Analysis and Probability Seminar

Abstract: The analytic torsion of a compact Riemannian manifold was introduced by Ray and Singer in the 70s to spectrally study the combinatorial Reidemeister torsion of the manifold. More recently, Bergeron, Venkatesh and others applied this to study torsion in the (co-)homology of cocompact arithmetic lattices in families. This is of number theoretic interest as such torsion classes are (expected to be) related to certain Galois representations. 

It is thus of interest to try to extend the definition of analytic torsion to non-compact locally symmetric spaces in a suitable way. The rank one (hyperbolic) case has been relatively well understood for a while, but the higher rank case comes with many new analytic difficulties. In this talk, I want to discuss some of the history and motivation for studying torsion, and then talk about some joint work with W. Mueller where we define the notion of analytic torsion for congruence quotients of SL(n,R)/SO(n).