Exponential mixing and spectral gaps in infinite volume

Abstract: Classically, the dynamics of geodesic and frame flows were studied for compact (and more generally, for finite volume) hyperbolic manifolds, and heavily relied on spectral gaps and representation theory. In recent decades, there have been many developments for infinite volume hyperbolic manifolds, in particular for exponential mixing. In this setting, It turns out that representation theory has limitations and Dolgopyat-type techniques are advantageous. Having established exponential mixing, it is then interesting to go in the reverse direction and look at spectral gaps and representation theoretic results. I plan to talk about some older work and a recent joint work with Dubi Kelmer and Osama Khalil to confirm a conjecture of Mohammadi--Oh.

number theoryrepresentation theory

Audience: researchers in the topic

University of Utah Representation Theory / Number Theory Seminar