# Zeta functions of nilpotent groups

### Ben Martin (University of Aberdeen)

Wednesday 30th September, 2015 16:00-17:00 Maths 522

#### Abstract

In asymptotic group theory, one associates to a group $\Gamma$ a sequence of numbers $a_n$ and studies the behaviour of $a_n$ as $n$ tends to infinity (for instance, $a_n$ can be the number of subgroups of $\Gamma$ of index $n$, or the number of isomorphism classes of irreducible complex representations of $\Gamma$ of degree $n$).  One way to do this is to use the $a_n$ as the coefficients of a zeta function $\zeta_\Gamma(s):= \sum_{n=1}^\infty a_n n^{-s}$, where $s$ is a complex parameter.  I will discuss subgroup and representation zeta functions of finitely generated nilpotent groups.  This involves ideas from model theory and $p$-adic integration.