Mathematical Sciences: Harmonic Maps, Foliations, and Manifolds with Special Holomony

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The principal investigator will continue his research on harmonic maps, foliations, and manifolds with special holonomy groups. In particular, he will study rigidity for lattices in certain rank one Lie groups, quotients of rank one symmetric spaces, and flat vector bundles over Kahler manifolds. 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.