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

**Time: **
Tue 2021-10-26 13.15 - 14.15

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan (alt. Zoom, meeting ID: 921 756 1880)

**Participating: **
Jørgen Rennemo (University of Oslo, online)

**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.