### Random walks and quasiconvexity in acylindrically hyperbolic groups

Geometry and Topology Seminar

23rd March 2021, 2:00 pm – 3:00 pm

Zoom seminar, if interested, please email one of the organisers to gain access to the Zoom link

The properties of a random walk on a group which acts on a hyperbolic metric space have been well-studied in recent years. In this talk, I will focus on random walks on acylindrically hyperbolic groups, a class of groups which includes mapping class groups, Out(F_n), and right-angled Artin and Coxeter groups, among many others. I will discuss how a random element of such a group interacts with fixed subgroups, especially so-called hyperbolically embedded subgroups. In particular, I will discuss when the subgroup generated by a random element and a fixed subgroup is a free product, and I will also describe some of the geometric properties of that free product. This is joint work with Michael Hull.

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