Studies in Riemannian and Complex Geometry

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Proposal 0305865PIs: Michael Anderson, Claude LeBrunSr. Assoc.: Justin SawonSTUDIES IN RIEMANNIAN AND COMPLEX GEOMETRYAnderson, LeBrun and Sawon will pursue research on various topics indifferential geometry with close links to other key areas of the mathematicalmainstream, such as mathematical physics, differential topology, partial differential equations, algebraic geometry, and several complex variables. Anderson will carry out research on general relativity, Einstein metrics, and the geometrization of 3-manifolds.LeBrun will work on the Riemannian geometry of low-dimensional manifolds,with a focus on curvature and topology in dimensions 3 and 4, andon Zoll metrics in dimension 2. Sawon will study compact hyper-Kaehlermanifolds and quaternion-Kaehler manifolds from the point of view ofRozansky-Witten invariants, knot invariants, and topological quantum field theories.It is expected that the broader impact of this research program will be significant.Many of the problems under study are of great interestto theoretical physicists working in general relativity, supergravity, andstring theory; moreover, members of the group are actively developinglinks with physicists working in these areas throughparticipation in conferences, seminars and collaborative projects.The project will also directly contribute to the training of anew generation of mathematical researchers, asmembers of the research group are actively engaged in the supervisionof many graduate students, including women and minorities.