Mathematical Sciences: Some Problems in K-Theory and Riemannian Geometry

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The principal investigator will continue his investigation of the G-theory of group rings and K-theory using Yao's noncommutative localization theorem. He will also continue his research in spectral geometry. In particular he will study Riemannian orbifolds and geometric invariants which detect isospectral deformations. 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.