Gauge theory in 3 and 4 dimensions

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Project objective

Research objectives and content The aim of the project is to study moduli spaces of singular monopoles on compact 3-manifolds. In our case, the monopoles are required to give rise to a non-singular circle-invariant connection on the 4-dimensional ball; for an appropriate metric, this connection has anti-self-dual curvature. I would like to obtain a twistor description of such moduli spaces for the three-dimensional sphere, paralleling previous work by Nigel Hitchin. Another point of interest is to determine if the moduli spaces (for arbitrary base manifolds) admit hyperkahler metrics. Training content (objective, benefit and expected impact) This research project requires a considerable amount of analysis, especially elliptic operator theory. Moreover, the question about a twistor interpretation involves an intensive study of complex geometry and holomorphic bundle theory. Links with industry / industrial relevance (22)

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Participants

• UNIVERSITE DE PARIS-SUD XI · ORSAYCoordinatorFrance

Links

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