AMR-RMA

Recent Mathematical Advances Distinguished Lecture Series

April 9, 2024

9:00 AM (Los Angeles), 12:00 PM (Montreal, New York), 5:00 PM (London) 6:00 PM (Madrid, Paris) 7:00 PM (Tel-Aviv)

Anton Zorich

Institut Mathématique de Jussieu

TITLE: Random square-tiled surfaces and random multicurves in large genus

Video of the lecture (coming)

Abstract

(after joint works with V. Delecroix, E. Goujard and P. Zograf)

We will start with a count of metric integer ribbon graphs (after Kontsevich and Norbury). The answer is expressed in terms of Witten-Kontsevich correlators, which will be introduced in the talk (and which should not scare the audience in advance). Having counted ribbon graphs, we will count square-tiled surfaces. In this way we will secretly count Masur-Veech volume of the moduli space of quadratic differentials, but this would, mostly remain as a secret. We will move to Mirzakhani’s count of simple closed geodesics on hyperbolic surfaces. At first glance, it might seem unrelated to the previous count. We will see, however, that the two counts are equivalent. We will proceed with a description of random geodesic multicurves and of random square-tiled surfaces in large genus. We will conclude with a universal asymptotic formula for the Witten-Kontsevich correlators predicted by Delecroix, Goujard, Zograf and myself and recently proved by Amol Aggarwal. I will do my best to make the talk self-contained and accessible to everybody.

About the speaker

Anton Zorich, Distinguished Professor at the Institut Mathématique de Jussieu,  made major contributions to the exploration of the moduli space of Riemann surfaces from the geometric, topological, and dynamical perspectives. Zorich’s honors include an invited talk at the ICM 2006, senior membership at the  Institut Universitaire de France (2011–2016), and Chern visiting professorship at MSRI, Berkeley (2019). Zorich’s discoveries, including the Kontsevich-Zorich cocycle, were discussed at the Bourbaki seminar in 2003 and 2012.

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Scientific committee of the AMR-RMA

Anna Felikson

Daniel Peralta Salas

Iosif Polterovich

Leonid Polterovich

Durham University, UK

ICMAT, Madrid, Spain

Université de Montréal, Canada

Tel Aviv University, Israel