Title: Divergence in groups with micro-supported actions

Abstract: The divergence of a group is a quasi-isometry invariant that measures how difficult it is to connect two points avoiding a large ball around the identity. It is easy to see that it is linear for direct products of infinite groups, and from that to deduce that it is linear for branch groups. In this talk, I will discuss divergence for weakly branch groups and, more in general, groups with a micro-supported action by homeomorphisms on a topological space. This is ongoing joint work with D. Francoeur and T. Nagnibeda.