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 2021-22, 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

Southampton, December 2 2022

The meeting will take place in building 2, room 1085, and you can find a map of the campus here.

1:15-2:15: The conjugacy problem for ascending HNN-extensions of free groups

Alan Logan (St Andrews)

In this talk, I will explain how to solve the conjugacy problem for ascending HNN-extensions of free groups. In 2006, Bogopolski+Martino+Maslakov+Ventura solved the conjugacy problem for free-by-cyclic groups. Their proof is based on 2 key components, which are both proven using an analysis of free groups automorphisms via train-track maps. We follow this same route, but instead use an analysis of free group endomorphisms via the "automorphic expansions" of Mutanguha to prove the analogous 2 key components.

2:30-3:30: Quasi-actions of groups on trees and quasi-trees

Jack Button (Cambridge)

A quasi-action of a group G on a metric space X associates a uniform quasi-isometry to each group element but these maps need not be bijective and so this need not be a genuine action, even if we just regard X as a set. We will review the definition and basic properties of quasi-actions with some examples. We then look at how we might turn a quasi-action into a genuine isometric action, which will require replacing X with some other space Y quasi-isometric to it on which G acts suitably by isometries. We conclude by taking X to be a (simplicial) tree and seeing what finiteness properties on G and on X are required to ensure that Y is also a tree.

3:30-4:00: TEA

4:00-5:00: Product set growth in mapping class groups

Alice Kerr (Bristol)

A standard question in group theory is to ask if we can categorise the subgroups of a group in terms of their growth. In this talk we will be asking this question for uniform product set growth, a property that is stronger than the more widely understood notion of uniform exponential growth. We will see how considering acylindrical actions on hyperbolic spaces can help us, and give a particular application to mapping class groups.

Reimbursements

There is travel money available for speakers and students. Please fill out this (please note the new form!) form and send it and your receipts to l.louder AT ucl.ac.uk.

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