April 23, 2024
Title: Enumerative invariants of twisted sheaves (MI talk)
Speaker: Dirk van Bree
Twisted sheaves are a variant of the notion of sheaves and behave similar in many ways. In this talk, I will define enumerative invariants of twisted sheaves on surfaces. These are needed to mathematically formulate the 30-year-old S-duality conjecture of Vafa-Witten. I will also show how the enumerative theory of twisted and untwisted sheaves is closely related, using deformation theory. This work is joint with A. Gholampour, Y. Jiang and M. Kool.
I will also discuss more recent work, generalising twisted invariants to dimensions 3 and 4, with possible applications to the period-index problem.