Back to Departmental Colloquium: Spring 2022
Departmental Colloquium
Date: Thursday, Jan 13, 2022
Time: 4:00PM
Location: JWB 335
Wenyu Pan
University of Chicago
Title |
Exponential mixing of flows for geometrically finite hyperbolic manifolds with cusps |
Abstract |
Let \mathbb{H}^n be the hyperbolic n-space and \Gamma be a geometrically finite discrete subgroup in Isom_{+}(\mathbb{H}^n) with parabolic elements. We investigate whether the geodesic flow (resp. the frame flow) over the unit tangent bundle T^1(\Gamma\backslash \mathbb{H}^n) (resp. the frame bundle F(\Gamma\backslash \mathbb{H}^n)) mixes exponentially. This result has many applications, including spectral theory, prime geodesic theorems, orbit counting, equidistribution, etc. I will start with a survey of the past results, methods, and related problems on this topic. Along the way, I will present the joint work with Jialun Li, Pratyush Sarkar. |
Topology