Speaker:   Wenjun Niu (Perimeter Institute)

Abstract:   In these two talks I will explain my joint work with R. Abedin, in which we construct new quantum algebras and spectral solutions of quantum Yang-Baxter equations. These quantum algebras are quantizations of Yang’s r matrix associated to the cotangent Lie algebra d=T^*g of a Lie algebra g. Our construction is based on the geometry of the equivariant affine Grassmannian associated to g, and is related to holomorphic-topological twist of 4d N=2 gauge theories. I will start by giving a brief review of the holomorphic-topological twist of 4d N=2 gauge theories, especially its relation to equivariant affine Grassmannians. I will also review the work of Costello-Witten-Yamazaki, in which the authors give a gauge-theoretic origin to spectral solutions of YB equations. Our constructions are inspired by these physical considerations. After that, I will explain our results in relation to the geometry of equivariant affine Grassmannians. Time permitting, I will also explain how we can dynamically twist the quantum algebra over formal neighborhoods of the moduli space of G-bundles, and obtain dynamical R-matrices as a consequence.