December 13, 2016
Mathematics Colloquium lecture Dec. 13
Timothy Logvinenko, Cardiff University, will present "Generalised Braid Category" as part of the Mathematics Department Colloquium Lecture series at 2:30 p.m. Tuesday, Dec. 13, in 122 Cardwell Hall.
The abstract for the lecture is: Ordinary braid group Br_n is a well-known algebraic structure which encodes configurations of n non-touching strands ("braids") up to continuous 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. Logvinenko will begin by reviewing the basics on braid group and flag varieties, and then give a sketch of the geometry involved in the Khovanon-Thomas construction of the categorical action of Br_n on T^* Fl_n.
Logvinenko will then describe a longstanding work-in-progress with Rina Anno: the categorification of generalized 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. A decade old conjecture states that generalized braids act categorically on the spaces of full and partial flags in C^n. Categorification will describe our present progress toward it and future expectations.