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Speaker:

Margherita Piccolo
Affiliation:

Universität Düsseldorf
Date:

Wed, 02/11/2022 - 14:30 - 15:30
Location:

MPIM Lecture Hall
Parent event:

Number theory lunch seminar

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 $G$.

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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.

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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.
```

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