Centralising Outer Automorphisms

Given a group G, one can seek to understand (some of) its subgroups. Centralisers of elements are easy to define, but maybe not so easy to understand: even in such well studied groups as Out(Fn) they are not yet understood in general. I'll discuss recent work with Armando Martino where we extend what is known in Out(Fn), involving a (surprising?) connection to free-by-cyclic groups and their automorphisms as well as working with actions on trees. The strategies seem like they should apply in many more cases, and if time allows I'll discuss ongoing work (with Gilbert Levitt and Armando Martino) exploring these possibilities.