Title of the course: Compact Riemann surfaces
Instructor: MSc. Andrea Tomatis
Institution: Hochschule fuer Technik und Wirtschaft Berlin
Dates: 7-13 August 2023
Prerequisites: Complex Analysis as in the first three chapters of the book Complex Analysis by Eberhard Freitag and Rolf Busam, Springer Verlag, 2009, basic differential geometry
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.
In this course we will cover the cohomology of compact Riemann surfaces leading to the Riemann Roch, Serre duality and Abel theorems. This course is the second in a sequence of three offered in subsequent weeks in Summer 2023 at the mathematics village. It can be attended independently of the other two. It is however necessary to have some knowledge of the material discussed in the previous course. If you are prepared to do some independent work it should be possible to fill in the gaps while attending the course.
Language: English