We study property (T ) and the fixed point property for actions on L and other Banach spaces. We show that property (T ) holds when L is replaced by L (and even a subspace/quotient of L), and that inâ€¦ (More)

I 1924, Banach and Tarski (1) accomplished a rather paradoxical feat. They proved that a solid ball can be decomposed into five pieces, which are then moved around and reassembled in such a way as toâ€¦ (More)

For every hyperbolic group and more general hyperbolic graphs, we construct an equivariant ideal bicombing: this is a homological analogue of the geodesic flow on negatively curved manifolds. We thenâ€¦ (More)

1.1. Superrigidity. In the early seventies, Margulis proved his celebrated superrigidity theorem for irreducible lattices in semisimple Lie and algebraic groups of higher rank. One of the motivationsâ€¦ (More)

We prove vanishing results for Lie groups and algebraic groups (over any local field) in bounded cohomology. The main result is a vanishing below twice the rank for semi-simple groups. Relatedâ€¦ (More)

We establish a connection between Dixmier's unitarisability problem and the expected degree of random forests on a group. As a consequence, a residually finite group is non-unitarisable if its firstâ€¦ (More)

A selection of aspects of the theory of bounded cohomology is presented. The emphasis is on questions motivating the use of that theory as well as on some concrete issues suggested by its study.â€¦ (More)

We study lattices in non-positively curved metric spaces. Borel density is established in that setting as well as a form of Mostow rigidity. A converse to the at torus theorem is provided. Geometricâ€¦ (More)

We establish an arithmeticity vs. non-linearity alternative for irreducible lattices in suitable product groups, for instance products of topologically simple groups. This applies notably to a (largeâ€¦ (More)

Supramenability of groups is characterised in terms of invariant measures on locally compact spaces. This opens the door to constructing interesting crossed product C-algebras for nonsupramenableâ€¦ (More)