Symplectic duality, 3d mirror symmetry, and the Coulomb branch construction of Braverman-Finkelberg-Nakajima

I'll explain 'symplectic duality', a surprising relationship between certain pairs of algebraic symplectic manifolds, under which Hamiltonian automorphisms of one are identified with Poisson deformations of the other, and which is ultimately characterized by a Koszul-type equivalence between categories of modules over their filtered quantizations. I'll outline why such relationships are expected from physics in terms of three dimensional mirror symmetry, and rediscover the Coulomb branch construction of Braverman-Finkelberg-Nakajima from this perspective. We'll see that this explicitly constructs the symplectic dual of any variety which is presented as the symplectic reduction of a vector space by a reductive group.