain universal invariance relation. In the first three lectures we will see three natural appearances of this space in Lie algebras and 3-dimensional topology, followed by one application in the fourth lecture.Jacobi diagrams are, in a certain sense, the universal metrized Lie algebra. They are the formulas that can be written down uniformly in any metrized Lie algebra. Jacobi diagrams may yield insights into Lie algebras. One instance is Deligne s conjecture: there exists a family of exceptional Lie algebras, analogous to the classical sln and ospn families. Vogel extended this conjecture to the existence of a 2-parameter family containing all simple Lie algebras and Lie super-algebras" |
April 10, 2001, 3:00-4:00 Pm at Science Center, Room 310 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Gang Liu (UNIVERSITY OF CALIFORNIA - LA) |
Virtual Moduli Cycle in Contact Geometry |
" |
April 10, 2001, 1:30pm at Science Center, Room 507 |
| HARVARD SEMINAR ON EDUCATION IN MATHEMATICAL SCIENCES |
Solomon Friedberg (BOSTON COLLEGE) |
Seeking Points: Case Discussion on Undergraduate Teaching and Learning |
Participants are encouraged to gather in the seminar room between 1:00 and 1:30 and are welcome to bring their lunch. Desserts and drinks will be provided." |
April 10, 2001, 1:30-2:30 at 317 Science Center |
| BASIC NOTIONS SEMINAR |
Grisha Mikhalkin (UTAH) |
"Algebraic varieties and their amoebas" |
" |
April 09, 2001, 3:00-4:00 Pm at Science Center, Room 507 |
| GEOMETRIZATION SEMINAR |
Maryam Mirzakhani (HARVARD) |
"Projective measured laminations and surface homeomorphisms" |
" |
April 06, 2001, 1:00-2:00 Pm at Science Center, Room 530 |
| GAUGE THEORY AND TOPOLOGY SEMINAR |
Gordana Matic (UNIVERSITY OF GEORGIA) |
"Convex decompositions of contact manifolds" |
" |
April 06, 2001, 3:30-5:00 Pm at Science Center, Room 309 |
| DIFFERENTIAL GEOMETRY SEMINAR |
Cedric Villani (ECOLE NORMALE SUPERIEURE DELYON) |
"On the Boltzmann equation with long-range interactions" |
" |
April 04, 2001, 4:00 Pm at Science Center, Room 530 |
| NUMBER THEORY SEMINAR |
Barry Mazur (HARVARD UNIVERSITY) |
"Anti-cyclotomic norms in Mordell-Weil group" |
" |
April 04, 2001, 3:00-4:00 Pm at Science Center, Room 507 |
| THE THURSDAY SEMINAR |
DAVID AYALA (HARVARD UNIVERSITY) |
Embedding calculus |
" |
November , 2000, 4 - 6 pm at 11/11/10 |
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December , 2000, at |