##### Department of Mathematics,

University of California San Diego

****************************

### Math 211B - Group Actions Seminar

## Osama Khalil

#### University of Utah

## Mixing, Resonances, and Spectral Gaps on Geometrically Finite Manifolds

##### Abstract:

I will report on work in progress showing that the geodesic flow on any geometrically finite, rank one, locally symmetric space is exponentially mixing with respect to the Bowen-Margulis-Sullivan measure of maximal entropy. The method is coding-free and is instead based on a spectral study of transfer operators on suitably constructed anisotropic Banach spaces, ala Gouezel-Liverani, to take advantage of the smoothness of the flow. As a consequence, we obtain more precise information on the size of the essential spectral gap as well as the meromorphic continuation properties of Laplace transforms of correlation functions.

Host: Brandon Seward

### April 28, 2022

### 10:00 AM

Zoom ID 967 4109 3409

Email an organizer for the password

****************************