Quantum cohomology of Kleinian resolutions and the quantum equivariant Hikita conjecture

In the past two decades $3d$ $N=4$ mirror symmetric has been widely studied by physicists and mathematicians. It is also closely related to symplectic duality proposed by Braden et al. One of the conjectures in symplectic duality theory, initiated by Hikita, says that the cohomology of one symplectic manifold is isomorphic to the coordinate ring of torus-fixed scheme of its symplectic dual. In this talk we show that a quantum version of Hikita’s conjecture holds for Kleinian singularities and the corresponding Slodowy slices. This talk is based on a joint work with He and Yu from Sun Yat-sen University.