Event № 631

Let G be a group and let r(n,G) denote the number of its n-dimensional complex irreducible representations up to isomorphism. Representation growth is a branch of asymptotic group theory that studies the asymptotic and arithmetic properties of the sequence (r(n,G)). Whenever the sequence grows polynomially it defines a Dirichlet generating function that converges on some right half-plane and known as the representation function of G. In this talk I will give an overview on the subject, describe some recent developments and mention some open problems.