In the context of CAT (0) cubical groups, we develop an analogue of the theory of curve
complexes and subsurface projections. The role of the subsurfaces is played by a collection …

We prove that any group acting essentially without a fixed point at infinity on an irreducible
finite-dimensional CAT (0) cube complex contains a rankone isometry. This implies that the …

We present a contribution to the structure theory of locally compact groups. The emphasis is
on compactly generated locally compact groups which admit no infinite discrete quotient. It is …

Given an irreducible non-spherical non-affine (possibly non-proper) building X, we give
sufficient conditions for a group G< Aut (X) to admit an infinite-dimensional space of non …

We show that any filtering family of closed convex subsets of a finite-dimensional CAT (0)
space X has a non-empty intersection in the visual bordification X= X ∪ ∂ X. Using this fact …

We motivate the study of metric spaces with a unique convex geodesic bicombing, which we
call CUB spaces. These encompass many classical notions of nonpositive curvature, such …

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 flat torus theorem is provided …

We give a detailed description of the possible limits in the equivariant-Gromov-Hausdorff
sense of sequences $(X_j, G_j) $, where the $ X_j $'s are proper, geodesically complete …

Extending and unifying a number of well-known conjectures and open questions, we
conjecture that locally elliptic (that is, every element has a bounded orbit) actions by …

Proper proximality of a countable group is a notion that was introduced by Boutonnet, Ioana
and Peterson as a tool to study rigidity properties of certain von Neumann algebras …