Jørgen Rennemo: K-theoretic sheaf counting invariants on C^4

Abstract: Oh and Thomas have recently defined a K-theoretic sheaf counting invariant for moduli spaces of sheaves on a Calabi-Yau 4-fold. One of the simplest examples of such a moduli scheme is the Hilbert scheme of n points on \(\mathbb{C}^4\). The topic of this talk is a proof of a formula for the generating functions of invariants of these Hilbert schemes, confirming a conjecture of Nekrasov (as well a generalisation to Quot schemes of \(\mathbb{C}^4\), conjectured by Nekrasov and Piazzalunga).

This is joint work with Martijn Kool.