Bachelor/Master Seminar

Theory and Numerics for Shape Spaces

summer 2025

Lecturer:  Dennis Wulle
 Benedikt Wirth

Information on the seminar

time, location: will be collectively determined at the beginning of term
HIS/LFS: BSc
MSc, Numerics
MSc, Analysis
learnweb: Seminar: Theory of Shape Spaces SoSe 2025
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.

Note that MSc students can take the seminar either in the scientific computing or the applied analysis module - which one will depend on the assigned seminar topic.
prerequisites:  Analysis I-III, basic courses in numerics/analysis or differential geometry or algebra.
choosing a topic: In case you are interested in the seminar, please sign up in the corresponding learnweb course and let us know via e-mail until April 4 (please let us know which article or direction you prefer; in case you do not yet pick an article, tell us your background such as previous attended courses so that we can make a suggestion suitable for you). 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 lecturers, if relevant sources are not accessible.