January 10th, 2023

Date:
10.01.2023

Speaker:
Anton Zorich (University Paris Cité)

Title
Random squaretiled 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 WittenKontsevich correlators (they will be defined in the lecture with no appeals to quantum gravity).
I will present a formula for the asymptotic count of squaretiled surfaces of any fixed genus g tiled with at most N squares as N tends to infinity. This count allows, in particular, to compute MasurVeech 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 WittenKontsevich correlators, proved by Aggarwal, combined with the results of Kontsevich, Norbury and Mirzakhani, allowed us to describe the
structure of a random multigeodesic on a hyperbolic surface of large genus and of a random squaretiled 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 GetTogether 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

Place:
HD