# 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, and Henry Wilton. We have been awarded LMS Scheme 3 funding.

In 2016-17, the meetings will tentatively be as follows:

• 28 October 2016, UCL
• 25 November 2016, Southampton
• 24 February 2017, Warwick
• 19 May 2017, Oxford

Abstracts and titles of previous talks are available here.

# Details of our next meeting

19 May, 2017

Location: University of Oxford, Mathematical Institute

### 1:15 Commensurating actions of groups of birational transformations

Yves Cornulier (Orsay)

We introduce a natural action of the group of birational transformations of a variety, namely on the (suitably defined) set of hypersurfaces of all smooth projective models of this variety. In particular, for some groups with some restrictions on their commensurating actions (or equivalently on their actions on CAT(0) cube complexes) such as groups with Property FW, we obtain corresponding restrictions on their actions by birational transformations. This is joint work with Serge Cantat.

### 2:30 Degenerations of maximal representations, non-Archimedean upper half space and laminations

Alessandra Iozzi (ETHZ)

We study degenerations of maximal representations into $$Sp(2n,R)$$ and identify phenomena already present in the Thurston boundary of Teichmüller apace as well as new geometric features. We give equivalent conditions for the existence of measured laminations in term of an appropriate notino of length. This is joint work with Marc Burger, Anne Parreau and Beatrice Pozzetti.

### 4:00 Recognition of fibring in compact 3-manifolds

Let $$M$$ be a compact orientable 3-manifold. We show that if the profinite completion of $$\pi_1(M)$$ is isomorphic to the profinite completion of a free-by-cyclic group or to the profinite completion of a surface-by-cyclic group, then $$M$$ fibres over the circle with compact fibre.