09/28: Alireza Salehi Golsefidy
Two new concepts for compact groups: Spectral independence and local randomness
Abstract: I will explain two new concepts for compact groups mentioned in the title. Their basic properties and their connections with the FAb property, quasi-randomness, and super-approximation will be outlined. I will present how these ideas help us show that a Borel probability measure m on the product of compact open subgroups of two locally non-isomorphic simple analytic groups has spectral gap when its projection to each factor has. (Joint work with Keivan Mallahi-Karai and Amir Mohammadi)