91社区

Title: Curvature of Shephard groups

Abstract: Shephard groups are closely related to complex reflection groups and generalize Coxeter groups and Artin groups. It is well known that Coxeter groups are CAT(0), and it is conjectured that Artin groups are CAT(0). But because their definition is quite general, there are Shephard groups which exhibit seemingly pathological behavior, at least in regards to curvature. We will focus on two such classes. The first is a class of CAT(0) Shephard groups which exhibit 鈥淐oxeter-like鈥� behavior, and strictly contains the Coxeter groups. The second class lies more squarely between the Artin and Coxeter groups, and consists of groups which cannot be CAT(0). However, they are relatively and acylindrically hyperbolic. We will give some motivation as to why this behavior occurs and why it doesn鈥檛 contradict the conjectural non-positive curvature of Artin groups.

We will have teatime in the lounge at 5pm after Katherine's talk.

听