Conjugacy growth in groups

Laura Ciobanu (Heriot-Watt)

Abstract

In this talk I will discuss various aspects of conjugacy growth in several classes of groups, such as (acylindrically) hyperbolic, right-angled Artin, Baumslag-Solitar or wreath products. In particular, I will show that the conjugacy growth series of a hyperbolic group is rational if and only if the group is virtually cyclic, answering a question of Rivin.