Gauge theory, mirror symmetry and Langlands duality -- Constantin Teleman, April 13, 2012

The work of Kapustin and Witten has confirmed the importance of Langlands duality in 4-dimensional gauge theory. Less known is the appearance of Langlands duality in 2-dimensional gauge theory (the one that relates to volumes of moduli of flat connections and Verlinde formulas). In this talk, I will spell out the appearance of this duality in relation to mirror symmetry, specifically in describing the mirror to gauged Gromov-Witten theory. This relates to older work of Donaldson and Hitchin on monopoles, of Seiberg and Witten on 3d gauge theory, and a beautiful description of the homology of the loop Grassmannian due to Bezrukavnikov-Finkelberg-Mirkovic. At a very impressionistic level, the talk will be accessible to people with no prior exposure to some of these notions.

Slides are available here.