##### Department of Mathematics,

University of California San Diego

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

### Postdoc Seminar

## Dr. Pratyush Sarkar

#### UCSD

## Exponential mixing of frame flows for geometrically finite hyperbolic manifolds

##### Abstract:

Let $\Gamma < G = \operatorname{SO}(n, 1)^\circ$ be a Zariski dense torsion-free discrete subgroup for $n \geq 2$. Then the frame bundle of the hyperbolic manifold $X = \Gamma \backslash \mathbb{H}^n$ is the homogeneous space $\Gamma \backslash G$ and the frame flow is given by the right translation action by a one-parameter diagonalizable subgroup of $G$. Suppose $X$ is geometrically finite, i.e., it need not be compact but has at most finitely many ends consisting of cusps and funnels. Endow $\Gamma \backslash G$ with the unique probability measure of maximal entropy called the Bowen-Margulis-Sullivan measure. In a joint work with Jialun Li and Wenyu Pan, we prove that the frame flow is exponentially mixing.

### May 4, 2023

### 3:00 PM

APM 5829

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