Lecture Preview: Spectral gaps of random hyperbolic surfaces
Publication Time:2026-03-09
Title: Spectral gaps of random hyperbolic surfaces
Time: March 12, 16:00
Place: Room 511, Lide Building
Abstract: Based on joint work with Davide Macera and Joe Thomas.
The first non-zero eigenvalue, or spectral gap, of the Laplacian on a closed hyperbolic surface encodes important geometric and dynamical information about the surface.
We study the size of the spectral gap for random large genus hyperbolic surfaces sampled according to the Weil-Petersson probability measure.
We show that there is a c>0 such that a random surface of genus g has spectral gap at least 1/4-O(g^-c) with high probability.
Our approach adapts the polynomial method for the strong convergence of random matrices, introduced by Chen, Garza-Vargas, Tropp and van Handel, and its generalization to the strong convergence of surface groups by Magee, Puder and van Handel, to the Laplacian on Weil-Petersson random hyperbolic surfaces.
RESUME: Will Hide is the Titchmarsh Fellow at the University of Oxford. He received his PhD from Durham University in 2024 under the supervision of Michael Magee. His research focuses on geometry and spectral theory, with publications appearing in journals including Ann. of Math., Int. Math. Res. Not., Comment. Math. Helv., and Commun. Math. Phys.
