The divergence of a pair of geodesic rays in a metric space is a measure of how fast they spread apart. For example, in the Euclidean plane the divergence of any pair of geodesic rays is linear, while in the hyperbolic plane it is exponential. In the 1980s Gersten used this idea to formulate a large-scale invariant of groups, also called divergence, which has been investigated for many important families. We study divergence in Coxeter groups, which are groups generated by sets of "reflections". We use the geometry of spaces on which Coxeter groups act, the algebraic structure of certain families of their subgroups, and the combinatorics of their reduced words. This is joint work with Pallavi Dani, Yusra Naqvi and Ignat Soroko.
University of Sydney
Tuesday 14 March 2023, 12:05 pm