# 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 2018-19, the meetings will tentatively be as follows:

- 26 October 2018, UCL
- 30 November 2018, Southampton
- 1 March 2019, Warwick
- May 24 2019, Oxford

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

## Friday 24 May, 2019

Locatation: Oxford, Mathematical Institute, Room L5.

### 1:15--2:15 Isoperimetric inequalities of Groups and Isoperimetric Profiles of surfaces

Panos Papasoglu

It is an interesting question whether Gromov's `gap theorem' between a sub-quadratic and a linear isoperimetric inequality can be generalized in higher dimensions. There is some evidence (and a conjecture) that this might be the case for CAT(0) groups. In this talk I will explain how the gap theorem relates to past work of Hersch and Young-Yau on Cheeger constants of surfaces and of Lipton-Tarjan on planar graphs. I will present some related problems in curvature-free geometry and will use these ideas to give an example of a surface with discontinuous isoperimetric profile answering a question of Nardulli-Pansu. (joint work with E. Swenson)

### 2:30--3:30 Conjugacy growth in groups, geometry and combinatorics

Laura Ciobanu

In this talk I will give an overview of what is known about conjugacy growth and the formal series associated with it in infinite discrete groups. I will highlight how the rationality (or rather lack thereof) of these series is connected to the geometry of groups such as (relatively) hyperbolic, groups acting on trees, or graph products, and how tools from analytic combinatorics can be employed in this context.

### 3:30--4:15 Tea/coffee

### 4:15--5:15 CAT(0) groups need not be biautomatic

Ian Leary

Ashot Minasyan and I construct (or should that be find?) examples of groups that establish the result in the title. These groups also fail to have Wise's property: they contain a pair of elements no powers of which generate either a free subgroup or a free abelian subgroup. I will discuss these groups.

# 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