Conjugacy growth and languages in groups (Laura Ciobanu, Heriot-Watt)

02.05.2023 10:30

Conjugacy growth in groups has been studied, from a geometric perspective, for many decades. Initially, the growth of conjugacy classes naturally occurred while counting closed geodesics (up to free homotopy) on complete Riemannian manifolds, as formulas for the number of such geodesics give, via quasi-isometry, good estimates for the number of conjugacy classes in the manifolds’ fundamental groups. More recently, the study of conjugacy growth has expanded to groups of all flavours, such as nilpotent, graph and wreath products, Baumslag-Solitar, and more.

In this talk I will give an overview of what is known about conjugacy growth and the formal series associated with it in infinite discrete groups. I will highlight how the rationality (or rather lack thereof) of these series is connected to both the algebraic and the geometric nature of groups such as (relatively) hyperbolic or nilpotent, and how tools from analytic combinatorics can be employed in this context. Time permitting, I will also mention results about the languages of conjugacy representatives in various groups.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Tuesday 02.05.2023, Séminaire "Groupes et géométrie"

entrée libre