Groups and Geometry in South England

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 Bristol, Cambridge, London, Oxford, Warwick, and Southampton, and organised by Martin Bridson, Mark Hagen, Peter Kropholler, Robert Kropholler, Lars Louder, John Mackay, Ashot Minasyan, Saul Schleimer, and Henry Wilton. We have been awarded LMS Scheme 3 funding, as well as support from the Isaac Newton Institute for Mathematical Sciences.

In 2023-24, the meetings will tentatively be as follows:

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Abstracts and titles of previous talks are available here.

Details of our next meeting

Oxford 21 June 2024

L6, Mathematical Institute

1:30 Dimensions of mapping class groups of orientable and non-orientable surfaces.

Luis Jorge Sánchez Saldaña (UNAM)

Mapping class groups have been studied extensively for several decades. Still in these days these groups keep being studied from several point of views. In this talk I will talk about several notions of dimension that have been computed (and some that are not yet known) for mapping class groups of both orientable and non-orientable manifolds. Among the dimensions that I will mention are the virtual cohomological dimension, the proper geometric dimension, the virtually cyclic dimension and the virtually abelian dimension. Some of the results presented are in collaboration with several colleagues: Trujillo-Negrete, Hidber, León Álvarez and Jimaénez Rolland.

2:45 Nonunique ergodicity in strata of geodesic laminations and the boundary of Outer space.

Mladen Bestvina (Utah)

It follows from the work of Gabai and Lenzhen-Masur that the maximal number of projectively distinct ergodic transverse measures on a filling geodesic lamination on a hyperbolic surface is equal to the number of curves in a pants decomposition. In a joint work with Jon Chaika and Sebastian Hensel, we answer the analogous question when the lamination is restricted to have specified polygons as complementary components. If there is enough time, I will also talk about the joint work with Elizabeth Field and Sanghoon Kwak where we consider the question of the maximal number of projectively distinct ergodic length functions on a given arational tree on the boundary of Culler-Vogtmann's Outer space of a free group.

4:00 Diffeomorphisms of reducible 3-manifolds

Rachael Boyd (Glasgow)

I will talk about joint work with Corey Bregman and Jan Steinebrunner, in which we study the moduli space B Diff(M), for M a compact, connected, reducible 3-manifold. We prove that when M is orientable and has non-empty boundary, B Diff(M rel ∂M) has the homotopy type of a finite CW-complex. This was conjectured by Kontsevich and previously proved in the case where M is irreducible by Hatcher and McCullough.


UPDATE: There is travel money available, prioritising speakers, PhD students, and ECRs. DO NOT FILL OUT ANY FORMS! Just send me an email at l.louder AT and I will set things in motion.

We are on less of a shoestring budget than we were, but still try to minimize your travel costs!