String-Math Seminar: Mirror symmetry and 4d gauge theories

Seminar | October 29 | 3:30-4:30 p.m. | 402 LeConte Hall

 Benjamin Gammage, Harvard & University of Miami

 Department of Mathematics

2d mirror symmetry relates the algebraic and symplectic geometry of a pair of Kahler manifolds obtained by dualizing a Lagrangian torus fibration. We will discuss some known and expected results in the case when the spaces involved are actually hyperkahler, arising as moduli spaces of 4-dimensional supersymmetric gauge theories (for instance, by a K-theoretic version of the Braverman-Finkelberg-Nakajima construction), and the torus fibration is a Hitchin system. In this case, the relation between the dual spaces can be seen as a Langlands duality, and many structures of interest in representation theory appear.