Divergence in Coxeter groups

Anne Thomas
Sydney

Abstract

The divergence of a pair of geodesic rays measures how fast they move away from each other. In the 1990s, Gersten used this idea to define a quasi-isometry invariant for finitely generated groups, also called divergence, and divergence has since been investigated for many families of groups of importance in geometric group theory. In this talk, we discuss progress on understanding divergence in (infinite) Coxeter groups. The right-angled case is now well-understood, and we have a partly conjectural picture for general Coxeter groups. This includes joint work and work-in-progress with Pallavi Dani, Max Mikkelsen, Yusra Naqvi and Ignat Soroko.