讲座预告 | Spectral gaps of random hyperbolic surfaces
Title: Spectral gaps of random hyperbolic surfaces
Time: 3月12日下午4：00
Place: 立德楼511
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.
个人简介：Will Hide 是 Oxford University 的 Titchmarsh Fellow。他于 2024 年在 Durham University 获得博士学位，导师为 Michael Magee，研究方向为几何与谱理论，成果发表于 Ann. of Math., Int. Math. Res. Not., Comment. Math. Helv., Commun. Math. Phys. 等期刊。
