Mathematical Sciences: Partial Differential Equations and Several Complex Variables

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Professor Stanton will continue her research in partial differential equations related to geometry and function theory of several complex variables. In particular, she will study the singularities of kernels associated with the d"-Neumann problem including the heat kernel. She will also study the heat kernel on a CR manifold and attempt to describe the behavior of the kernel in terms of the geometry of the manifold. This award will support research in an area of mathematics which relates geometry to partial differential equations. The equations contain local information about a space and the goal of the research is to patch together this local information to obtain global geometric information. The partial differential equation which is central to this research is tied to the equation which models heat flow in a material.