Alladi Ramakrishnan Hall

Representation growth of arithmetic groups

Uri Onn

Australian National University

Representation growth is a branch of asymptotic group theory that studies
the arithmetic and asymptotic properties of sequences (r_n(G)), whose n-th term
enumerates the number of equivalence classes of n-dimensional irreducible
representations of a group G. For groups with polynomial representation growth one may
encode the representation growth sequence in a Dirichlet generating function, called the
representation zeta function. In this talk I will describe recent developments in the
study of representation zeta functions of arithmetic groups.