Mathematical Sciences: Mathematical Physics and Non- commutative Differential Geometry

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The principal investigator will study applications cyclic homology and related algebraic constructions such as the deformation theory of algebras to quantum mechanics, microlocal analysis, index theory, and algebraic K-theory. 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.