Mathematical Sciences: The Geometry and Topology of Moduli Spaces

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The principal investigators will continue their study of the homotopy of instanton moduli spaces. They will use the relationship between instantons and holomorphic bundles to continue work related to their recent solution of the Atiyah- Jones conjecture. The principal investigators will also study families of compact, non-homogeneous Einstein manifolds of positive scalar curvature. This award will support research in the general area of differential geometry and global analysis. Differential geometry is the study of the relationship between the geometry of a space and analytic concepts defined on the space. Global analysis is the study of the overall geometric and topological properties of a space by piecing together local information. Applications of these areas of mathematics in other sciences include the structure of complicated molecules, liquid-gas boundaries, and the large scale structure of the universe.