A graph is Helly if every family of pairwise intersecting combinatorial balls has a nonempty
intersection. We show that weak Garside groups of finite type and FC-type Artin groups are …

This article investigates structural, geometrical, and topological characterizations and
properties of weakly modular graphs and of cell complexes derived from them. The unifying …

Starting with a lattice with an action of $\mathbb {Z} $ or $\mathbb {R} $, we build a Helly
graph or an injective metric space. We deduce that the $\ell^\infty $ orthoscheme complex of …

We study the noncommutative rank (nc-rank) computation of a symbolic matrix whose
entries are linear forms in noncommutative variables. For this problem, polynomial time …

While finite type Artin groups and right-angled Artin groups are well understood, little is
known about more general Artin groups. In this paper we use the action of an infinite type …

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 …

Hadamard spaces have traditionally played important roles in geometry and geometric
group theory. More recently, they have additionally turned out to be a suitable framework for …

For a two-dimensional Artin group whose associated Coxeter group is hyperbolic, we prove
that the action of on the hyperbolic space obtained by coning off certain subcomplexes of its …

We prove that Artin groups from a class containing all large‐type Artin groups are systolic.
This provides a concise yet precise description of their geometry. Immediate consequences …

We give a conjectural classification of virtually cocompactly cubulated Artin–Tits groups (ie,
having a finite index subgroup acting geometrically on a CAT (0) cube complex), which we …