Course content

This is an introduction to some topics of contemporary complex analysis, in particular spaces of analytic functions, quasiconformal mappings, univalent functions. The purpose is to prepare the student to independent work in these topics and especiaslly to use the methods of complex analysis in other areas of mathematics, (for example harmonic analysis and differential equations) as well as in applied areas (fluid dynamic, signal analysis, statistics). The content may vary, dependent on the needs and interests of the students.

Learning outcome

1. Knowlegde. The course presents an introduction to some topics of contemporary complex analysis, in particular spaces of analytic functions, quasiconformal mappings, univalent functions. The purpose is to prepare the student to independent work in these topics and especially to use the methods of complex analysis in other areas of mathematics, (for example harmonic analysis and differential equations) as well as in applied areas (fluid dynamic, signal analysis, statistics). The content may vary, dependent on the needs and interests of the students. 2. Skills. The students should learn the basic techniques of contemporary complex analysis as well as use methods of complex analysis in various applications such as harmonic analysis, differential equations as well as in the applied disciplines which are mentioned above. 3. Competence. The students should be able to participate in scientific discussions and conduct researches on high international level in contemporary and classical complex analysis and its applications.

Learning methods and activities

Lectures, alternatively guided self-study.

The course will be taught as needed. If there are few PhD students, the course is only given as a guided self-study.

Course materials

Will be announced at the start of the course.