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250093 VO G-Structures (2021W)
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GEMISCHT
An/Abmeldung
Hinweis: Ihr Anmeldezeitpunkt innerhalb der Frist hat keine Auswirkungen auf die Platzvergabe (kein "first come, first served").
Details
Sprache: Englisch
Prüfungstermine
Lehrende
Termine (iCal) - nächster Termin ist mit N markiert
- Mittwoch 06.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 07.10. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 13.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 14.10. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 20.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 21.10. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 27.10. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 28.10. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 03.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 04.11. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 10.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 11.11. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 17.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 18.11. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 24.11. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 25.11. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 01.12. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 02.12. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 09.12. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 15.12. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 16.12. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 12.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 13.01. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 19.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 20.01. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Mittwoch 26.01. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
- Donnerstag 27.01. 10:45 - 11:45 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Information
Ziele, Inhalte und Methode der Lehrveranstaltung
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.
Art der Leistungskontrolle und erlaubte Hilfsmittel
oral exam after the end of the course
Mindestanforderungen und Beurteilungsmaßstab
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
Prüfungsstoff
the contents of the course
Literatur
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).
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).
Zuordnung im Vorlesungsverzeichnis
MGEV
Letzte Änderung: Mi 15.11.2023 00:20