STUDIES IN RIEMANNIAN AND COMPLEX GEOMETRY

Proposal 0305865 PIs: Michael Anderson, Claude LeBrun Sr. Assoc.: Justin Sawon STUDIES IN RIEMANNIAN AND COMPLEX GEOMETRY Anderson, LeBrun and Sawon will pursue research on various topics in differential geometry with close links to other key areas of the mathematical mainstream, 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, and on Zoll metrics in dimension 2. Sawon will study compact hyper-Kaehler manifolds and quaternion-Kaehler manifolds from the point of view of Rozansky-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 interest to theoretical physicists working in general relativity, supergravity, and string theory; moreover, members of the group are actively developing links with physicists working in these areas through participation in conferences, seminars and collaborative projects. The project will also directly contribute to the training of a new generation of mathematical researchers, as members of the research group are actively engaged in the supervision of many graduate students, including women and minorities.