MAT 543  Complex Analysis II: Riemann Surfaces   Fall 2013 

Tue & Thu 11:30am - 12:50pm Math 4-130

Instructor: Ljudmila Kamenova

Office: Math Tower 3-115
Office hours: Wednesdays from 1:30 to 3:30 pm or by appointment

This course will provide a gentle introduction to complex geometry starting with complex curves, or Riemann surfaces.

Topics will include: holomorphic maps, the fundamental group, coverings, sheaves,Mittag-Leffler's problem, Cech cohomology groups, harmonic forms, the Hodge decomposition, Serre duality, Riemann-Roch's theorem, Riemann-Hurwitz' formula, Abel's theorem, etc.

Text: Lectures on Riemann Surfaces, by O. Forster

Additional references:

Prerequisites and grading: We will assume some of the material covered in the core courses (Topology-Geometry: MAT 530/531, Algebra: MAT534/535, Algebraic Topology: MAT539 and Complex Analysis I: MAT542).

Grades will be based upon class participation.

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