Please note special location (Fine 224) and time (3:00-4:00).   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.)