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250093 VO G-Structures (2021W)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik
MIXED

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

Language: English

Lecturers

Classes (iCal) - next class is marked with N

Thursday 07.10. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 13.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 14.10. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 20.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 21.10. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 27.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 28.10. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 03.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 04.11. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 10.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 11.11. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 17.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 18.11. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 24.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 25.11. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 01.12. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 02.12. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 09.12. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 15.12. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 16.12. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 12.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 13.01. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 19.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 20.01. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 26.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Thursday 27.01. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

This is a topics course in the area of specialization "geometry and topology" of the master program which is also suitable for doctoral students. It can be used as an elective in other areas of the master program, too.

G-structures provide a general approach to the concept of a "geometric structure" in differential geometry. We start by discussing from the examples of Riemannian metrics and (almost) symplectic structures, which look similar, but have very different properties. To formulate the general concept of a G-structure, we have to develop the language of fiber bundles and in particular principal bundles that is fundamental for several areas of differential geometry and theoretical physics. The concept of principal connections then leads to compatible connections on G-structures which are the fundamental tool for studying their properties. It turns out that a surprising amount of information about these properties can be deduces using finite dimensional linear algebra and representation theory. The discussion of a large number of examples will be a substantial part of the course. Depending on the available time, I will also discuss Cartan geometries and/or filtered analogs of G-structures.

The current plan is to teach the course in presence. To be on the safe side, there will be a moodle page for the course which will be the main point of contact for the course, in particular if distance teaching becomes neccessary.

Assessment and permitted materials

oral exam after the end of the course

Minimum requirements and assessment criteria

Students know the fundamental concepts and results of fiber bundles, connections and the theory of G-structures as discussed in the course and can describe the proofs of the central results presented in the course; the usual standards for topics courses in the master program will be employed

Examination topics

the contents of the course

Reading list

Lecture notes for the course will be distributed via the webpage
https://www.mat.univie.ac.at/~cap/lectnotes.html in parts during the semester. Discussions of G-structrues in the literature are available for example in the classical books "Transformation groups in differential geometry" by S. Kobayashi (Springer, 1972) and "Lectures on differential geometry" by S. Sternberg (2nd edition, Chelsea Publishing, 1983).

Association in the course directory

MGEV

Last modified: We 15.09.2021 16:08