Algebra and Geometry Seminar

We will discuss the Plücker coordinate method on the mirror symmetry of flag varieties. In the first part, we will review the current study on mirror symmetry of flag varieties. In the second part, we will introduce the construction of our Plücker coordinate superpotential. We will explain the idea of our proof on the first Chern class conjecture that the critical values of mirror superpotential are the eigenvalues of quantum multiplication of first Chern class in the cases of complex flag varieties. In the third part, we will show some examples about the images of the mirror isomorphism and briefly mention how quantum Schubert calculus plays a role in the story. The talk is based on my joint work with Changzheng Li, Konstanze Rietsch, and Mingzhi Yang.