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:

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 1 March, 2019

Location: University of Warwick, Zeeman Building, MS.05

1:15-2:15 TITLE

Nicholaus Heuer (Oxford)

ABSTRACT

2:30-3:30 Sofic approximations — what’s the problem?

Andreas Thom (Dresden)

I am planning to give a general introduction to sofic groups, mention a few applications to fundamental conjectures about groups and group rings, and explain Misha Gromov’s conjecture that all groups are sofic. Finally I want to present a natural generalization of Gromov’s conjecture due to Laszlo Lovasz and Balasz Szegedy that has recently been disproved in joint work with Gabor Kun.

4:00-5:00 GGSE/Warwick Mathematics Colloquium: Building more automatic structures for groups

Sarah Rees (Newcastle)

I'm talking about some new composition theorems for automatic groups, joint work with Hermiller, Holt and Susse, specifically relating to HNN extensions, amalgamated products, and more generally graphs of groups that are (coset) automatic relative to appropriate subgroups.

The concept of automaticity for a group was introduced by Thurston in the late 1980's, based on properties of the groups of compact hyperbolic 3-manifolds that had been identified by Cannon, which in particular facilitated computation with these groups. Automatic groups are finitely presented, with recognisable normal forms and word problem soluble in quadratic time, and if biautomatic they have soluble conjugacy problem. A number of properties of closure and composition for this class of groups were proved almost immediately after its definition; hence in particular the fundamental group of most (but certainly not all) compact 3-manifolds could be proved automatic.

I'll provide some background on the subject of automatic groups, providing some motivation and summarising what is known, what is open, and what cannot be true of groups in this class. I'll define Holt and Hurt's related concept of coset automaticity. And I'll provide some details of the methods we used to provide our recent results, and describe a few groups for which our results give automatic structures, where none were previously known.

5:00-6:30 Wine and cheese

6:30-8:30 Dinner. Get in touch with Saul.

Reimbursements

There is travel money available for speakers and students. Please fill out this form and send it, along with receipts, to
Lars Louder
Dept of Mathematics
University College London
Gower St
London
WC1E 6BT