Representation growth of p-adic analytic groups

The representation growth of a group $G$ measures the asymptotic distribution of its 
irreducible representations.

Whenever the growth is polynomial, a suitable vehicle for studying it is a Dirichlet generating 
series called the representation zeta function of $G$.

One of the key invariants in this context is the abscissa of convergence of the representation 
zeta function. 
The spectrum of all abscissae arising across a given class of groups is of considerable 
interest and has been studied in some cases.

In the realm of $p$-adic analytic groups (with perfect Lie algebra), the abscissae of convergence 
are explicitly known only for groups of small dimensions. But there are interesting asymptotic 
results for 'simple' $p$-adic analytic groups of increasing dimension.  

In this talk, I will give an overview of the main tools and ingredients in this area and I will 
report on recent work joint with Moritz Petschick to enlarge the class of groups.