Kasia Jankiewicz (University of California Santa Cruz)
Title:聽Centers of Artin groups.
Abstract:聽Artin groups are a family of groups generalizing braid groups and closely related to Coxeter groups. They can be realized as the fundamental groups of certain complex hyperplane arrangements, which conjecturally are their K(pi,1) spaces. This is known as the K(pi,1) conjecture. There is also a conjectural description of the center of every Artin group. Irreducible Artin groups, i.e. those that do not split as direct products, are conjectured to have trivial centers, unless they are of finite type, in which case they are known to have infinite cyclic centers. In my talk, I will present joint work with Kevin Schreve, where we show that the Artin groups satisfying the K(pi,1) conjecture also satisfy the center conjecture.