Rankin Lecture 2024/25: Random square-tiled surfaces and random multicurves in large genus
Rankin Lecture 2024/25: Random square-tiled surfaces and random multicurves in large genus
Distinguished Lecture Series of the School of Mathematics & Statistics
Date: Friday 20 September 2024
Time: 16:00 - 17:00
Venue: LT 116, Mathematics & Statistics Building, UofG
Category: Public lectures, Academic events, Student events, Alumni events, Staff workshops and seminars
Speaker: Professor Anton Zorich
Website: rankin-lecture-2024-25.eventbrite.co.uk
The School of Mathematics and Statistics is delighted to invite you to its Rankin Lecture 2024-25 on Random square-tiled surfaces and random multicurves in large genus to be given by Professor Anton Zorich (University of Paris). This lecture will be held in-person on Friday, 20th September 2024, at 4:00pm in LT 116 of the Mathematics and Statistics Building, University of Glasgow, followed by a wine reception at 5:00pm.
To attend, please register in advance at:
https://rankin-lecture-2024-25.eventbrite.co.uk
Title: Random square-tiled surfaces and random multicurves in large genus
Speaker: Professor Anton Zorich, University of Paris
Date/Time: Friday 20th September 2024, 4pm with a wine reception to follow at 5pm
Location: LT 116 of the Mathematics and Statistics Building, University of Glasgow
About the speaker
Prof Anton Zorich is a Distinguished Professor of Mathematics, Institute of Mathematics of Jussieu, University of Paris 7 (Paris Diderot). He got his Phd in Moscow under the supervision of the late Fields medalist Sergei Novikov. He is a recipient of numerous accolades in mathematics such as the Decerf Prize of the French Mathematical Society and was an invited speaker at the International Congress of Mathematics in Madrid in 2006. Zorich is a leading expert in the theory of surfaces and his far reaching mathematical vision has spearheaded phenomenal advances in our understanding of surfaces, over the past two and a half decades.
Abstract
Moduli spaces of Riemann surfaces and related moduli spaces of quadratic differentials are parameterized by a genus g of the surface. Considering all associated hyperbolic (respectively flat) metrics at once, one observes more and more sophisticated diversity of geometric properties when genus grows. However, most of metrics, on the contrary, progressively share certain rules. Here the notion of “most of” has explicit quantitative meaning, for example, in terms of the Weil-Petersson measure. I will present some of these recently discovered large genus universality phenomena.
I will use count of metric ribbon graphs (after Kontsevich and Norbury) to express Masur-Veech volumes of moduli space of quadratic differentials through Witten-Kontsevich correlators. Then I will present Mirzakhani's count of simple closed geodesics on hyperbolic surfaces. We will proceed with description of random geodesic multicurves and of random square-tiled surfaces in large genus. I will conclude with a beautiful universal asymptotic formula for the Witten-Kontsevich correlators predicted by Delecroix, Goujard, Zograf and myself and recently proved by Amol Aggarwal.