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.