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Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.
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Algebraic microlocal analysis and nonlinear PDE
Though originating in the study of linear partial differential equations, microlocal analysis has become an invaluable tool in the study of nonlinear pde. Of particular importance has been the applica …