### Conjugacy growth in groups, geometry and combinatorics

Colloquia Seminar

9th November 2020, 4:15 pm – 5:15 pm

Fry Building, https://zoom.us/j/94815175876

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, ranging from nilpotent to linear to acting on cube complexes, and beyond.

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 groups acting on trees, and how tools from analytic combinatorics can be employed in this context.

The Zoom link for this meeting is https://zoom.us/j/94815175876

Please note that all participants are expected to abide by the Code of Conduct, which can be found at http://www.bristol.ac.uk/maths/working-environment/code-of-conduct/

*Biography:*

Dr. Laura Ciobanu is Associate Professor in the School of Mathematical and Computer Sciences at Heriot-Watt University. She received her PhD from Rutgers University in 2005, and held postdocs in Barcelona and Auckland. She was Swiss National Science Foundation Professor and Ambizione Fellow at the University of Neuchatel from 2012 to 2016.

*Organiser*: Ayalvadi Ganesh

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