On Wednesday the 16th of December 2020, Michele Zordan (Imperial College London) will be giving an online seminar at the Charlotte Scott Centre for Algebra at the University of Lincoln. His talk will be at 3pm and the details of his talk are as follows:

Title: Rationality of the representation zeta function for compact $p$-adic analytic groups.

Abstract:

Let $\Gamma$ be a topological group such that the number $r_n(\Gamma)$ of its irreducible continuous complex characters of degree $n$ is finite for all $n\in\mathbb{N}$. One goal in studying a sequence of numbers is to show that it has some sort of regularity. Working with zeta functions, this amounts to showing that the Dirichlet generating function related to that sequence is rational. Rationality results for the zeta function related to $r_n$ have been first obtained by Jaikin-Zapirain for FAb $p$-adic analytic groups and for almost all primes $p$. In this talk we shall see a new unified proof (joint work with Stasinski) giving rationality without restriction on the prime. The argument combines model theory and group cohomology of pro-$p$ groups, and (with the necessary extensions) it can be expanded to encompass representation zeta functions of a larger class of groups.

Reblogged this on Maths & Physics News.

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