65-403 Complex Analysis (in English)

Instructors: Prof. Dr. Jörg Alexander Teschner

Event type: Lecture

Displayed in timetable as: M-VFT-V

Hours per week: 4

Language of instruction: English

Min. | Max. participants: - | -

Comments/contents:
Complex Analysis

The goal of this course is to introduce into the complex analytic theory of Riemann surfaces. Requisites are only the most basic notions and results from the theory of functions of a single complex variable like notion of holomorphic function, Laurent series expansions, and the Residue theorem.

On the content:

- Definition of Riemann surfaces, Sheaves, Differential Forms
- Compact Riemann surfaces:
Cohomology Groups, Riemann-Roch Theorem, Serre Duality
- Line bundles, Divisors and Jacobian
- Theta functions, Abel's Theorem and Jacobi Inversion

If time permits we might be able to cover also some aspect of

- Vector bundles
- The Riemann-Hilbert problem

The recorded lectures will be made available on Lecture2Go and the Moodle course page. They will be uploaded twice a week, and should be available at the time announced in the course catalogue unless there is a special announcement.

There will be a script made available via Moodle, and weekly exercise sheets
to work on.

The exams at the end of the semester will be oral. I will provide details about this closer to the time.
To be admitted to the oral exam you should present solutions in the exercise class twice!