Papers

Papers

Bibliography
2008: 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; Rational maps and Teichmüller space; 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; Prime implicants, minimum covers, and the complexity of logic simplification; Hausdorff dimension of general Sierpinski carpets

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

Complex Analysis on Riemann Surfaces

Riemann surfaces, dynamics and geometry

Hyperbolic manifolds, discrete groups and ergodic theory

Algebra and Dynamics

Curtis T McMullen