This course is intended as a panorama of the fascinating geometry of Riemann surfaces. Riemann surfaces are classical geometric objects which can be studied using a myriad of tools ranging from topology, differential geometry, complex analysis, and commutative algebra. They are a great topic to get acquainted with for anybody curious about geometry.
We start by describing various models of the hyperbolic space and introducing the notions of metrics, geodesics, hyperbolic isometries, and Fuchsian groups. We define Riemann surfaces from the real, complex, and algebraic perspectives, and build many examples of them using these different viewpoints. After these notions are properly defined and illustrated, we focus on defining, understanding, and describing the “space of all Riemann surfaces”. This is a gentle introduction to moduli spaces and Teichmüller theory.
- Kursleiter/in: Cécile Gachet