We will discuss the general notion of symplectic duality between symplectic resolutions of singularities and give examples. Equivariant Hikita-Nakajima conjecture is a general conjecture about the relation between the geometry of symplectically dual varieties. We will consider the example of the Hilbert scheme of points on the affine plane and discuss the proof of the equivariant Hikita-Nakajima conjecture in this particular case. We will also briefly discuss the generalization of this proof to the case of ADHM spaces (moduli spaces of instantons on R^4). Time permitting, we will say about the possible approach towards the proof of Hikita-Nakajima conjecture for other symplectically dual pairs (such as Higgs and Coulomb branches of quiver gauge theories). The talk is based on the joint work with Pavel Shlykov arXiv:2202.09934.