Coulomb branches and geometry of shift operators

Geometric Representation Theory Seminar

Organizers：

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

Speaker：

Chin Hang Eddie Lam(The Chinese University of Hong Kong)

Time：

Fri., 13:30-15:00, May 22, 2026

Venue：

B627, Shuangqing Complex Building A

Title：

Coulomb branches and geometry of shift operators

Abstract:

In this talk, we construct an action of Coulomb branch algebra on the equivariant quantum cohomology of a semiprojective variety X. Our approach is based on shift operators defined via Gromov-Witten theory of certain X-bundles. A key feature of this construction is that the action is well-defined without localizing the equivariant parameters. We explain how this "non-localizing" property leads to a new characterization of Coulomb branch algebras.

As a concrete example, we describe the (Iwahori-)Coulomb branch action on QH(T*(G/P)) using stable envelopes. Finally, we discuss two major applications: (1) a new, geometric proof of Peterson's isomorphism for G/B, and (2) a proof of a conjecture relating the Coulomb branch and the spherical subalgebra of the trigonometric double affine Hecke algebra. This is a joint with Ki Fung Chan, Kwokwai Chan and Chi Hong Chow.