Time and Room: Tue, Fri 11-13, E 27
Starts on Tuesday, October 21, 2003, at 11:15h
Problem sessions: Tuesday 14-16, E 47
What this course is about: Every serious study of analytic functions of one complex variable will need Riemann surfaces. For example, "multi-valued" functions like square root or logarithm can be treated in a satisfactory way using Riemann surfaces covering the complex plane. Abstractly speaking, a Riemann surface is simply a complex 1-dimensional manifold (which looks locally like an open set in the complex plane). Some topics treated in this course: Definitions and basic properties. Construction of Riemann surfaces associated to algebraic functions (the square root is the most elementary example). Quotients of Riemann surfaces by discontinuous automorphism groups (this allows an elegant treatment of modular functions and forms). Divisors, line bundles, Theorem of Riemann-Roch
Prerequisites: A first course on the theory of analytic functions of one complex variable (e.g. Funktionentheorie I). Basic notions of algebra and topology.
Studierende der Mathematik (und Theoretischen Physik)
Students of the International Master Program