Mathematical Sciences: Real Submanifolds and Holomorphic Functions

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The principal investigator will focus on two lines of research in the theory of functions of several complex variables. He will study the holomorphic symplectic geometry of real functions and the holomorphic contact geometry of real submanifolds. He will also study the regularity of a particular solution to the integrability problem for CR structures and for CR vector bundles. 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.