Divergence in Coxeter Groups

Explore the concept of divergence in Coxeter groups through this 49-minute lecture by Ignat Soroko from Florida State University. Delve into the fascinating world of metric spaces and learn how divergence functions as a quasi-isometry invariant, measuring the separation of geodesic rays outside a ball of radius r. Discover the historical context of divergence in symmetric spaces and Gromov's conjecture about CAT(0) spaces. Uncover the rich spectrum of possible divergence functions in groups, challenging previous assumptions. Examine the groundbreaking research conducted by Soroko and colleagues on divergence in general Coxeter groups. Learn about the innovative 'hypergraph index' and its role in characterizing linear, quadratic, and exponential divergence in Coxeter groups. Gain insights into when a Coxeter group's divergence is bounded by a polynomial, expanding your understanding of this complex mathematical concept.