Parametrised gauge theory and positive scalar curvature

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This project aims to study innovative extensions of Seiberg-Witten gauge theory with new applications to the topology of metrics of positive scalar curvature on four-dimensional manifolds. Since Atiyah-Bott, Donaldson, Hitchin, and Seiberg-Witten’s work on various equations in gauge theory, profound applications have changed the geometry and topology of low dimensional manifolds. Parametrised index theory has obtained deep results on the topology of metrics of positive scalar curvature in higher dimensions, but these methods do not work in the case of the fourth dimension. This project will develop (parametrised) Seiberg-Witten gauge theory as a new approach to the study of the topology of metrics of positive scalar curvature in four dimensions. Expected outcomes include new invariants related to positive scalar curvature in four dimensions.