10.01.2023

Anton Zorich (University Paris Cité)

Title

Random square-tiled surfaces of large genus and random multicurves on surfaces of large genus.

Abstract

I will remind how Maxim Kontsevich and Paul Norbury have counted metric ribbon graphs and how Maryam Mirzakhani has counted simple closed geodesic multicurves on hyperbolic surfaces. Both counts use Witten-Kontsevich correlators (they will be defined in the lecture with no appeals to quantum gravity).

I will present a 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 Amol Aggarwal, and the uniform large genus asymptotics of intersection numbers of Witten-Kontsevich correlators, proved by Aggarwal, combined with the results of Kontsevich, Norbury and Mirzakhani, allowed us to describe the
structure of a random multi-geodesic on a hyperbolic surface of large genus and of a random square-tiled surface of large genus (joint work with V. Delecroix, E. Goujard and P. Zograf).

Schedule

9:45 -  10:00 Common coffee | 5. OG, Common Room
10:00 - 11:30 RTG Lecture 1 (Ana Chavez Caliz) | 5. OG, Konferenzraum
11:30 - 12:00 Get-Together with speaker | 5. OG, Konferenzraum
12:00 - 13:00 Common lunch | reserved at BräuStadel
13:00 - 13:30 Informal meeting of PhD students | 5. OG, Common Room
13:30 - 14:30 RTG colloquium: Prof. Anton Zorich | EG Seminarraum B
14:30 - 15:30 Common tea | 5. OG, Common Room
15:30 - 17:00 RTG Lecture 2 (Wilderich Tuschmann)| 5. OG, Konferenzraum

HD