Kavli Affiliate: Hiraku Nakajima | First 5 Authors: Alexander Braverman, Michael Finkelberg, Hiraku Nakajima, , | Summary: Consider the $3$-dimensional $mathcal N=4$ supersymmetric gauge theory associated with a compact Lie group $G_c$ and its quaternionic representation $mathbf M$. Physicists study its Coulomb branch, which is a noncompact hyper-K"ahler manifold with an $mathrm{SU}(2)$-action, possibly with singularities. […]