## Math
608: Riemann Surfaces

**Fall 2018**

**Textbook**

Riemann Surfaces by way of Analytic
Geometry by D. Varolin,
AMS 2011.

**Course
Description**

An introduction to Analysis on
(mainly compact) Riemann surfaces. In complex analysis one studies analytic
functions-- their zeros, growth and mapping properties. There are no holomorphic
functions on compact Riemann surfaces. Instead
one has twisted holomorphic functions-- namely, holomorphic sections of line
bundles and meromorphic functions. We will
concentrate on holomorphic line bundles, their holomorphic sections, and Hermitian metrics on line bundles and
their curvature forms. The topics will include: the uniformization
theorem, HormanderŐs theorem, Mittage-Leffler
problem, KodairaŐs Embedding theorem and Riemann-Roch theorem.

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**Instructor**

Hang Xu

Email: hxu@math.jhu.edu

Office Location: Krieger Hall Rm 220

Office Hours: W 3:00-5:00

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**Lecture**

MW 12:00-1:15 at Charles Commons 324

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