Quantum difference equations, 3d mirror symmetry and wall-crossing operators

Geometry, Symmetry and Physics
Event time: 
Monday, September 13, 2021 - 4:30pm
Yakov Kononov
Speaker affiliation: 
Yale University
Event description: 

Zoom link: https://yale.zoom.us/j/99305994163, contact the organizers (Gurbir Dhillon and Junliang Shen) for the passcode.

Abstract: The talk is based on joint work with A.Smirnov. We obtain a factorization theorem about the limit of elliptic stable envelopes to a point on a wall in H^2(X,R), which generalizes the result of M.Aganagic and A.Okounkov. This approach allows us to extend the action of quantum groups, quantum Weyl groups, R-matrices, etc., to actions on the K-theory of the symplectic dual variety. In the case of the Hilbert scheme of points in the plane, our results imply the conjectures of E.Gorsky and A.Negut. As another application of this technique, we gain a better geometric understanding of the wall crossing operators and the quantum difference equations.