Applied Harmonic Analysis
Course Description
Applied Harmonic Analysis is a subarea of Harmonic Analysis and studies efficient representations and the analysis of functions. Methods from this area are today used in a variety of fields ranging from operator theory over partial differential equations up to real-world applications in data science. This makes it not only a very exciting and versatile research area, but also a foundational area of mathematics. The results in this field draw from several topics such as approximation theory, Fourier analysis, functional analysis, and microlocal analysis.
- Frame Theory
- Wavelet and Shearlet Theory
- Theory of Compressed Sensing
- If time permits, a short excursion to the Theory of Deep Neural Networks
Schedule and Venue
- Lecture (Prof. Gitta Kutyniok): Tue, 14.00-16.00, and Thu, 10.00-12.00 (Room 504, Akademiestr. 7)
- Exercise Class (Adalbert Fono): Wed, 14.00-16.00 (Room B 134)
- Office Hour (Adalbert Fono): Tue, 13.00-14.00 (Room 510, Akademiestr. 7). Please email me the day before office hours to let me know if you plan to attend.
Requirements
The course is targeted at Master students from mathematics. The course requires knowledge of the topics from the course “Maßtheorie und Integralrechnung mehrerer Variablen”. Moreover, basic knowledge of functional analysis is highly recommended.
Creditable Modules
Master in Mathematics: WP35 Fortgeschrittene Themen aus der künstlichen Intelligenz und Data Science (9 ECTS)
Master in Financial and Insurance Mathematics: WP12 Advanced Topics in Mathematics A (9 ECTS) or WP22 Advanced
Topics in Computer and Data Science A (9 ECTS)
Registration
Register at moodle: Applied Harmonic Analysis (Kutyniok, Fono), enrollment key is AHA23/24.