Changzheng Li, (part 2) "A Plucker mirror for partial flag varieties and quantum Schubert calculus"

Abstract: In this talk, we will discuss an interaction between mirror symmetry and quantum Schubert calculus. In the first part, we will review the current study on mirror symmetry for flag varieties. In the second part, we will show a folklore conjecture in mirror symmetry that the eigenvalues for the action of the first Chern class on the quantum cohomology ring of a partial flag variety are equal to the critical values of the mirror superpotential. We will see new identities in quantum Schubert calculus that are inspired by our Plucker coordinate formula for the mirror superpotential and the mirror symmetry conjecture. This is based on my joint work with Konstanze Rietsch, Mingzhi Yang and Chi Zhang.