Transcription of Advanced Complex Analysis - Harvard Mathematics Department
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Advanced Complex AnalysisCourse Notes Harvard University Math 213aC. McMullenDecember 4, 2017 Contents1 Basic Complex Analysis ..22 The simply-connected Riemann surfaces .. 393 Entire and meromorphic functions .. 594 Conformal mapping .. 815 Elliptic functions and elliptic curves .. 108 ForwardComplex Analysis is a nexus for many mathematical fields, including:1. Algebra (theory of fields and equations);2. Algebraic geometry and Complex manifolds;3. Geometry (Platonic solids; flat tori; hyperbolic manifolds of dimen-sions two and three);4. Lie groups, discrete subgroups and homogeneous spaces ( (Z);5. Dynamics (iterated rational maps);6.)
Several complex variables and complex manifolds; 9. Real analysis and PDE (harmonic functions, elliptic equations and distributions). This course covers some basic material on both the geometric and analytic ... complex analysis (hence the forgetability of the de nition of the integral). it = a
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