Wednesday 4 June 2014 h. 14:30, room 2BC30

Michele Zordan (Bielefeld)

"Introduction to representation growth"

Abstract

This seminar is intended as an accessible introduction to representation zeta functions. Given a group, representation zeta functions are Dirichlet generating functions encoding the numbers of its irreducible representations sorted by dimension.

This analytic tool allows the use of analytic methods to compute the rate of growth of the numbers of irreducible representations as their dimension grows.

Much akin to the Riemann's zeta function, these representation zeta functions are often Euler's product of local factors. The computation of these factors, therefore, holds the key to understanding the representation growth of the group.

In this talk I shall introduce the subject with appropriate examples and discuss the methods that given a group allow us to compute the local factors.