Title of the course: Introduction to Riemann surfaces
Instructor: Dr. Davide Cesare Veniani
Institution: Universität Stuttgart
Dates: 4-10 September 2023
Prerequisites: Groups, Basics of topology and complex analysis
Level: Graduate, Advanced undergraduate
Abstract: Riemann surfaces are connected one-dimensional complex manifolds. Examples include the complex plane, the sphere and the torus. Building intuition on Riemann surfaces is extremely useful to explore other mathematical objects like higher dimensional complex manifolds and algebraic varieties. In this course, we will introduce holomorphic functions and divisors on a Riemann surface, with the aim of proving the Riemann–Roch theorem.
Language: English
Textbook: “Algebraic Curves and Riemann Surfaces” by Rick Miranda