CMSA Mathematical Physics Seminar: Verlinde/Grassmannian correspondence and applications


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October 5, 2020 10:30 am - 11:30 am
via Zoom Video Conferencing

Ming Zhang - UBC

In the 90s', Witten gave a physical derivation of an isomorphism between the Verlinde algebra of $GL(n)$ of level $l$ and the quantum cohomology ring of the Grassmannian $\text{Gr}(n,n+l)$. In the joint work arXiv:1811.01377 with Yongbin Ruan, we proposed a K-theoretic generalization of Witten's work by relating the $\text{GL}_{n}$ Verlinde numbers to the level $l$ quantum K-invariants of the Grassmannian $\text{Gr}(n,n+l)$, and refer to it as the Verlinde/Grassmannian correspondence.

The correspondence was formulated precisely in the aforementioned paper, and we proved the rank 2 case (n=2) there. In this talk, I will discuss the proof for arbitrary rank. A new technical ingredient is the virtual nonabelian localization formula developed by Daniel Halpern-Leistner.  At the end of the talk, I will describe some applications of this correspondence.