# Groups and Geometry in the South East

This is a series of meetings, with the aim of bringing together the geometric group theorists in the South East of England. The meetings are sponsored by mathematicians from the Universities of Cambridge, London, Oxford, Warwick, and Southampton, and organised by Martin Bridson, Peter Kropholler, Lars Louder, Ashot Minasyan, Saul Schleimer, and Henry Wilton. We have been awarded LMS Scheme 3 funding.

In 2020-21, the meetings will tentatively be as follows:

- October 23 2020, UCL/Zoom
- December 11 2020, Southampton/Zoom
- March 26 2021, Warwick/Zoom
- June 18 2021, Oxford/Zoom

To get regular updates about GGSE, please send an email to ggse-join@ucl.ac.uk.

Abstracts and titles of previous talks are available here.

# Details of our next meeting

## Location: Oxford/Zoom, June 18 2021

### Tits Alternative in dimension 2

#### 1:30-2:30PM

Piotr Przytycki (McGill)

A group G satisfies the Tits alternative if each of its finitely generated subgroups contains a non-abelian free group or is virtually solvable. I will sketch a proof of a theorem saying that if G acts geometrically on a simply connected nonpositively curved complex built of equilateral triangles, then it satisfies the Tits alternative. This is joint work with Damian Osajda.

### Coarse-median preserving automorphisms

#### 2:45-3:45

Elia Fioravanti (Bonn)

We study fixed subgroups of automorphisms of right-angled Artin and Coxeter groups. If Phi is an untwisted automorphism of a RAAG, or an arbitrary automorphism of a RACG, we prove that Fix(Phi) is finitely generated and undistorted. Up to replacing Phi with a power, the fixed subgroup is actually quasi-convex with respect to the standard word metric (which implies that it is separable and a virtual retract, by work of Haglund and Wise). Our techniques also apply to automorphisms of hyperbolic groups and to certain automorphisms of hierarchically hyperbolic groups. Based on arXiv:2101.04415.

### Some new CAT(0) free-by-cyclic groups

#### 4:00-5:00PM

Rylee Lyman (Rutgers-Newark)

I will construct several infinite families of polynomially-growing automorphisms of free groups whose mapping tori are CAT(0) free-by-cyclic groups. Such mapping tori are thick, and thus not relatively hyperbolic. These are the first families comprising infinitely many examples for each rank of the nonabelian free group; they contrast strongly with Gersten's example of a thick free-by-cyclic group which cannot be a subgroup of a CAT(0) group.

# Reimbursements

There is travel money available for speakers and students. Please fill out this form and send it, along with receipts, to

Lars LouderDept of Mathematics

University College London

Gower St

London

WC1E 6BT

We are on a shoestring budget, so please try to minimize your travel costs!