Dinakar Muthiah (Glasgow): Symplectic duality, Coulomb branches, and Kac-Moody affine Grassmannian slices

I will discuss the idea of symplectic duality. Symplectic duality now has a precise mathematical meaning in a 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 gives rise to the Geometric Satake Correspondence for Kac-Moody groups. I will discuss joint work with Alex Weekes.