Oct 26 at 17:30 in 507

Tianqing Zhu

Title:  Stability condition wall-crossing for Nakajima quiver varieties I: Wall-crossing phenomenon for the geometric quantum loop groups 

Abstract: Strong connections between the representation theory of the quantum group and the enumerative geometry of quiver varieties have been deeply studied for decades from many directions. In particular for the case of the quantum loop groups, there are geometric constructions given by the stable envelopes of the Nakajima quiver variety, which also plays the key role in understanding the  quantum difference/differential equation for the Nakajima quiver variety in the K-theoretic/cohomological quasimap counting. In this talk, we are going to investigate on how to relate the quantum loop groups of different generic stability conditions via the wall-crossing auto-equivalence, and show how to construct some new automorphisms of the quantum loop group using these auto-equivalences. This will construct the base on proving the wall-crossing covariance for the quantum difference operator for the quantum K-theory of Nakajima quiver varieties.