##### Department of Mathematics,

University of California San Diego

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### Enumerative Geometry Seminar

## Ming Zhang

#### University of British Columbia

## The Verlinde/Grassmannian Correspondence

##### Abstract:

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 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 $GL_n$ Verlinde numbers to the level l quantum K-invariants of the Grassmannian 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 first explain the background of this correspondence and its interpretation in physics. Then I will discuss the main idea of the proof for arbitrary rank. A new technical ingredient is the virtual nonabelian localization formula developed by Daniel Halpern-Leistner.

Host: Dragos Oprea

### November 25, 2020

### 12:00 PM

### Zoom ID: 915 7233 7015

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