Higher rank K-theoretic Donaldson-Thomas theory of points

Recently Okounkov proved Nekrasov’s conjecture expressing the partition function of K-theoretic DT invariants of the Hilbert scheme of points Hilb(C^3,points) on affine 3-space as an explicit plethystic exponential. The higher rank analogue of Nekrasov’s formula is a conjecture in String Theory by Awata-Kanno. We state this conjecture and sketch how to prove it mathematically via Quot schemes. Specialising from K-theoretic to cohomological invariants, we obtain the statement of a conjecture of Szabo. This is joint work with Nadir Fasola and Sergej Monavari.