Half-twists and equations in genus 2.
Harmonic diffeomorphisms and Teichmüller theory.
Harmonic Maps of the Moduli Space of Compact Riemann Surfaces.
Holomorphic Families of Open Riemann Surfaces.
Holomorphic Maps of Compact Riemann Surfaces Into 2-Dimensional Compact C-Hyperbolic Manifolds.
Homology of origamis with symmetries
Given an origami (square-tiled surface) with automorphism group , we compute the decomposition of the first homology group of into isotypic -submodules. Through the action of the affine group of on the homology group, we deduce some consequences for the multiplicities of the Lyapunov exponents of the Kontsevich-Zorich cocycle. We also construct and study several families of interesting origamis illustrating our results.
Hyperbolic spaces in Teichmüller spaces
We prove, for any , that there is a closed connected orientable surface so that the hyperbolic space almost-isometrically embeds into the Teichmüller space of , with quasi-convex image lying in the thick part. As a consequence, quasi-isometrically embeds in the curve complex of .