Artin groups of infinite type: trivial centers and acylindical hyperbolicity

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 Artin group $A_{\mathrm{\Gamma }}$ on a CAT(0) cube complex to prove that $A_{\mathrm{\Gamma }}$ has trivial center providing the graph $\mathrm{\Gamma }$ is not the star of a single vertex, and is acylindrically hyperbolic providing $\mathrm{\Gamma }$ is not a join.