Bachelor/Master Seminar
Shape Spaces and Shape Optimization
summer 2022
| Lecturer: |
Christoph Böhm Benedikt Wirth |
Information on the seminar
| time, location: | will be collectively determined at the beginning of term |
| HIS/LFS: | BSc MSc |
| learnweb: | Seminar-Boehm-Wirth-2022_1 |
| contents: | In this seminar we will treat current research articles and book chapters on topics from the field of shape spaces. Shapes play a role in many application areas, e.g. the statistical distribution of organ shapes is examined in computational anatomy in order to detect illnesses from deviations (e.g. shape changes of the brain). For such applications one needs to provide the set of all shapes with an additional structure. This is typically a Hilbert manifold structure; some shape spaces also possess a lie group structure. The seminar theme allows to assign papers from a broad mathematical range, e.g. from differential geometry all the way to numerical analysis. |
| prerequisites: | Analysis I-III, basic courses in numerics/analysis or differential geometry or algebra. |
| initial meeting: |
First organizational meeting: We, March 16, 14:00, via zoom (access data available in learnweb course).
In case you are interested in the seminar, you can let us already know beforehand via e-mail. If you would like to already find a topic or start working, please drop an e-mail as well. |
| assessment: | 60-minute seminar talk and written report (ca. 7-page handout, to be presented and discussed with the lecturer ca. 10 days before the talk, to allow for improvements and further assistance) |
| literature: | An introductory book on some aspects of shape spaces is the following. A quick and application-oriented introduction into necessary differential-geometric tools are provided in Chapters 3 and 5.2-5.4 of the following book. |
| topics: |
Below you find a list of possible topics. The given literature will be understood as an outline for the according topics. The participants can and should base their presentation on additional relevant sources. Please contact the docents, if relevant sources are not accessible.
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