Title: Skein-triangulated representations of generalised braids
Speaker: Timothy Logvinenko - Cardiff Unviersity

Data: 08 de outubro
Horário: 12:30h
Local: Transmissão online

Abstract: Ordinary braid group Br_n is a well-known algebraic structure which encodes configurations of n non-touching strands (“braids”) up to continious transformations (“isotopies”). A classical result of Khovanov and Thomas states that there is a natural categorical action of Br_n on the derived category of the cotangent bundle of the variety of complete flags in C^n. In this talk, I will introduce a new structure: the category GBr_n of generalised braids. These are the braids whose strands are allowed to touch in a certain way. They have multiple endpoint configurations and can be non-invertible, thus forming a category rather than a group. In the context of triangulated categories, it is natural to impose certain relations which result in the notion of a skein-triangulated representation of GBr_n. A decade-old conjecture states that there a skein-triangulated action of GBr_n on the cotangent bundles of the varieties of full and partial flags in C^n. We prove this conjecture for n = 3. We also show that any categorical action of Br_n can be lifted to a skein-triangulated action of GBr_n, which behaves like a categorical nil Hecke algebra. This is a joint work with Rina Anno and Lorenzo De Biase.

Host: Ivan Cheltsov
Zoom ID: 991 849 3831
Zoom link: https://us02web.zoom.us/j/9918493831?pwd=UWZkTDJ3WG5GMHJRTVQ4STdWeHF4Zz09
Password: October