Hai Dong: Grassmanian via Dual Grassmanian
Abstract: Grassmannian Gr(r,n) is geometrically isomorphic to dual Grassmannian Gr(n-r,n). However, they have very different combinatorial structures, originated from their GIT presentations. It is a mysterious and yet highly nontrivial problem to match their combinatorial structures directly. A famous example is level-rank duality from physics. In this talk, I will examine the relation of I-functions of Grassmannian and its dual in both quantum cohomology and quantum K-theory cases. Furthermore, the twisted I-functions of vector bundles of Grassmannians in quantum cohomology and I-functions with the level structure in quantum K-theory, which is introduced by Yongbin Ruan and Ming Zhang, will also be examined.