Lecture: Wednesdays, 10:00-12:00, SR 5 (every week)
Exercise session: Thursdays, 12:00-14:00, SR 5 (once every two weeks)
Note: The course will be held in English.
The goal of this course is to learn the basics of differentiable/complex manifolds and Hodge theory.
Differentiable/complex manifolds and differentiable/holomorphic vector bundles
Differential forms on differentiable/complex manifolds
De Rham and Dolbeault cohomology
Riemannian/hermitian/Kähler manifolds
Harmonic forms on compact riemannian/hermitian manifolds
The Hodge decomposition on compact Kähler manifolds
Linear Algebra I & II, Analysis I & II & III, Complex Analysis
Exercise sheets will appear in our MS Teams - Complex Geometry Team once every two weeks. They must be solved until the following week and the solutions shall be submitted via the MS Teams - Complex Geometry Team. The solutions will be corrected and graded, and then they will be returned to you in the next exercise session.
Exam Criteria: In order to be permitted to take part in the exam at least 50% of the total points from the exercise sheets must be collected.
Exam Type: There will be an oral exam at the end of the semester.
Exam Dates: The exam dates will be arranged individually.
If you cannot register in the LSF for the exam, please send an email to Nikolaos Tsakanikas (your Prüfungssekretariat should send us a confirmation that you are allowed to take part in the exam in time before the exam). Moreover, if your Prüfungsordnung allows it, you may use the second exam to improve your grade.
The Campus-Bibliothek für Informatik und Mathematik set up a course reserve for this lecture, see here.