Syllabus
Definition and examples of Riemann surfaces.
Holomorphic maps between Riemann surfaces. Meromorphic functions.
Riemann-Hurwitz theorem.
Elliptic functions. The Weierstrass p-function. Jacobi theta functions.
Classification of Riemann surfaces (Uniformization theorem).
Riemann-Roch theorem.
Annotation
In the lecture, we deal mainly with topological and analytical properties of Riemann surfaces and holomorphic maps between them. Basic concepts we try to explain are covering, homotopic group, divisors, Čech cohomology and the Riemann-Roch theorem.