GRASP LECTURE Ben Webster S-duality for symplectic varieties and representation theory

I'll discuss some conjectures (joint with T. Braden, A. Licata and N. Proudfoot) relating S-duality in 3-dimensional field theory to the geometry of certain symplectic varieties and the representation theory of "universal enveloping algebras" attached to these varieties. We will start with a very down to earth description of the abelian case (which can be stripped down to some combinatorics of hyperplane arrangements), and proceed toward a broader and more geometric view. These conjectures also relate to my other talk on the categorification of quantum groups, and they hope to relate the two of the great universes of geometric representation theory: quiver varieties and the affine Grassmannian.