### Conjugacy growth in (some Artin) groups

Geometry and Topology Seminar

30th April 2024, 2:00 pm – 3:00 pm

Fry Building, 2.04

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.

I will then present recent work on the conjugacy growth of dihedral Artin groups, joint with Gemma Crowe.

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