Mikolaj Fraczyk : Benjamini-Schramm convergence for congruence arithmetic lattices

Posted by Wouter Van Limbeek , part of the Graduate Groups and Dynamics Seminar.

At

March 13, 2019, 4 p.m.

In

612 SEO

Abstract

I will explain the relation between Benjamini-Schramm convergence of sequences of locally symmetric spaces and certain bounds on the geometric side of the Arthur-Selberg trace formula. After giving a brief description of arithmetic congruence lattices I will sketch a proof of the Benjamini-Schammm convergence for sequences of congruence arithmetic hyperbolic 2 and 3 orbifolds. We will treat the number theoretic estimates as a black box and focus on the “ergodic” part of the proof, which is a nice application of the Borel density theorem for IRS’ses (joint work with Jean Raimbault).