Hiraku Nakajima

      •  Professor, Kavli Institute for The Physics And Mathematics of The Universe, University of Tokyo

      •  President, International Mathematical Union

Title :

3d Quantum Field Theories and Langlands duality

Abstract :

In joint works with Braverman and Finkelberg, I studied 3-dimensional supersymmetric quantum field theories (QFT) by mathematically rigorous approaches in recent years. As an application, we give a recipe to construct (partially conjectural) pairs of affine algebraic symplectic manifolds with group action, where the group for the second manifold is replaced by Langlands dual group. The definition of these pairs was motivated by the S-duality of boundary conditions of 4d gauge theory, studied by Gaiotto-Witten. This S-duality gave a new connection between 3d QFT and Langlands duality as pointed out by Gaiotto, and also by Ben-Zvi, Sakellaridis, and Venkatesh as relative Langlands duality.