Speaker: Iva Halacheva (Northeastern University)

Title: Categorified braid group actions and perverse equivalences

Abstract: In the setting of quantum group representations, two natural braid group actions arise: Lusztig’s ‘internal’  action, in which the braid group type matches the underlying Lie algebra, and the action via the R-matrix of the n-strand braid group on n-fold tensor products. These actions have been categorified: in the first instance by Chuang and Rouquier via so-called Rickard complexes, and in the second by Webster using KLRW algebras. 

I will discuss these two constructions with a view toward perverse equivalences and the recovery of the action of the corresponding cactus group on crystals---including known results for the former and work in progress with Erika Beserra on the latter.