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 2019-20, 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 13 December, 2019

Location: Building 56 "Mathematics Student Centre", Highfield Campus, University of Southampton.

1:30-2:30 On Finitely Presented Groups that Contain Q

James Belk (University of St Andrews)

It is a consequence of Higman's embedding theorem that the additive group Q of rational numbers can be embedded into a finitely presented group. Though Higman's proof is constructive, the resulting group presentation would be very large and ungainly. In 1999, Pierre de la Harpe asked for an explicit and "natural" example of a finitely presented group that contains an embedded copy of Q. In this talk, we describe some solutions to de la Harpe's problem related to Thompson's groups F, T, and V. Moreover, we prove that there exists a group containing Q which is simple and has type F infinity. This is joint work with J. Hyde and F. Matucci.

2:40-3:40 Ramification structures for quotients of generalised Grigorchuk-Gupta-Sidki groups

Anitha Thillaisundaram (University of Lincoln)

Groups of surfaces isogenous to a higher product of curves can be characterised by a purely group-theoretic condition, which is the existence of a so-called ramification structure. Gul and Uria-Albizuri showed that quotients of the periodic Grigorchuk-Gupta-Sidki groups, GGS-groups for short, admit ramification structures. We extend their result by showing that quotients of generalisations of the GGS-groups also admit ramification structures, with some deviations for the case p=2. This is joint work with Elena Di Domenico and Sukran Gul.

3:40-4:00 TEA

4:00-5:00 Commensurability of Baumslag-Solitar groups

Alexander Zakharov (Chebyshev Laboratory, Saint Petersburg State University)

Two groups are called commensurable if they have isomorphic subgroups of finite index. In particular, finitely generated commensurable groups are quasi-isometric. Baumslag-Solitar groups form an interesting and important class of one-relator groups with unusual properties. While the quasi-isometry classification for them was known previously, due to Farb, Mosher and Whyte, the commensurability classification was not. In joint work with Montse Casals-Ruiz and Ilya Kazachkov we fill this gap by providing a complete commensurability classification of Baumslag-Solitar groups.

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

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