Tuomas Sahlsten (Manchester)

Delocalisation of waves under scaling limits

We establish quantitative quantum ergodicity type delocalisation theorem for waves on hyperbolic surfaces of large genus. In the compact setting our assumptions hold for random surfaces in the sense of Weil-Petersson volume in the Teichm├╝ller space due to the work of Mirzakhani and in non-compact setting for arithmetic surfaces coming from congruence covers of the modular surface. The methods are based on Benjamini-Schramm scaling limits of metric measure spaces and Stein type harmonic analysis ergodic theorems, and are inspired by similar results on graphs. We plan to give a gentle introduction to the field before going to our results. Joint work with Etienne Le Masson (Cergy-Pontoise University, France).