We introduce a number of tools for finding and studying hierarchically hyperbolic spaces
(HHS), a rich class of spaces including mapping class groups of surfaces, Teichmüller space …

We give a simple combinatorial criterion, in terms of an action on a hyperbolic simplicial
complex, for a group to be hierarchically hyperbolic. We apply this to show that quotients of …

We provide geometric methods to both lower-and upper-bound the large-scale dimension of
CAT (0) cube complexes quasiisometric to a given group $ G $. When these bounds …

Finite rank median spaces are a simultaneous generalisation of finite dimensional CAT (0)
cube complexes and real trees. If Γ is an irreducible lattice in a product of rank-one simple …

We show that uniform lattices of isometries of products of real hyperbolic spaces act properly
discontinuously and cocompactly on a median space. For lattices in products of at least two …

We give a simple combinatorial criterion, in terms of an action on a hyperbolic simplicial
complex, for a group to be hierarchically hyperbolic. We apply this to show that quotients of …

Median spaces are spaces in which for every three points the three intervals between them
intersect at a single point. It is well known that rank-1 affine buildings are median spaces, but …

Notre mémoire se penche sur divers aspects de théorie géométrique des groupes, où l'on s'
intéresse essentiellement à l'étude de groupes via leurs actions par isométries sur des …

We introduce a number of tools for finding and studying hierarchically hyperbolic spaces
(HHS), a rich class of spaces including mapping class groups of surfaces, Teichmüller space …