Title of the course: Introduction to Riemann Surfaces
Instructor: Msc. Andrea Tomatis
Institution: Beuth Hochschule fuer Technik
Dates: 20-24 July 2020
Prerequisites: Complex Analysis
Level: Advanced undergraduate
Abstract:
Riemann surfaces are complex differential manifolds of (complex) dimension one. They lie at the crossroads of complex analysis, differential geometry and algebra and their theory is thus very rich. This is the first course in a sequence of three given in subsequent weeks at the mathematics village in Summer 2020. It can be attended independently of the other two. It will be an introduction to the topology and differential geometry of Riemann surfaces including covering spaces, sheaves and differential forms. A working knowledge of complex analysis as in the first three chapters of the book Complex Analysis by Eberhard Freitag and Rolf Busam, Springer Verlag, 2009, will be assumed.
Language: English
Textbook or/and course webpage: Lectures on Riemann Surfaces, Otto Forster, Springer Verlag