Hauptseminar Geometrie

RTG Kolloquium "Random square-tiled surfaces of large genus and random multicurves on surfaces of large genus" Prof. Anton Zorich, University Paris Cité 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).

Dienstag, den 10. Januar 2023 um 13:30 Uhr, in INF205, SR B Dienstag, den 10. Januar 2023 at 13:30, in INF205, SR B

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. B. Pozzetti, Prof. P. Albers