Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Geometry and spectrum of random hyperbolic surfaces

Laura Monk talk

**Date:** 15.03.21 **Time:** 15.00 - 16.15 **Room:** ETH HG G 19.2

The main aim of this talk is to present geometric and spectral properties of typical hyperbolic surfaces. More precisely, I will: - introduce a probabilistic model, first studied by Mirzakhani, which is a natural and convenient way to sample random hyperbolic surfaces - describe the geometric properties of these random surfaces - explain how one can deduce from this geometric information estimates on the number of eigenvalues of the Laplacian in an interval [a,b], using the Selberg trace formula.