Coulomb Branches and quasimaps to quiver varieties

From 3d mirror symmetry, any Nakajima quiver variety comes with a dual variety known as the Coulomb branch. A conjecture proposed by Bullimore–Dimofte–Gaiotto–Hilburn–Kim and, independently, by Okounkov asserts that the cohomology of the moduli space of quasimaps to a quiver variety admits a canonical action by the quantized coordinate ring of the dual Coulomb branch. In this talk, I will propose a refinement of this conjecture and discuss its proof. The construction relies on a -1 shifted symplectic structure on the moduli space of quasimaps and a compatible critical description of the BFN Coulomb branch. Time permitting, I will discuss the relation to critical Hall algebras and shifted Yangians.

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