Venue: TBA
Class Timings: To be decided on the first day. Meet twice a week (1.5 hrs each session). Separate TA sessions will be arranged.
First Meeting: 8th August 2024 at 4:00 PM
Course Description: Definition and examples of Riemann surfaces, topology and differential forms on Riemann surfaces, homology and cohomology of Riemann surfaces, Euler characteristics of Riemann surfaces, holomorphic and meromorphic functions on Riemann surfaces, holomorphic maps between Riemann surfaces, global properties of holomorphic and meromorphic functions, covering manifolds (ramified coverings), Riemann-Hurwitz theorem, underlying Riemann surface structure on minimal surfaces, Weierstrass-Enneper representation of minimal surfaces and some constructions of particular minimal surfaces.
Books: Parts of
1. Riemann surfaces, Farkas and Kra
2. Algebraic curves and Riemann surfaces, Rick Miranda.
3. Surveys on minimal surface, R Osserman.
Course Evaluation: Grading will be based on presentations which will include working out some problems
Course Outcome: The students will get an introduction to Riemann surfaces with many examples. In the process they will learn about homology, cohomology of Riemann surfaces, holomorphic and meromorphic maps between Riemann surfaces with examples. They will also learn about ramified coverings of Riemann surfaces and Riemann-Hurwitz theorem. They will also learn about underlying Riemann surface structure of minimal surfaces and their Weirstrass-Enneper representation with examples. They will get working knowledge in all these topics.