Combinatorics Seminar: "Algebraic weaves and braid varieties"

Abstract: I will define braid varieties, a class of affine algebraic varieties associated with positive braids and closely related to augmentation varieties of Legendrian links and to open Bott-Samelson varieties. We will discuss a Soergel-like diagrammatic calculus for correspondences between them. I will explain how these correspondences induce stratifications for braid varieties and their quotients, unifying certain previously known constructions. If time permits, I will briefly explain the relation between open toric charts appearing in these stratifications and cluster algebras. This is a joint work with Roger Casals, Eugene Gorsky, and José Simental Rodríguez.

Host: Laura Escobar Vega