GAAG seminar - K-theoretic invariants of the Quot scheme of curves

I will begin by reviewing some basic facts about vector bundles on the Grassmannian Gr(r,N). The Quot scheme over a smooth curve C provides a compactification for the space of morphisms from C to Gr(r,N). The (virtual) intersection theory of Quot, as studied by Oprea and Marian, recovers the Vafa–Intriligator formula that counts the number of maps from C to Gr(r,N). In this talk, I present formulas for Euler characteristics of vector bundles over the Quot schemes of curves, offering a K-theoretic analogue of the Vafa–Intriligator formula. This is based on joint works with Dragos Oprea and with Ming Zhang.