Michael Viscardi (UCB) “Equivariant quantum cohomology and the geometric Satake equivalence”

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Recent work on equivariant aspects of mirror symmetry has discovered relations between the equivariant quantum cohomology of symplectic resolutions and Casimir-type connections (among many other objects). We provide a new example of this theory in the setting of the affine Grassmannian, a fundamental space in the geometric Langlands program. More precisely, we identify the equivariant quantum connection of certain symplectic resolutions of slices in the affine Grassmannian of a semisimple group G with a trigonometric Knizhnik-Zamolodchikov (KZ)-type connection of the Langlands dual group of G. These slices arise as Coulomb branches of 3D N=4 SUSY framed quiver gauge theories, so that our result is an analogue of (part of) the work of Maulik and Okounkov in the Higgs branch setting.