Joint IAS/Princeton University Symplectic Geometry Seminar

In recent work of Braden, Licata, Proudfoot, and Webster, a "symplectic duality" was described between pairs of module categories $O(M)$, $O(M')$ associated to certain pairs of complex symplectic manifolds $(M, M')$. The duality generalizes the Koszul duality of Beilinson-Ginzburg-Soergel for categories of modules associated to flag varieties. I will discuss how symplectic duality can be obtained from the physics of boundary conditions in three-dimensional supersymmetric gauge theories, and some new structure that arises from these boundary conditions. (Joint work with M. Bullimore, D. Gaiotto, & J. Hilburn.)