Website
http://dataportal.arc.gov.au/NCGP/API/grants/DP170101054
Funding Status
Closed
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Funded Activity Summary
Parametrised gauge theory and positive scalar curvature. 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.Funded Activity Details
Start Date: 06-2017
End Date: 06-2020
Funding Scheme: Discovery Projects
Funding Amount: $335,000.00
Funder: Australian Research Council
Research Topics
ANZSRC Field of Research (FoR)
Pure Mathematics | Algebraic and Differential Geometry | Topology
ANZSRC Socio-Economic Objective (SEO)
Expanding Knowledge in the Physical Sciences | Expanding Knowledge in the Mathematical Sciences |
