Computation of Vertical Vafa-Witten Invariants

Explore advanced concepts in algebraic geometry through this seminar on the computation of vertical Vafa-Witten invariants. Delve into nested Hilbert schemes and their role in expressing vertical Vafa-Witten as intersection numbers. Review previous material before examining Laarakker's structure theorem, which expresses these invariants using universal generating functions and Seiberg-Witten invariants. Understand the proof's reliance on cobordism invariants of intersection numbers on Hilbert schemes of points. Learn how to explicitly determine the generating function for Vertical-Vafa-Witten invariants by focusing on toric surfaces and localizing on their Hilbert schemes of points. This one-hour lecture, presented by Lothar Goettsche from ICTP, offers a deep dive into cutting-edge research in algebraic geometry and mathematical physics.