K-theoretical Hikita conjecture

Ilya Dumanskiy (MIT)

Wednesday 22nd January 16:00-17:00 Maths 311B

Abstract

We will discuss the general notion of symplectic duality (also known as 3D mirror symmetry) between symplectic resolutions of singularities. We then restrict our attention to the case of quiver gauge theory and formulate the Hikita conjecture, which relates the equivariant cohomology of a Nakajima quiver variety with the algebra of functions on the torus-fixed points on the corresponding BFN Coulomb branch. We propose a "multiplicative" variant of this conjecture, in which one has to replace equivariant cohomology by the equivariant K-theory, and the Coulomb branch by the K-theoretical Coulomb branch. We prove it in some cases, deducing from the homological version. Time permitting, we also describe how our method of dealing with K-theoretical Coulomb branches allows to find its generators.

All objects mentioned will be defined. Based on joint work with V. Krylov.

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