Quantum difference equations and elliptic stable envelopes

2021/06/24 Thu 10:30 - 12:00
Andrey Smirnov
University of North Carolina at Chapel Hill

A remarkable class of differential and q-difference equations emerges naturally in the study of enumerative geometry of quiver varieties. This class includes Knizhnik-Zamolodchikov equations, quantum dynamical equations and other important objects in representation theory. In my talk I overview a geometric approach to these equations based on the theory of elliptic stable envelopes and three-dimensional mirror symmetry. In this approach we use geometric methods to constrain the monodromy of the associated q-difference equations. Then, the equations can be reconstructed from the monodromy via a simple limiting procedure. The three-dimensional mirror symmetry of the elliptic stable envelopes relates the equations associated to a quiver variety with those of symplectic dual variety.

This will be a zoom seminar.
Zoom URL: https://kyoto-u-edu.zoom.us/j/84065950696
passcode: The order of the Weyl group of type $E_6$