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Instructors: Prof. Dr. rer. nat. Moritz Egert; Prof. Dr. rer. nat. Robert Haller; M.Sc. Tim Böhnlein
Event type:
Lecture & Exercise
Org-unit: Dept. 04 - Mathematics
Displayed in timetable as:
04-10-0626-vu
Subject:
Crediting for:
Hours per week:
6
Language of instruction:
Englisch
Min. | Max. participants:
- | 26
Course Contents:
Introduction to Fourier analysis, weak derivatives and Sobolev spaces, form method, elliptic operators in divergence form, functional calculus, off-diagonal estimates, solution of the Kato square root problem.
Literature:
ISem script
Preconditions:
Basic knowledge in functional analysis, bounded operators, foundations of Hilbert spaces and some familiarity with the Fourier transform in one complex variable.
Further Grading Information:
The course is divided into three phases.
(1) (October to February)
During the semester there will be 2 lectures per week. Both lectures will be recorded and there will be an additional script that provides more sources for interested students. The contents will be presented self contained. Furthermore, there will be exercises each week that supplement the lectures.
It is possible to take an exam at the end of this phase (9CP).
(2) (March to June)
The participants will form small international groups to work on different topics that complement the first phase and provide some applications.
(3) (17.06.24 to 21.06.24)
The final workshop will take place at CIRM in Luminy (Marseille, France). Here, the participants will present their projects and further lectures will be given by world leading experts in the field of Harmonic Analysis.
(2) and (3) can be taken as a Master Analysis seminar (5CP).
Additional Information:
The associated Moodle course to this lecture is located on the moodle guest system of the TU Darmstadt, since there will be many particiapants from other universities involved. Clicking the above link brings you directly to the moodle course of the isem, or, to the login for the moodle guest system. Click here on "login (Shibboleth)" and you will encounter the usual TU-Id-login. (It might be that in order to get there, you must choose TU Darmstadt from a looong drop down menu.) Please enrol then for the course "27. International Internet Seminar: Harmonic Analysis Techniques for Elliptic Operators". The enrolment key is "$me\inIsem$" (without the "").
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