## Dynamics, Geometry, & Groups Seminar

### Thursday, November 19th, 2020

**Time:** 2:00 p.m** Place:**

**Speaker:** Elia Fioravanti (Max Planck Institute for Mathematics and at the University of Bonn)

**Title:** Coarse-median preserving automorphisms of special groups.

**Abstract:** We introduce the class of "coarse-median preserving" automorphisms of coarse median groups. For instance, we show that automorphisms of right-angled Artin groups are coarse-median preserving if and only if they are untwisted (in the sense of Charney-Stambaugh-Vogtmann), while all automorphisms of hyperbolic groups are coarse-median preserving. Our main result is that, for every special group G (in the sense of Haglund-Wise), every infinite-order, coarse-median preserving outer automorphism of G can be realised as a homothety of a finite-rank median space X equipped with a ``moderate'', isometric G-action. This generalises Paulin's result that every infinite-order outer automorphism of a hyperbolic group G can be realised as a homothety of a real tree equipped with a small, isometric G-action."]