Lorenzo De Biase
- Room M/2.52, 21-23 Senghennydd Road, Cathays, Cardiff, CF24 4AG
Algebraic geometry, Derived categories
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 this group acts categorically on the space Fl_n of complete flags in C^n. The project is to make progress towards extending this result to the categorification of the generalised braid category. Generalised braids 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. A decade old conjecture states that generalised braids act categorically on the spaces of full and partial flags in C^n.