AMR-RMA
Recent Mathematical Advances Distinguished Lecture Series
December 9, 2025
8:00 AM (Los Angeles), 11:00 AM (Montreal, New York), 4:00 PM (London) 5:00 PM (Leipzig, Madrid, Paris) 6:00 PM (Tel-Aviv)
Nalini Anantharaman
University of Strasbourg
TITLE: Optimal spectral gap of the Laplacian for random hyperbolic surfaces
Abstract
Although there are several ways to ”choose a compact hyperbolic surface at random”, putting the Weil-Petersson probability measure on the moduli space of hyperbolic surfaces of a given topology is certainly the most natural.
The work of M. Mirzakhani has made possible the study of this probabilistic model: it is one of the only models of ”random Riemannian manifolds” where some explicit calculations are actually possible. One may thus ask questions about the geometry and the spectral statistics of the Laplacian of a randomly chosen surface – in analogy with what is usually asked for models of random graphs.
I will be interested in the spectral gap of the Laplacian for a random compact hyperbolic surface, in the limit of large genus (joint with Laura Monk).
Video of the Lecture
Will be posted following the lecture.
About the speaker
References and Related material
- Growth of Weil-Petersson Volumes and Random Hyperbolic Surface of Large Genus, Maryam Mirzakhani J. Differential Geom. 94(2): 267-300 (June 2013).
- Spectral gap of random hyperbolic surfaces, Nalini Anantharaman, Laura Monk https://arxiv.org/abs/2403.12576