220426 Nick Kuhn

April 26, 2022

Title: The blowup formula for instanton Vafa-Witten invariants

Speaker: Nick Kuhn (Max Planck Institute, Bonn)

As a consequence of the S-duality conjecture, Vafa and Witten conjectured certain symmetries concerning invariants derived from spaces of vector bundles on a closed Riemannian four-manifold. We focus on the case of a smooth complex projective surface X, where a satisfying mathematical definition of Vafa-Witten invariants has been given by Tanaka and Thomas. Their invariants are a sum of two parts, one of which can be defined in terms of moduli spaces of stable vector bundles on X. Focusing on this instanton part of the VW invariants one can ask how it changes under a basic algebraic operation: Blowing up the surface X at a point. I will report on joint work with Oliver Leigh and Yuuji Tanaka towards an answer to this question.

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