Seminario Teoría de grupos 10/03

11:30 Aula Naranja ICMAT

Speaker: Matteo Vannacci (University of the Basque Country)

Title: Representations over finite fields, Probability and Zeta Functions

Abstract: In this talk we will study representation growth of a profinite group G over finite fields. On one hand, having "asymptotically few" representations over finite fields connects to (surprising) probabilistic generation properties of the completed group-ring of G. On the other hand, we can encode the number of representations of G over finite fields into a zeta-function and we will investigate how analytic properties of this zeta-function connect to properties of the original group G and its completed group-ring. This is joint work with Ged Corob-Cook and Steffen Kionke.