Geometry of braidings

Abstract: Solutions to the Yang Baxter Equation (or braidings) play an important role in the theory of Hopf algebras and monoidal categories. In this talk we will consider the YB Equation from an algebro-geometric perspective. I will explain how algebraic group actions and invariant theory enter the picture, and some applications in the theory of Nichols algebras. If time permits, we will also discuss a conjecture relating the irreducible components of the variety of solutions and set-theoretical solutions to the YB Equation. The talk is based on a joint work with Ben Martin, and with Leandro Vendramin and Istvan Heckenberger.