Eigenfunctions on random hyperbolic surfaces

Abstract: High frequency eigenfunctions on hyperbolic surfaces are known to exhibit some universal behaviour of delocalisation and randomness. We will introduce some results on the behaviour of eigenfunctions on random compact hyperbolic surfaces, in the limit where the genus (or equivalently the volume) tends to infinity, and the frequency is in a fixed window. These results suggest that in this large scale limit we can expect similar universal behaviour. We will focus on the Weil-Petersson model of random surfaces introduced by Mirzakhani.

Based on joint works with Tuomas Sahlsten and Joe Thomas.

analysis of PDEsnumber theoryrepresentation theory

Audience: researchers in the topic

Harmonic Analysis and Symmetric Spaces 2021