Functor categories for groups

29th August, 13:30-17:00, Lecture Room L6, Maths Institute, Oxford.

Schedule

13:30 Shaked Bader (Oxford)
14:45 Giovanni Italiano (Oxford)
16:00 Robert Kropholler (Warwick)

Topic: Finiteness properties and geometry in groups

The meeting will focus on the rich interactions between finiteness properties, both homological and homotopic, and geometry, mostly in the guise of negative curvature and Gromov hyperbolicity.

The meeting will be in person only. People who would like to stay for dinner need to let Dawid Kielak know at kielak@maths.ox.ac.uk on Monday 25th Aug at the latest.

Titles and abstracts

Shaked Bader: Group cohomology with Banach space coefficients

Gromov conjectured that the L^p-cohomology of simple groups vanishes below the rank.Farb conjectured a fixed point property for actions of lattices in such groups on CAT(0) cell complexes of dimension lower than the rank.In this talk I will give a short introduction to group cohomology and prove that vanishing of \ell^1-cohomology up to degree n implies a finite orbit for every action on an n-dim contrcatible complex, thus in particular establishing that Gromov's conjecture implies Farb's conjecture. I will then give some insight to the proof of Gromov's conjecture. This talk is based on joint work with Saar Bader, Uri Bader and Roman Sauer

Giovanni Italiano: Virtual fibring of manifolds and groups

Fibrations of hyperbolic 3-manifolds have attracted a lot of attention in the early 2000s, culminating in the Virtual Fibring Theorem of Agol in 2012. This raises the question on whether this phenomenon occurs also in higher dimensions. After a short survey about recent results, I will talk about recent progress on fibrations of Poincaré-duality groups, which is joint work with Sam Fisher and Dawid Kielak.

Robert Kropholler: TBC

About FCG

The FCG Research Group is supported by an LMS Joint Research Groups in the UK Scheme 3 grant. Current corresponding organisers for this are Dawid Kielak (Oxford), Nadia Mazza (Lancaster) and Simon Smith (Lincoln). Limited funding is available for PhD students, allocated on a first come first served basis.For UK-based mathematicians with caring duties the LMS has a Caring Supplementary Grant scheme which allows participants of meetings like ours to apply for help covering caring costs. See London Mathematical Society grants for other funding possibilities.