Séminaires : Séminaire Géométrie et Topologie

Equipe(s) : aa, acg,
Responsables :B. Petri, A. Sambarino, S. Seyfaddini et M. Zavidovique
Email des responsables :
Salle : 15-25-502
Adresse :Campus Pierre et Marie Curie
Description

Ce séminaire s’adresse aux géomètres, topologues et dynamiciens au sens large. Il est rattaché aux équipes Analyse Algébrique et Analyse Complexe et Géométrie. Les exposés seront accessibles à une audience large, doctorants inclus. Il se tiendra à Jussieu, le jeudi à 11h, en salle 15-25 502. Le séminaire a l'agenda google suivante: https://calendar.google.com/calendar/b/0?cid=dDgzNTJoczNmdDhlMm5nb2IzMXJwaWpsdHNAZ3JvdXAuY2FsZW5kYXIuZ29vZ2xlLmNvbQ


Orateur(s) Anton Zorich - ,
Titre Masur-Veech volume of the moduli space of quadratic differentials, random square-tiled surfaces of large genus and random multicurves of surfaces of large genus
Date10/02/2022
Horaire11:00 à 12:00
Diffusion
RésumeIt is common in mathematics to study decompositions of compoundobjects into primitive blocks. For example, the Erdos-Kac Theorem describes the prime decomposition of a random integer number into prime factors. The Theorem of Goncharov describes the decomposition of a random permutation into disjoint cycles. I will present our formula for the asymptotic count of square-tiled surfaces of any fixed genus g tiled with at most N squares as N tends to infinity. This count allows, in particular, to compute Masur-Veech volumes of the moduli spaces of quadratic differentials. A deep large genus asymptotic analysis of this formula performed by Aggarwal and the uniform large genus asymptotics of intersection numbers of psi-classes on the moduli spaces of complex curves proved by Aggarwal allowed us to describe the decomposition of a random square-tiled surface of large genus into maximal horizontal cylinders. Our results imply, in particular, that with a probability which tends to 1, as genus grows, all ``corners'' of a random square-tiled surface live on the same horizontal and on the same vertical critical leave, and with probability 71% a random square-tiled surface is composed of a single horizontal band of squares. (joint work with V. Delecroix, E. Goujard and P. Zograf)
Salle15-25-502
AdresseCampus Pierre et Marie Curie
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