Stable envelopes for critical loci

Geometric Representation Theory Seminar

Organizers：

Lin Chen, Will Donovan, Penghui Li, Peng Shan, Changjian Su, Wenbin Yan

Speaker：

Yalong Cao 曹亚龙 (MCM）

Time：

Mon., 15:30-16:30, May 11, 2026

Venue：

B627, Shuangqing Complex Building

Title:

Stable envelopes for critical loci

Abstract:

Stable envelopes are geometric objects introduced by Maulik-Okounkov on cohomology of Nakajima quiver varieties. They can be used to construct R-matrices and Yangian type quantum groups.

In a joint work with Andrei Okounkov, Yehao Zhou and Zijun Zhou. We extend the theory of stable envelopes to critical cohomology of symmetric quiver varieties with potentials. We prove that critical stable envelopes are compatible with dimensional reductions, specializations, Hall products, and other geometric constructions.

Applications to enumerative geometry of critical loci have been elaborated in the talk of Andrei in this seminar series. Applications to geometric representation theory of shifted quantum groups will be explained more in Yehao’s talk next week.