國立清華大學 數學系

This is joint work with Richard P. Thomas at Imperial College London. We consider a set of gauge-theoretic equations on closed four-manifolds, introduced by Vafa and Witten in the study of S-duality conjecture. In this talk, we restrict ourselves to the case that the underlying manifolds are projective surfaces, and define invariants from the moduli space of solutions to the equations by localisations to the fixed loci of its natural C^* action. We then describe the partition functions of them in examples.