Jan 31. Stretch maps, after Thurston
Feb 14. The WeilPetersson gradient flow of renormalized volume uniformizes relatively acylindrical manifolds Feb 28. Isoperiodic forms and invariant subvarieties of moduli space Mar 20. Clusters algebras and Teichmueller theory Apr 3. A new proof of Mordell's conjecture (for Riemann surfaces; after Xie  Yuan) Apr 17. TBA May 1. Counting minimal surfaces in hyperbolic 3manifolds 
Oct 4 Automorphism of complex surfaces:
What is the simplest interesting dynamical system?
Oct 11 Islands on K3 surfaces Oct 18. Connectedness of moduli spaces: From plane curves to rational maps Oct 25 Dynamics on blowups of P2 Nov 1. The 3D dimer model Nov 15. Multipliers of rational maps Nov 29. Monodromy over Riemann surfaces 
Feb 8. Galois orbits, equidistribution, and the moduli space of all triangles
Feb 15. Entropy and geodesic currents on surfaces Feb 22. Earthquakes, triangulations and circle homeomorphisms Sep. 7, 14: Exotic homeomorphisms and flows (after Sullivan and Freedman) Sep. 21, 28, Oct 5, 12, 19: Billiards and Teichmuller theory Oct 26: Unramified correspondences (Bogomolov, Tschinkel) Nov 2: A norm for the homology of 3manifolds (Thurston) Nov 9, 16: Bers, Hénon, Painlevé and Schrödinger (Cantat) Nov 30: Triangles groups and Hilbert modular varieties. 
Sep. 11: Absolute periods of holomorphic 1forms on Riemann surfaces
Sep. 18: On the Loewner energy of simple planar curves Oct. 2: Elementary surfaces in the Apollonian manifold Oct. 9: From veering triangulations to pseudoAnosov flows (and back again) Oct. 23: The WeilPetersson gradient flow for renormalized volume Oct. 30: A walk from knots to exotic smooth Stein 4manifolds Nov. 6: Level sets of length function in moduli space Nov. 13: Experimental study of a meromorphic analogue of Teichmüller space Nov. 20: Volumes and intersection theory on moduli spaces of differentials 
25 April:
Andreev's theorem on hyperbolic polyhedra and Kleinian reflection groups
18 April: Galois conjugates of PCF generalized betatransformations 11 April: Kaehler groups and surface bundles 4 April: What to do when you cannot confine your planes? Teichmüller spaces of noncompact Riemann surfaces 28 March: Planes immersed in hyperbolic 3manifolds 21 March: Bounds on renormalized volume and the volume of the convex core 14 March: 7 March: The geometry of Hilbert's 13th problem *7 March: The theory of resolvent degree, after Hamilton, Klein, Hilbert, and Brauer 28 Feb: 5 points on the sphere 21 Feb: Convex cores of thick hyperbolic 3manifolds with bounded rank 14 Feb: Hypergeometric equations and Lyapunov exponents (via Hodge theory) 7 Feb: Penrose Tilings of Riemann Surfaces 31 Jan: The behavior of planes in confinement 29 Nov: Finitely many algebraically primitive Teichmüller curves in genus g at least 3 8 Nov: Squaretilings of modular curves X(d) 1 Nov: Cohomology of arithmetic groups and characteristic classes of manifold bundles 25 Oct: The metastable homology of mapping class groups 18 Oct: Algebraic dynamics from topological and holomorphic dynamics 4 Oct: Divergent trajectories in arithmetic homogeneous spaces of rational rank two 27 Sep: Trees in degenerating families of rational maps and isometric Gactions 20 Sep: Plane curves, (higher) spin structures, and mapping class groups 13 Sep: Tilings and Hurwitz theory 
Feb 2: The number of nonnegative curvature triangulations of the sphere
Feb 8: Flat surfaces and stability structures on categories Feb 15: Constructing pseudoAnosov mapping classes with small stretch factor Feb 22: Strata of abelian differentials and the effective cone of M_g,n March 1: Global dynamics of multicurves in complex dynamics March 8: Extremal and rigid divisors on moduli spaces of curves March 22: Differentiating Blaschke products March 29: Smooth compactifications of strata of abelian differentials April 5: Berkovich spaces and complex dynamics April 12: Rationality of canonical height April 19: Affine surfaces part I April 25: Affine surfaces part II 
Sep 14, 21: Almost simple geodesics on the triplypunctured sphere 
Feb 4: Kronecker's congruence and Teichmüller curves in
positive characteristic Feb 11: Transversality Feb 18: Rubber Bands and Rational Maps Feb 25: Equidistribution of Shears and Applications March 4: Circle actions on the boundary of Schottky space March 11: Hyperbolic extensions of free groups March 18: Have a good Spring Break! March 25: Generalizing Douady's Magic Formula April 1: On the classification of critically fixed rational maps April 15: Families of K3 surfaces and their asymptotic properties April 22: A case of the dynamical AndréOort conjecture April 29: A polynomial endomorphism of C^2 with a wandering Fatou component May 13: Reading Group Reunion, Harvard University May 13: Complex dynamics and elliptic curves 


R. Mukamel, Stanford University G. Tiozzo, Harvard University H. Masur, University of Chicago H. Shiga, Tokyo Institute of Technology A. Karlsson, University of Geneva K. Pilgrim, Indiana University J. Smillie, Cornell University L. DeMarco, University of Illinois at Chicago A. Sambarino, Orsay M. Bainbridge, Indiana University S. Antonakoudis, Harvard University Y. Ishii, Kyushu University J. H. Hubbard, Université de Provence/Cornell University B. Farb, University of Chicago 
O. Ivrii. Ghosts of the mapping class group. 11 Jan. G. Tiozzo. Entropy and dimension of sets of external rays. 11 Jan. C. McMullen. Navigating moduli space with complex twists. 11 Jan. 2/29: Matings with laminations Dzmitry Dudko, Jacobs University X. Buff. Antipodepreserving cubic rational maps. 6 June 
10/12: A proof of Pilgrim's conjecture Nikita Selinger, SUNY Stony Brook 
C. McMullen. Periodic, Diophantine and ergodic foliations on surfaces. 9 Feb  9 Mar. J. Hubbard. On the density of Strebel differentials. 23 March. S. Koch. On the DeligneMumford compactification of moduli space. 6, 13 April. N. Dunfield. The least spanning area of a knot and the Optimal Bounding Chain Problem. 20 April. M. Duchin. Flat structures as currents. 27 April. C. McMullen. Manifolds, topology and dynamics: Milnor's work and subsequent developments. 11 May. C. McMullen. What is a K3 surface? 2730 June. 
R. Kirby. A new calculus for 4manifolds. 8 Sep. L. DeMarco. Dynamics of cubic polynomials and enumeration of cusps. 15 Sep. C. McMullen The evolution of geometric structures on 3manifolds. 20 Sep. (Monday) T. Koberda. A pingpong theorem for the mappingclass group. 29 Sep. V. Gadre. Singularity of harmonic measures for random walks on the mapping class group. 6 Oct. J. Bourgain. Expansion in linear groups (4:30, Lecture Hall D). 13 Oct. R. Roeder. Blaschke products and renormalization on the diamond hierarchical lattice. 20 Oct. X. Buff. Transversality for Herman rings. 27 Oct. E. Uhre. The Mandelbrot set and its deformations. 3 Nov. G. Tiozzo. Continued fractions and kneading sequences of unimodal maps. 17 Nov. D. Meyer. Invariant Peano curves of expanding Thurston maps. 1 Dec. 
C. McMullen. Entropy. 10, 17 Feb. M. Baker. Complex dynamics and adelic potential theory. 24 Feb C. McMullen. Surface dynamics. 3, 10 March T. Koberda. Surface bundles of small volume. 24 March G. Tiozzo. Absolute continuity of invariant measures for random walks on Lie groups. 31 March R. Mukamel. Teichmueller dynamics in genus two, modular forms and zeta functions. 7 April S. Koch. Dynamics in superattracting basins. 14 April A. Putnam. The Picard group of the moduli space of curves with level structures. 21 April D. Margalit. Symplectic representations of braid groups. 28 April G. Walsh. The bumping set and the characteristic submanifold. 5 May 
E. Hironaka. Small dilatation pseudoAnosov mapping classes coming from the simplest pseudoAnosov braid.
H. Oh. Equidistribution and counting for geometrically finite hyperbolic groups. S. Fenley. PseudoAnosov flows and large scale geometry of 3manifolds. S. Koch. Dynamics of maps on moduli space. M. Bridgeman. The orthospectra of finite volume hyperbolic manifolds with totally geodesic boundary and associated volume identities. A. CottonClay. Holomorphic Pants in R times a mapping torus. D. Margalit. Small dilatation pseudoAnosovs and 3manifold. G. Walsh. Commensurability of knot complements. G. Tiozzo. The entropy of alphacontinued fractions 
H. Oh.
Apollonian circle packings and horosphercial flows on hyperbolic
3manifolds.
Wed, 18 Feb D. Margalit. Torelli groups and the complex of minimizing cycles. Wed, 25 Feb R. Devaney. Dynamics of z^{n} + C/z^{n}: Why n=2 is crazy. Wed, 4 March E. Hironaka. PseudoAnosov mapping classes with small dilatation constructed from graphs. Wed, 11 March A. Wilkinson. Absolute continuity, Lyapunov exponents and rigidity. Wed, 18 March D. Damjanovic. Perturbations of some higher rank unipotent actions Wed, 1 Apr N. Shah. Limits of expanding translates of shrinking curves on hyperbolic manifolds. Wed, 8 April C. Taubes. An introduction to geometric quantization. Wed, 15 Apr A. Bufetov. Suspension flows over Vershik's automorphisms. Wed, 22 Apr E. Ghys. Dynamics in Dimension 3. (Talk at MIT: room 34101, 4:30 pm.) Wed, 29 Apr T. Koberda. Braids and Their Dilatations: The Burau, Gassner and Bigelow representations. Wed, 3 May 
C. McMullen.
Random walks on the hyperbolic plane and barycenter subdivision.
Wed, 15 Oct C. McMullen. Braid groups and Hodge theory. Wed, 22 Oct R. Schwartz. Outer billiards and the modular group. Wed, 29 Oct D. Fisher. The space of discrete linear groups. Wed, 5 Nov J. Duncan. Fuchsian groups and affine Dynkin diagrams. Wed, 12 Nov N. Avni. Dynamics on representation varieties  finite, compact and hyperbolic. Wed, 19 Nov S. Sheffield Hamburgers, cheeseburgers, and scaling limits of discrete random surfaces. Wed, 3 Dec R. Mukamel Surfaces with triangular veech broups Wed, 10 Dec 
G. Mondello.
Hyperbolic surfaces and systems of arcs.
Wed, 14 March D. Kleinbok. Expanding translates of horospheres and applications to number theory. Wed, 21 March J. Behrstock. Asymptotic geometry of the mappingclass group. Wed, 4 April L. Silberman. Measure rigidity for Cartan actions: the "lowentropy" method. Wed, 11 April D. Damjanovic. Littlewood's conjecture and SL_3(R)/SL_3(Z). Wed, 25 April S. Brooks. Halfway to quantum unique ergodicity. Wed, 2 May C. McMullen. Complex dynamics on the unit disk: measures, multipliers and Rtrees. Wed, 9 May 
D. Dumas. Grafting and shearing hyperbolic surfaces M. Bainbridge. Volumes of Hilbert modular surfaces M. Mirzakhani. Ergodic properties of the space of measured laminations C. McMullen. Thermodynamics, dimension and the WeilPetersson metric R. Schwartz. Nearly isosceles billiards, Veech points, and universal power series expansions J. Brock. Heegaard splittings, handlebodies and the geometry of hyperbolic 3manifolds 
Mon, May 9. Prym varieties and Teichmüller space.
Curt McMullen Wed, May 11. Euler characteristics of Teichmüller curves. Matt Bainbridge Mon, May 16. Coble sextics and holomorphic actions of lattices on P^{1}. Izzet Coskun Wed, May 18. Polynomial dynamics and trees. Laura DeMarco Wed, May 25. Hausdorff dimension and bendings of Fuchsian groups. Martin Bridgeman Fri, May 27. Train tracks. Maryam Mirzakhani 
Oct. 22. Markov maps and discreteness tests for punctures torus
groups. David Dumas
Oct. 29. The boundary of the space of rational maps. Laura DeMarco. Nov. 5. Is there a polynomial Julia set of positive measure? Matt Bainbridge. Nov. 20. Crystals and algebraic curves. Colloquium, Andrei Okounkov (Princeton) Dec. 12. Billiards and dynamics over moduli space. Gauge theory seminar, Curt McMullen 
Sept. 25. Billiards and Riemann surfaces of infinite complexity. Curt McMullen.
Oct. 2. Galois flux and measured foliations. Curt McMullen. Oct. 9. What is a random 3manifold and what does it look like? Nathan Dunfield. Oct. 16. Does a random 3manifold fiber over the circle? Nathan Dunfield. Oct. 23. No meeting. Go to Rich Schwartz's colloquium on Thursday instead. Oct. 30. Physical measures and periodic orbits of quadratic polynomials. Matt Bainbridge. Nov. 6. Moduli of Polyhedra. Laura DeMarco. Nov. 13. Ergodic theory of horocycles and the earthquake flow on moduli space. Maryam Mirzakhani. Nov. 20. Is the Jones polynomial the same size as the Alexander polynomial? Jacob Rasmussen. Nov. 27. No meeting Dec. 4. Abelian differentials and dynamics Izzet Coskun. Dec. 11. Projective Riemann surfaces with Fuchsian holonomy David Dumas. Dec. 18. The PattersonSullivan theory of discrete quasiconformal groups Ed Taylor. 
Jan 30. Billiards and Curves of Genus 2. Curt McMullen.
Feb 6. Laminations and groups of homeomorphisms of the circle. Nathan Dunfield. Feb 13. The configuration space of points on the projective line and the moduli of polygons. Haruko Nishi. Feb 20. Simple geodesics and the WeilPetersson volume of the moduli space of Riemann surfaces. Maryam Mirzakhani. Feb 27. Experiments with Quasifuchsian Groups and Projective Structures. David Dumas. Mar 6 (starts 4:30). Growth of the number of periodic points for generic diffeomorphisms. Vadim Kaloshin. Mar 13. Some algebraic questions related to the Poincaré Conjecture. Andrew Casson. Mar 20. A Variational Study of Curvature and Potential Theory. Laura DeMarco. Mar 27. Spring Break. Apr 3. Complex hyperbolic reflection groups: a primer. Daniel Allcock. Apr 10. Rigidity and nonrigidity of hyperbolic 3manifolds. Kevin Scannell. Apr 17. Shadow pictures: pairofpants decompositions of 3manifolds. Dylan Thurston. Apr 24. WeilPetersson and Hodge volumes of moduli space, and the Schottky problem. Samuel Grushevsky. May 1. Mostow Rigidity and Lattice Classification. Kathy Paur. 
2. The boundary of an abstract group and simple loops on the torus, C. McMullen 3. Surfaces in finite covers of 3manifolds: the virtual Haken conjecture, N. Dunfield
4. Circles and hyperbolic geometry I, D. Calegari Euler class of E <= Euler class of TS. 5. Circles and hyperbolic geometry II, D. Calegari 6. Hyperbolic volume and the Jones polynomial, D. Thurston 7. Lyapunov exponents and complex dynamics, L. DeMarco 8. Julia sets, harmonic measure and rotation, I. Binder 9. The topology of the space of hyperbolic structures on a 3manifold, J. Holt 10. Complex projective structures on Riemann surfaces, D. Dumas 11. Simple closed curves on surfaces and the volume of moduli space, M. Mirzakhani 12. Dynamics on K3 surfaces, C. McMullen 13. Exotic complex projective surfaces and the boundaries of quasifuchsian and Schottky spaces, H. Tanigawa 
2. Cusps of hyperbolic manifolds and the boundary of the Mandelbrot set, C. McMullen 3. 3manifold groups, surfaces and actions on trees, N. Dunfield. 4. Surgery on 3manifolds and volume rigidity, N. Dunfield. 5. Teichmüller space, quadratic differentials and rational billards, H. Masur. 6. Counting periodic points for billiards and flat structures, H. Masur. 7. Salem numbers in geometry, Eriko Hironaka 8. Average bending of convex hull boundaries, M. Bridgeman 9. Currents and instability in complex dynamics, Laura DeMarco 10. Foliated Teichmüller theory, C. McMullen 11. Diophantine numbers, quadratic differentials and failure of ergodicity, Yitwah Cheung 12. An Approach to the LowVolume Question for Hyperbolic 3Manifolds, Robert Meyerhoff 
2. Lipschitz maps and nets in Euclidean space 3. Periods; dynamics 4. The Mandelbrot set is connected 5. Schottky groups and Teichmüller space 6. Earthquakes and hyperbolic geometry 7. Complex dynamics, measures and foliations 8. Compactness in moduli space 9. Simple closed curves 10. Geodesic currents 11. The Nielsen problem 12. Teichmüller space is a domain of holomorphy 13. Extremal length, univalent maps and Teichmüller space 