Quantum algebras and R-matrices from the equivariant affine grassmannians

In this talk, I will explain my joint work with R. Abedin, in which we construct, for each Lie algebra g, a Hopf algebra and a spectral R-matrix satisfying quantum Yang-Baxter equation. This Hopf algebra is a quantization of the Lie bi-algebra structure on T^*g[t] defined by Yang’s r-matrix, and therefore we call it the Yangian of T^*g. The construction is based on the category of coherent sheaves on the equivariant affine grassmannian associated to the formal group of g, and is motivated by the study of the category of line defects in a 4 dimensional holomorphic-topological field theory.