Georgia Institute of Technology College of Sciences

Quiver varieties provide a fundamental bridge between representation theory, enumerative geometry, and physics.  From 3d mirror symmetry, any quiver variety comes with a dual variety known as the Coulomb branch.  A conjecture proposed by Bullimore-Dimofte-Gaiotto-Hilburn-Kim and, independently, 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 BFN Coulomb branch.  In this talk, I will report on progress on refining this conjecture and proving it.  The construction relies on a -1 shifted symplectic structure on the moduli space of quasimaps and the theory of cohomological Hall algebras.  Based on work in preparation with Spencer Tamagni.