| Speaker: Anne Thomas Affiliation: University of Sydney Time: 15:00 Thursday, 5 August, 2021 Location: MLT3/303-101 |
| The divergence of a pair of geodesic rays is a measure of how fast they spread apart. For example, in Euclidean space the divergence of any pair of geodesic rays is linear, while in hyperbolic space it is exponential. In the 1980s Gersten used this idea to formulate a quasi-isometry invariant, also called divergence, which has been investigated for many important families of groups. We begin the study of divergence for arbitrary Coxeter groups, by formulating a combinatorial invariant of Coxeter systems called hypergraph index. We show that hypergraph index gives an upper bound on the divergence rate and conjecture that it gives a lower bound as well. This is joint work with Pallavi Dani, Yusra Naqvi and Ignat Soroko. |