Geometric and Analytic Problems in Several Complex Variables

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ABSTRACT:Rothschild and BaouendiA basic geometric and analytic problem in several complex variables is to determine when two real manifolds in multidimensional complex space are equivalent under an analytic transformation. The principal investigators will continue their research on several aspects of this fundamental problem. In particular, they will focus on determining when it is possible to reduce the equivalence problem to the much simpler one of solving systems of polynomial equations. They will also study which mappings between such manifolds are determined by finitely many derivatives at a given point. They expect that this study will lead to the discovery of new geometric, analytic, and algebraic properties of these important geometric objects. The study of the geometry of real manifolds in complex spaces is central to the field of several complex variables and to other areas of science, including geometry, mathematical physics and engineering. Progress on the problems proposed will likely have impact on these areas as well.