Special Zoom talk

Speaker: Keke Zhang (Perimeter Institute)

Title: An Operator-Theoretic Approach to Twisted Traces and the Quantum Hikita Conjecture

Abstract: Let $X$ and $X^{!}$be a pair of dual conical symplectic singularities, and let $\tilde{X}^{!} \rightarrow X^{!}$be a symplectic resolution. The quantum Hikita conjecture states that the D-module of graded traces for $X$, denoted $M$ reg, is isomorphic to the specialized quantum D-module of $\tilde{X}^{!}$after localization. This talk introduces an operator-theoretic framework to construct these traces and apply them to the conjecture. We discuss representation of Coulomb branches as operators acting on a two-parameter function space. This concrete representation provides a direct path to constructing integral form twisted traces for conical theories. This also gives an expla