Hiraku Nakajima: Towards a mathematical definition of Coulomb branches of gauge theories

Suppose a pair of a compact Lie group G and its quaternionic representation M is given. Physicists associate a hyper-Kaehler manifold, called the Coulomb branch, to (G,M). I will explain my proposal for a mathematically rigorous definition of its coordinate ring, based on the affine Grassmannian of G. This is a joint work with A. Braverman and M. Finkelberg.