Virtual Structure on Hilbert Schemes of Affine 4-Space

In this 1 hour 18 minute M-Seminar talk from Kansas State University, join Martijn Kool from Utrecht University as he explores K-theoretic invariants of Hilbert schemes of points on affine 4-space. Learn how torus localization reduces these generating series to weighted counts of solid partitions, and discover the proof of Nekrasov's conjectural closed formula by demonstrating that K-theoretic insertions lift to spin modules and create factorizable sequences of sheaves in Okounkov's sense. The presentation also touches on connections to Nekrasov's origami gauge theory, offering a comprehensive look at virtual structures in algebraic geometry. Scheduled for April 3, 2025.