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Syllabus Riemannian geometry of diffeomorphism groups - 80833

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Last update 14-09-2020
HU Credits: 2

Degree/Cycle: 2nd degree (Master)

Responsible Department: Mathematics

Semester: 2nd Semester

Teaching Languages: Hebrew

Campus: E. Safra

Course/Module Coordinator: Dr. Cy Maor

Coordinator Email: cy.maor@mail.huji.ac.il

Coordinator Office Hours: By Appointment

Teaching Staff:
Dr. Cy Maor

Course/Module description:
Riemannian geometry of diffeomorphism groups (and related spaces) arises naturally in a variety of different contexts from completely pure to applied and even computational mathematics. I will give an introduction to the topic, with a tentative outline as follows:
1. Introduction to infinite dimensional Riemannian geometry
2. Spaces of interest and metrics of interest (mainly in shape analysis and mathematical hydrodynamics)
3. Metric properties of diffeomorphism groups: vanishing distance phenomenon, diameter, metric completeness
4. Geodesic equations: short time existence, regularity of geodesics (following EbinMarsden), geodesic completeness

Course/Module aims:
Same as in learning outcomes.

Learning outcomes - On successful completion of this module, students should be able to:
Familiarity with the subject and open questions in it.

Attendance requirements(%):
100

Teaching arrangement and method of instruction: Irrelevant - determined between the teacher and the student.

Course/Module Content:
See course description

Required Reading:
Course notes

Additional Reading Material:
Irrelevant

Course/Module evaluation:
End of year written/oral examination 0 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 0 %
Assignments 0 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 100 %
100

Additional information:
 
Students needing academic accommodations based on a disability should contact the Center for Diagnosis and Support of Students with Learning Disabilities, or the Office for Students with Disabilities, as early as possible, to discuss and coordinate accommodations, based on relevant documentation.
For further information, please visit the site of the Dean of Students Office.
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