# 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 London, Oxford and Southampton, and organised by Martin Bridson and Henry Wilton. We have been awarded LMS Scheme 3 funding.

In 2013-14, the meetings will be as follows:

- 25 October 2013, UCL
- 6 December 2013, Southampton
- 21 February 2014, Warwick
- 9 May 2014, Oxford

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Here are some details of our next meeting.

## Friday 9th May, 2014

Location: Lecture Room 6, The Mathematical Institute, Andrew Wiles Building, Woodstock Road, Oxford.

### 1.15pm Cutting and pasting: a group for Frankenstein

Nicolas Monod (EPFL)

We know since almost a century that a ball can be decomposed into five pieces and these pieces rearranged so as to produce two balls of the same size as the original. This apparent paradox has led von Neumann to the notion of amenability which is now much studied in many areas of mathematics. However, the initial paradox has remained tied down to an elementary property of free groups of rotations for most of the 20th century. I will describe recent progress leading to new paradoxical groups.

### 2.30pm Embeddability between right-angled Artin groups and its relation to model theory and geometry

Montserrat Casals-Ruiz (Oxford)

In this talk we will discuss when one right-angled Artin group is a subgroup of another one and explain how this basic algebraic problem may provide answers to questions in geometric group theory and model theory such as classification of right-angled Artin groups up to quasi-isometries and universal equivalence.

### 4pm Some subgroups of topological Kac–Moody groups

Inna Capdeboscq (Warwick)

This talk is based on a joint work with B. Rémy (Lyon) in which we study some subgroups of topological Kac–Moody groups and the implications of this study on the subgroup structure of the ambient Kac–Moody group.