University of Cambridge > Talks.cam > Junior Geometry Seminar > Understanding automorphisms through actions on trees

Understanding automorphisms through actions on trees

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  • UserNaomi Andrew, Oxford University
  • ClockFriday 25 November 2022, 16:00-17:00
  • HouseMR13.

If you have a question about this talk, please contact Macarena Arenas.

On some level, group theory is the study of “symmetries of something”, so it becomes tempting to investigate the automorphisms (symmetries) of a given group. These automorphism groups can have some surprising behaviour: for instance, changing a single integer in the presentation of a Baumslag–Solitar group can turn a finite outer automorphism group into one which is not even finitely generated.

I will introduce Bass–Serre theory, the study of group actions on trees, and discuss how these actions can provide information about the automorphisms of your group. As time allows, I will also introduce joint work with Armando Martino where we apply these techniques to certain groups related to Out(F_n).

This talk is part of the Junior Geometry Seminar series.

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