Congruence subgroups associated to the Monster.
Congruence subgroups of groups commensurable with of genus 0 and 1.
Congruence subgroups of ) of genus less than or equal to 24.
Connected components of the strata of the moduli spaces of quadratic differentials
In two fundamental classical papers, Masur [14] and Veech [21] have independently proved that the Teichmüller geodesic flow acts ergodically on each connected component of each stratum of the moduli space of quadratic differentials. It is therefore interesting to have a classification of the ergodic components. Veech has proved that these strata are not necessarily connected. In a recent work [8], Kontsevich and Zorich have completely classified the components in the particular case where the quadratic...
Conservative action and the horospheric limit set.
Constructing an automorphic form from the orbit of a transformation.
Convex bodies of constant width and the Apollonian metric.
Coordinates for Teichmüller spaces of -groups with torsion.
Correction to the paper: Simultaneous uniformisation.
Correction to "Two Generator Fuchsian Groups of Genus One".
Counting immersed surfaces in hyperbolic 3-manifolds.
Counting walks in a quadrant: a unified approach via boundary value problems
The aim of this article is to introduce a unified method to obtain explicit integral representations of the trivariate generating function counting the walks with small steps which are confined to a quarter plane. For many models, this yields for the first time an explicit expression of the counting generating function. Moreover, the nature of the integrand of the integral formulations is shown to be directly dependent on the finiteness of a naturally attached group of birational transformations...
Covering spaces of families of compact Riemann surfaces.
Cross ratios, Anosov representations and the energy functional on Teichmüller space
We study two classes of linear representations of a surface group: Hitchin and maximal symplectic representations. We relate them to cross ratios and thus deduce that they are displacing which means that their translation lengths are roughly controlled by the translations lengths on the Cayley graph. As a consequence, we show that the mapping class group acts properly on the space of representations and that the energy functional associated to such a representation is proper. This implies the existence...
Cross ratios, surface groups, and diffeomorphisms of the circle
This article relates representations of surface groups to cross ratios. We first identify a connected component of the space of representations into PSL(n,ℝ) – known as the n-Hitchin component– to a subset of the set of cross ratios on the boundary at infinity of the group. Similarly, we study some representations into associated to cross ratios and exhibit a “character variety” of these representations. We show that this character variety contains alln-Hitchin components as well as the set of...
Cusp algebras.
Cusp Forms and Eigenfunctions of the Laplacian.
Cyclic extensions of Schottky uniformizations.
Cyclic projective planes and Wada dessins.
Cylinders in Riemann surfaces