I will discuss the idea of symplectic duality. Symplectic duality now has precise mathematically meaning in large class of examples. The key ingredient is the Braverman-Finkelberg-Nakajima construction of Coulomb branches. Coloumb branches also give precise meaning to the notion of Kac-Moody affine Grassmannian slices. I will discuss some challenges that arise in understanding their geometry and how that geometry conjecturally give rises to Geometric Satake Correspondence for Kac-Moody groups.
I will discuss joint work with Alex Weekes.