Rankin Lecture 2024/25

The School of Mathematics and Statistics invites you to

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.

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.

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.

Host or Publisher Mathematics & Statistics, University of Glasgow