Rankin Lecture 2024-25 - Random square-tiled surfaces and random multicurves in large genus
Professor Anton Zorich (University of Paris)
Friday 20th September 16:00-17:00
Abstract
The Rankin Lecture 2024-25, as part of the Distinguished Lecture Series in Mathematics & Statistics, will take you through a tour of the theory of surfaces by a world leading expert in the field, with a chance to ask questions over a wine reception afterwards.
The lecture, entitled Random square-tiled surfaces and random multicurves in large genus, will be given by Professor Anton Zorich (University of Paris) 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.
Add to your calendar
Download event information as iCalendar file (only this event)