Mathematical Sciences: Partial Differential Equations and Several Complex Variables

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This project will study regularity and solvability of linear partial differential equations related to several complex variables. This will include local and global solvability, existence and regularity of solutions to the Cauchy-Riemann and tangential Cauchy-Riemann problems, the closed range property and local embeddability of Cauchy-Riemann operators, analytic hypoellipticity of operators, and CR functions. Results from this project will contribute to understanding fundamental behavior of equations arising in science and engineering.