Time: 14:00-15:00, Thursday, May 23 2024

Venue: E4-233

Host: Thierry De Pauw, ITS

Speaker: Adrien Boyer, Université Paris Cité

Biography: Professor Boyer was a student at the Ecole Normale Supérieure, Lyon. He graduated with a Phd from Aix-Marseille Université, under the direction of Christophe Pittet in 2014. He spent three years as a postdoctoral fellow in Israel; at the Technion and at the Weizmann Institute of Sciences. He joined the Université Paris Diderot (now Paris Cité) in 2017 as an Associate Professor.

Title: On some aspects of boundary representations

Abstract: I will discuss, in the case of the group SL(2,R), some aspects of boundary representations. Such a group acts naturally on its symmetric space. This action extends to the boundary on which almost all irreducible unitary representations can be realized. All these representations restrict to some interesting discrete subgroups: the lattices in SL(2,R). I will try to explain the interplay between ergodic theory, potential theory, and spectral estimates to obtain an ergodic theorem "à la von Neumann" for boundary representations. If time permits, I will discuss generalizations to other contexts of these tools and state some open conjecture.