Abstract: In the first part of the talk, I'll give an introduction to the 2CY categories associated to Coxeter systems, stability conditions on them, and the relevance of these objects in the study of Artin-Tits braid groups. In the second part of the talk, I'll explain how the spherical objects in these categories have a PL structure closely related to the geometry of the stability manifold. (Joint work with Asilata Bapat and Anand Deopurkar).
