Quantum K-theory of flag varieties

The K-theoretic Gromov-Witten (KGW) theory studies enumerative invariants of varieties through counting nodal curves. It naturally arises in the framework of 3D mirror symmetry, a duality between mirror holomorphic symplectic varieties, of which (type-A) flag varieties are among the first examples. In this talk, we study the genus-zero KGW theory of flag varieties from the perspective of Givental cone. We prove a reconstrction theorem of the cone, and discuss several implications. The proof involves torus fixed point localization and abelian/non-abelian correspondence.