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.