Jonas Flechsig: The automorphism group of the universal Coxeter group
Coxeter groups are groups with 'nice and symmetric' presentations. In my talk we want to study the automorphism group of a Coxeter group which is isomorphic to a free product \(\frac{\mathbb{Z}}{2\mathbb{Z}} \ast \cdots \ast \frac{\mathbb{Z}}{2\mathbb{Z}}\). In the first part of the talk we will look at algebraic properties of the automorphism group. In particular we will give an embedding into another automorphism group and we will study representations. The second part will focus on geometric properties–more precisely fixed point properties–of the automorphism group. We will investigate the question whether 'nice' actions on trees and \(\mathrm{CAT}(0)\) spaces have a fixed point.
