Attention à l’heure inhabituelle.

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. 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 Fl(1,n-1;n). The proof is based on showing that Gromov-Witten varieties of stable maps to Fl(1,n-1;n) with markings sent to a Schubert variety, a Schubert divisor, and a point are rationally connected. As applications, I will also discuss positive formulas that determine the equivariant quantum K-theory ring of Fl(1,n-1;n). The talk is based on the arxiv preprint at https://arxiv.org/abs/2112.13036.