SUBJECT

Title

Riemann surfaces

Type of instruction

lecture

Level

master

Part of degree program
Credits

3

Recommended in

Semesters 1-4

Typically offered in

Autumn/Spring semester

Course description

Abstract definition, coverings, analytic continuation, homotopy, theorem of monodromy, universal covering,  covering group, Dirichlet's problem, Perron's method, Green function, homology, residue theorem, uniformization theorem for simply connected Riemann surfaces.

 Determining the Riemann surface from its covering group. Fundamental domain, fundamental polygon. Riemann surface of an analytic function, compact Riemann surfaces and complex algebraic curves.

Readings

O. Forster: Lectures on Riemann surfaces, GTM81, Springer-Verlag, 1981