EVENT DETAILS AND ABSTRACT

Title: Exponential mixing of flows for geometrically finite hyperbolic manifolds with cusps
Speaker: Wenyu Pan
Speaker Info: U. Chicago
Brief Description: Part of Midwest Dynamics Conference
Special Note: Part of Midwest Dynamics Conference
Abstract:

Let H^n be the hyperbolic n-space and \Gamma be a geometrically finite discrete subgroup in Isom_{+}(H^n) with parabolic elements. We investigate whether the geodesic flow (resp. the frame flow) over the unit tangent bundle T^1(\Gamma\H^n) (resp. the frame bundle F(\Gamma\H^n)) mixes exponentially. This result has many applications, including spectral theory, orbit counting, equidistribution, prime geodesic theorems, etc.

In the joint work with Jialun LI, we show that the geodesic flow mixes exponentially. I will describe some ingredients in the proof. If there is time, I will also discuss the difficulty of obtaining exponential mixing of the frame flow.