Logic Seminar

I will explain a "local" spectral gap theorem for translation actions of dense subgroups generated by algebraic matrices on arbitrary simple Lie groups. This extends to the non-compact setting works of Bourgain-Gamburd and Benoist-de Saxce. I will also present several applications to the Banach-Ruziewicz problem, strong ergodicity of actions on homogenous spaces, orbit equivalence rigidity, and spectra of averaging operators on compact groups. This is joint work with Remi Boutonnet and Alireza Salehi-Golsefidy.