Stony Brook University 3 credits MAT
Definition and basic properties of holomorphic functions and mappings. Analytic sets: Basic definitions, Local theory of Weierstrass, Meromorphic functions. Hartogs Phenomenon. Domains of convergence of power series. Domains of holomorphy. Pseudoconvexity and the Levi Problem. Complex manifolds, holomorphic vector bundles and Hermitian metrics. Cousin problems. L2 estimates for the inhomogeneous Cauchy-Riemann Equations and applications. Note: This course was previously known as MAT 537 and is not to be repeated for additional credit. 3 credits Prerequisite: MAT 536 Grading Letter graded (A, A-, B+, etc.)
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