Bibliography
Books and Course Notes
Papers
2023-present
Billiards in regular polygons
Triangle groups: Cusps, congruence and chaos
Triangle groups and Hilbert modular varieties
Galois orbits in the moduli space of all triangles
2016-2022
Billiards and Teichmüller curves
Billiards, heights and the arithmetic of non-arithmetic groups
Modular symbols for Teichmüller curves
Teichmüller dynamics and unique ergodicity via currents and Hodge theory
Billiards, quadrilaterals and moduli spaces
On the postcritical set of a rational map
Geodesic planes in the convex core of an acylindrical 3-manifold
Almost simple geodesics on the triply punctured sphere
Cubic curves and totally geodesic subvarieties of moduli space
2012-2015
Horocycles in hyperbolic 3-manifolds
Geodesic planes in hyperbolic 3-manifolds
The mathematical work of Maryam Mirzakhani
Entropy and the clique polynomial
The Gauss-Bonnet theorem for cone manifolds and volumes of moduli spaces
Knots which behave like the prime numbers
Moduli spaces in genus zero and inversion of power series
Moduli spaces of isoperiodic forms on Riemann surfaces
Cascades in the dynamics of measured foliations
2008-2011
Navigating moduli space with complex twists
Diophantine and ergodic foliations on surfaces
Automorphisms of projective K3 surfaces with minimum entropy
The evolution of geometric structures on 3-manifolds
Entropy on Riemann surfaces and Jacobians of finite covers
K3 surfaces, entropy and glue
Winning sets, quasiconformal maps and Diophantine approximation
Braid groups and Hodge theory
Rigidity of Teichmüller curves
Uniformly Diophantine numbers in a fixed real quadratic field
2004 - 2007
Ribbon R-trees and holomorphic dynamics on the unit disk
Cyclotomic factors of Coxeter polynomials
Dynamics on the unit disk: short geodesics and simple cycles
A compactification of the space of expanding maps on the circle
MPI Arbeitstagung 2007 - Dynamics on algebraic surfaces
Trees and the dynamics of polynomials
Thermodynamics, dimension and the Weil-Petersson metric
Dynamics on blowups of the projective plane
Prym varieties and Teichmüller curves
Foliations of Hilbert modular surfaces
Minkowski's conjecture, well-rounded lattices and topological dimension
Teichmüller curves in genus two: Torsion divisors and ratios of sines
Teichmüller curves in genus two: The decagon and beyond
Teichmüller curves in genus two: Discriminant and spin
2000-2003
Dynamics of SL2R over moduli space in genus two
MPI Arbeitstagung 2003 - Billiards and Hilbert modular surfaces
Teichmüller geodesics of infinite complexity
Billiards and Teichmüller curves on Hilbert modular surfaces
Coxeter groups, Salem numbers and the Hilbert metric
Automorphisms of even unimodular lattices and unramified Salem numbers
Dynamics on K3 surfaces: Salem numbers and Siegel disks
Gaps in Sqrt[n] mod 1 and ergodic theory
Local connectivity, Kleinian groups and
geodesics on the blowup of the torus
1997-1999
4-manifolds with inequivalent symplectic forms and
3-manifolds with inequivalent fibrations
Polynomial invariants for fibered 3-manifolds
and Teichmüller geodesics for foliations
From dynamics on surfaces to rational points on curves
The moduli space of Riemann surfaces is Kähler hyperbolic
The Alexander polynomial of a 3-manifold and
the Thurston norm on cohomology
Rigidity and inflexibility in conformal dynamics
Hausdorff dimension and conformal dynamics I:
Strong convergence of Kleinian groups
Hausdorff dimension and conformal dynamics II:
Geometrically finite rational maps
Hausdorff dimension and conformal dynamics III: Computation of dimension
Lipschitz maps and nets in Euclidean space
The Mandelbrot set is universal
1994-1996
Kleinian groups and John domains
Elder siblings and the taming of hyperbolic 3-manifolds
Complex earthquakes and Teichmüller theory
Self-similarity of Siegel disks and Hausdorff dimension of Julia sets
The classification of conformal dynamical systems
Quasiconformal homeomorphisms and dynamics III:
The Teichmüller space of a rational map
Mixing, counting and equidistribution in Lie groups
Frontiers in complex dynamics
1989-1992
Riemann surfaces and the geometrization of 3-manifolds
Amenable coverings of complex manifolds and
holomorphic probability measures
Rational maps and Kleinian groups
Geometrically finite rational maps and Kleinian groups (problems)
Rational maps and Teichmüller space (problems)
Multiple intersections on negatively curved surfaces
Cusps are dense
Iteration on Teichmüller space
Amenability, Poincaré series and quasiconformal maps
1984-1989
The spectral geometry of flat disks
Solving the quintic by iteration
Braiding of the attractor and the failure of iterative algorithms
Automorphisms of rational maps
Quasiconformal isotopies
Area and Hausdorff dimension of Julia sets of entire functions
Families of rational maps and iterative root-finding algorithms
The motion of the maximal measure of a polynomial
Prime implicants, minimum covers, and the complexity of logic simplification
Simultaneous uniformization of Blaschke products
Hausdorff dimension of general Sierpiński carpets
The Pisot-Vijayaraghavan Numbers
Books
Renormalization and 3-Manifolds which Fiber over the Circle, 1996
Complex Dynamics and Renormalization, 1994
Logic Minimization Algorithms for VLSI Synthesis, 1984
Course Notes
Sets, Groups and Knots
Real Analysis
Topology and Fundamental Group
Probability Theory
Advanced Real Analysis
Advanced Complex Analysis
Complex Analysis on Riemann Surfaces
Riemann Surfaces, Dynamics and Geometry
Ergodic Theory, Geometry and Dynamics
From Conformal Invariants to Percolation
Algebra and Dynamics
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