November 25: Justin Hilburn

Title: 3d Mirror Symmetry and (S-)ymplectic duality

Abstract:

Thanks to work of Kapustin-Witten it is well known that geometric Langlands is the mathematical incarnation of S-duality of topologically twisted 4d N=4 gauge theories. It is less well known that that the mathematical theory of symplectic duality is a manifestation of mirror symmetry for 3d N=4 supersymmetric theories. (Not to be confused with what the mathematical theory of mirror symmetry which is mirror symmetry for 2d N=(2,2) theories.) In this talk I will show how understanding the relationship between these physical theories lets one deduce interesting mathematical conjectures. Much of this work is joint with various subsets of Tudor Dimofte, Philsang Yoo, Joel Kamnitzer, Alex Weekes, and Nik Garner with lots of help from Davide Gaiotto, Kevin Costello, and Ben Webster.