Mathematical Sciences: Microlocal Methods In Analysis

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This project will develop microlocal methods in partial differential equations and several complex variables. The main problems to be undertaken are the regularity of solutions to first order PDEs, the analytic regularity for operators with double characteristics, and the Szego kernel. The questions to be analyzed build on recent results by the PI and his collaborators. The project considers state of the art mathematical questions. Ample areas of applied mathematics will benefit from the results of this research.