### Naomi Andrew

University of Oxford

Thursday 12 October 2023, 4.00pm – 5.00pm

Lecture Theatre D (Mathematical Institute)

** Centralisers in outer automorphism groups **

Given a group *G*, we can ask about its subgroups. Centralisers of elements are easy to define, but maybe not so easy to understand: even in such well studied groups as Out(*F _{n}*) they are not yet understood in general. I'll discuss work with Armando Martino where we extend what is known in Out(

*F*), 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 as time allows I'll discuss ongoing work (with Gilbert Levitt and Armando Martino) exploring these possibilities.

_{n}
series: Pure Mathematics Colloquium

organiser: Scott Harper