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:

To get regular updates about GGSE, please subscribe to the mailing list. Abstracts and titles of previous talks are available here.

Here are some details of our next meeting.

Friday 21st February, 2014

There will be additional talks on the Thursday afternoon and Friday morning. Full details are available here. If you plan to attend, please register. Lunch will be provided on Friday—please indicate if you do not require lunch. There is also some funding available for accommodation; you can apply for this on the registration form.

Location: Warwick Mathematics Institute. The first two talks are in room MS.04, the final one in room B3.03.

1.15pm On the difficulty of inverting automorphisms of free groups

Enric Ventura (UPC)

We introduce a complexity function α (resp. β) to measure the maximal possible gap between the norm of an automorphism (resp. an outer automorphism) of a finitely generated group G, and the norm of its inverse. We shall concentrate in the case of free groups Fr and prove some results about the growth of these functions αr and βr: for rank r=2, α2 is quadratic and β2 is linear; and for higher rank, we will give polynomial lower bounds for both functions, and a polynomial upper bound for βr (the lower bounds use just manipulation of automorphisms and counting techniques, while the proof of the upper bound makes use of a recent result by Algom-Kfir and Bestvina about the asymetry of the metric in the Outer Space). This is joint work with P. Silva and M. Ladra.

2.30pm Pro-p ends

Pavel Zalesskii (Brasilia)

We shall discuss a pro-p analogue of Stallings' theory of ends.

4pm Hyperbolic groups, Cannon–Thurston maps, and hydra

Tim Riley (Cornell)

Groups are Gromov-hyperbolic when all geodesic triangles in their Cayley graphs are close to being tripods. Despite being tree-like in this manner, they can harbour extreme wildness in their subgroups. I will describe examples stemming from a re-imagining of Hercules' battle with the hydra, where wildness is found in properties of "Cannon-Thurston maps" between boundaries. Also, I will give examples where this map between boundaries fails to be defined.