Metric-Functional Boundary of Cayley Graphs

Explore the horofunction boundary of metric spaces in this 37-minute lecture from the Workshop on "Geometric and Asymptotic Group Theory with Applications 2023 - Groups and Dynamics" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the study of "small" finitely generated groups and their Cayley graph structures, with a focus on the Gap Conjecture by Grigorchuk. Learn about the characterization of finitely generated groups with linear growth and their relation to finite Busemann boundaries. Gain insights from joint works with L. Ron-George and M. Tointon, with all concepts thoroughly explained for audiences without prior knowledge.