Martin Finn-Sell: C*-exactness and almost quasi-isometric embeddings into groups

In this talk I will discuss families of finite graphs of large girth and the role they play in constructing groups that are not C*-exact. In particular, I will describe a permanence result concerning coarse amenability for the types of maps, called almost quasi-isometries, that occur in the probabilistic construction of Gromov. In the remaining time, I will indicate how these ideas interact with the Baum-Connes conjecture for discrete groups.