Quantum Schubert calculus from lattice models
Organizers
Speaker
Leonardo Mihalcea
Time
Thursday, September 18, 2025 10:00 AM - 11:00 AM
Venue
A6-101
Online
Zoom 638 227 8222
(BIMSA)
Abstract
In geometry, the quantum K theory of Grassmannians is a ring with a product deforming the usual K theory product. In (mathematical) physics, it is the coordinate ring of an affine variety given by the Bethe Ansatz equations. I will discuss a dictionary between these two perspectives, with emphasis on geometric interpretations. In particular, the graphical calculus from a 5-vertex lattice model yields Pieri-type rules, to quantum K multiply Schubert classes by Hirzebruch lambda_y classes of tautological bundles. One may also construct eigenvectors of the previous quantum multiplication operators, called Bethe vectors, which quantize the usual classes of torus fixed points. I will discuss how the existence of these Bethe vectors leads to a theory of quantum equivariant localization for Grassmannians. This is joint work with V. Gorbounov and C. Korff, following earlier work with W. Gu, E. Sharpe, and H. Zou.