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Hinweis Bitte informieren Sie sich auf den jeweiligen GRIPS-Seiten über den digitalen Ablauf der Lehrveranstaltungen.  Note For our digital courses all relevant information can be found on the appropriate GRIPS sites.Seminar: Lie groups, Lie algebras and their representations SemesterWiSe 2020 / 21 Lecturer Jonathan Glöckle, Matthias Ludewig Type of course (Veranstaltungsart) Seminar Contents Lie groups are important to describe symmetries, both in mathematics and in application (physics, chemistry, engineering, ...). The classical Lie groups are for example the orthogonal groups O(n), the unitary groups U(n), but mathematicians and physicists are also fascinated by more exotic examples such as the symmetry group of the octonions which is discussed a lot in modern mathematical physics. Many of these Lie groups can be represented as subgroups of Gl(k,R) for some sufficiently large k, but there are also Lie groups which cannot. Lie groups are manifolds G with a group structure on the underlying set such that the group multiplication is smooth. Lie groups and their representation is a mighty theory which allows effect calculations both for problems inside mathematics and also for applications outside (e.g. if in physics or chemistry the coupling of two electrons with various spin is described, this can be nicely described in terms of representaions of the Liegroup SU(2)=Spin(3)). This seminar mainly addresses to students in the fifth semesters and may lead directly to bachelor theses in global analysis. But also other students are very welcome. The subject fits well with the lecture about Differential Geometry I by Clara Löh: the contents are almost disjoint but allow many interesting topics for bachelor and master theses buildung on both courses. If all participants are fluent in German, the seminar will be held in German, otherwise the English on demand rule of the department will apply. Literature A. Knapp, Lie groups beyond an introduction. Birkhäuser 1996. For further literature, refer to seminar homepage. Recommended previous knowledge Analysis I & II, Linear Algebra I & II, Analysis on Manifolds (Analysis IV). Time/Date Wednesday 16-18 Location digital Course homepage https://homepages.uni-regensburg.de/~lum63364/LieGroupSeminar/ (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
BV, BSem, MV, MSem, LA-GySem ECTS Siehe Modulkatalog. MV und Nebenfach: 4,5 LP bei Studienbeginn ab WS 15/16, 6 LP bei Studienbeginn vor WS 15/16 |