Séminaires : Séminaire de Systèmes Dynamiques

Equipe(s) : gd,
Responsables :H. Eliasson, B. Fayad, R. Krikorian, P. Le Calvez
Email des responsables :
Salle : 15-25-502
Adresse :Campus Pierre et Marie Curie

Archive avant 2015

Hébergé par le projet Géométrie et Dynamique de l’IMJ

Orateur(s) Anton Zorich - IMJ-PRG,
Titre Masus-Veech volumes, square-tiled surfaces and count of multicurves and of meanders
Horaire14:00 à 15:45
RésumeThe Teichmuller geodesic flow in the moduli space of Abelian and quadratic differentials is a powerful tool in the study of measured foliations on surfaces, of billiards in rational polygons, of interval exchange transformations, to name only some applications. To obtain qualitative information based on ergodicity of the Teichmuller geodesic flow (like diffusion rate of Ehrensfest billiard or the error term in ergodic averages of interval exchanges) one has to know how to normalize the finite invariant measure for the Teichmuller geodesic flow. The total measure of the moduli space of Abelian or quadratic differentials is called the Masur-Veech volume of the corresponding space. One of the approaches to evaluation of the Masur-Veech volume is through count of square-tiled surfaces, analogous to count of integer points in a ball of huge radius $R$. In this talk I will present our approach to count of Masur-Veech volumes and of square-tiled surfaces. I will also explain the relations between this count and Mirzakhani's count of simple closed geodesic multicurves on hyperbolic surfaces. I will illustrate how this count allows to count meanders on surfaces of any genus g. This is a joint work with V. Delecroix, E. Goujard and P. Zograf.
AdresseCampus Pierre et Marie Curie