Abstract: I will describe a classical formula by Frobenius that computes moments of dimensions of irreducible representations of finite groups. This formula leads to a notion of zeta function of a group and to an interesting equivalence relation between groups.
I will then discuss the pro-finite version of this theory, concentrating on the group $SL_d(Z_p)$. It turns out that in this case the zeta function is related to the following analytic question:

"When a push-forward of a smooth measure under an algebraic map is continuous?".

This question, in turn, is related to the study of the singularities of certain moduli spaces. The talk is based on a recent work, joint with Nir Avni: http://arxiv.org/abs/1307.0371 and its continuation.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006