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