MIT-Harvard-MSR Combinatorics Seminar

Speaker:  Weihong Xu  (Virginia Tech.)

Title:   Quantum k-theory of Incidence Varieties

Abstract: 

Buch, Mihalcea, Chaput, and Perrin proved that for cominuscule flag varieties, (T-equivariant) K-theoretic (3-pointed, genus 0) Gromov-Witten invariants can be computed in the (equivariant) ordinary K-theory ring, where combinatorial formulas are available. Buch and Mihalcea have a related conjecture for all type A flag varieties. In this talk, I will discuss work that proves this conjecture in the first non-cominuscule case--the incidence variety X=Fl(1,n-1;n). As applications, I will discuss positive combinatorial formulas (an equivariant Chevalley formula and a non-equivariant Littlewood-Richardson rule) which determine the (equivariant) quantum K-theory ring of X. The Littlewood-Richardson rule implies that non-empty Gromov-Witten varieties of stable maps to X with markings sent to three Schubert varieties in general position have arithmetic genus 0. The talk is based on the arxiv preprint at https://arxiv.org/abs/2112.13036.