Mathematical Sciences: The Geometry of Cycle Spaces and Moduli Spaces

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The principal investigators will continue their investigation of problems in differential and algebraic geometry. In particular they will investigate the structure of Chow varieties via the method of characteristic classes. Results are expected to have relationships with Bott periodicity, the Hodge conjecture, and the Schubert calculus. 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.