I'll describe how to define Vafa-Witten invariants -- and refined Vafa-Witten invariants -- of projective surfaces. Then I'll explain how to calculate some parts of the theory via degeneracy loci and "Carlsson-Okounkov operators". The talk describes different projects joint with Yuuji Tanaka, Davesh Maulik and Amin Gholampour.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/5285