05/10: Pratyush Sarkar
Generalization of Selberg’s 
theorem for convex cocompact thin subgroups of 
Abstract: Selberg’s theorem for congruence covers of the modular surface is a beautiful theorem which has a natural dynamical interpretation as uniform exponential mixing. Bourgain-Gamburd-Sarnak’s breakthrough works initiated many recent developments to generalize Selberg’s theorem for infinite volume hyperbolic manifolds. One such result is by Oh-Winter establishing uniform exponential mixing for convex cocompact hyperbolic surfaces. These are not only interesting in and of itself but can also be used for a wide range of applications including uniform resonance free regions for the resolvent of the Laplacian, affine sieve, and prime geodesic theorems. I will present a further generalization to higher dimensions and some of these immediate consequences.
theorem for congruence covers of the modular surface is a beautiful theorem which has a natural dynamical interpretation as uniform exponential mixing. Bourgain-Gamburd-Sarnak’s breakthrough works initiated many recent developments to generalize Selberg’s theorem for infinite volume hyperbolic manifolds. One such result is by Oh-Winter establishing uniform exponential mixing for convex cocompact hyperbolic surfaces. These are not only interesting in and of itself but can also be used for a wide range of applications including uniform resonance free regions for the resolvent of the Laplacian, affine sieve, and prime geodesic theorems. I will present a further generalization to higher dimensions and some of these immediate consequences.