Number Theory – Representation Theory Seminar

Nir Avni, Northwestern. Abstract: I will talk about connections between the following: 1) Asymptotic representation theory of an arithmetic lattice G(Z). More precisely, the question of how many n-dimensional representations does G(Z) have. 2) The distribution of a random commutator in the p-adic analytic group G(Z_p). 3) The complex geometry of the moduli spaces of G-local systems on a Riemann surface, and, more precisely, the structure of its singularities.