Title: A uniform spectral gap for congruence covers of arithmetic hyperbolic manifolds
Speaker: Lior Silberman
Speaker Info: UBC
Special Note: The speaker will give a preseminar talk for graduate students at 11 am in Lunt 102.
I will describe work with Dubi Kelmer on the first Laplace eigenvalue in towers of manifolds covered by real or complex hyperbolic n-space. All congruence quotients in a given dimension have a uniform spectral gap; we show how to deduce from this a uniform spectral gap for the family of congruence covers of a fixed arithmetic (non-congruence) manifold. A key ingredient is a lower bound on the dimensions of irreducible representations of groups defined over finite local rings.Date: Monday, May 09, 2011