Mathematical Sciences: Spectral Geometry for Riemann Surfaces and the Moduli Space

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The principal investigator will continue his research in Teichmuller theory and spectral geometry. He will consider three new topics: degeneration of the spectrum, special values of Rankin-Selberg L-functions, and a mapping class group invariant Poisson kernel for the Teichmuller space. 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.