Algebraic Geometry Seminar
Coulomb branches, and geometry of shift operators
2026/05/06 (Wed.) 15:00~17:00
- Date : 2026/05/06 (Wed.) 15:00~17:00
- Location : Seminar Room 638, Institute of Mathematics (NTU Campus)
-
Speaker : Eddie Lam (Chinese University of Hong Kong)
- Organizer : Ionut Ciocan-Fontanine and Adeel Khan and Y.P. Lee (AS)
- 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 work with Ki Fung Chan, Kwokwai Chan and Chi Hong Chow.
