Title: Riemann surfaces

Description: Basic definitions and examples. Holomorphic differential forms. Riemann-Hurwitz Theorem. The Riemann-Roch Theorem. The Dirichlet Problem. The Hodge theorem for Riemann surfaces. Embeddings into Projective Space. Uniformization theorem(s). Abel's Theorem and Jacobi’s inversion theorem. Further topics may include: Sheaves and cohomology. Fields of meromorphic functions, valuations and connections with algebraic number theory. Monodromy and classification of branched covers.

Offered: Fall

Prerequisite: MAT 531, MAT 533, MAT 536

Credits: 3

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