11/20 at 17:30 in 507

Vasily Krylov 

Title: On the Hikita-Nakajima conjecture

Abstract: 

Symplectic duality predicts that symplectic singularities should come in pairs with matching properties. For instance, Nakajima quiver varieties are conjecturally dual to the BFN Coulomb branches of the corresponding quiver gauge theories. In this talk, I will discuss the Hikita-Nakajima conjecture that relates dual varieties. I will explain a possible approach to proving this conjecture when both symplectic singularities admit symplectic resolutions. I will illustrate the approach on the example of the moduli space of instantons on the projective plane. Time permitting, I will discuss the quantum version of the Hikita-Nakajima conjecture (formulated by Kamnitzer, McBreen, and Proudfoot) and its relation to enumerative geometry.  The talk is based on the joint work with Pavel Shlykov (arXiv:2202.09934) and the work in progress with Do Kien Hoang and Dmytro Matvieievskyi.