Tsung-Hsuan Tsai

Parallel geodesics and minimal stable length in random groups

A random group is a group presentation with a randomly chosen set of relations. The first half of this talk is an introduction to random groups (which are mostly hyperbolic) and their most remarkable properties. In the second half, I will present the structure of parallel geodesics in the Cayley graphs of random groups and apply this result to show that the stable lengths of loxodromic elements in random groups cannot be smaller than 1.