9h30 : Zachary Munro (University of Bristol), Constructing groups with cubical fixed-point properties

A group has FW_n if every action on an n-dimensional CAT(0) cube complex has a global fixed point. In this talk we demonstrate how to construct C'(\lambda) groups for arbitrarily large n>0 and arbitrarily small \lambda>0. Time permitting, we will show that for any n, random groups in the Gromov density model have FW_n with overwhelming probability.

10h45 : Sam Fisher (ICMAT Madrid), Coherent RFRS groups

A group is coherent if all its finitely generated subgroups are finitely presented. A conjecture of Gromov and Wise proposes a characterisation of coherence in cohomological dimension two: G is coherent if and only if its second L^2-Betti number vanishes. In this talk we will address this conjecture in the class of virtually RFRS groups and propose a characterisation of coherence in higher cohomological dimension. This is based on joint work with Pablo Sánchez-Peralta.