#### 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.

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