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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.Differential Geometry I SemesterWiSe 2020 / 21 Lecturer Clara Löh Type of course (Veranstaltungsart) Vorlesung Contents Differential geometry is the study of geometric objects by analytic means. Geometric objects in this context usually are Riemannian manifolds, i.e., smooth manifolds with a Riemannian metric. This allows to define lengths, volumes, angles, ... in the language of (multilinear) analysis. A central concern of differential geometry is to define and compare (intrinsic) notions of curvature of spaces. A particularly fascinating aspect is that many local curvature constraints are reflected in the global shape. Differential geometry has various applications in the formalisation of Physics, in medical imaging, and also in other fields of theoretical mathematics. For example, certain phenomena in group theory and topology can only be understood via the underlying geometry. In this course, we will introduce basic notions of differential geometry. This includes, in particular, the Riemannian curvature tensor, sectional curvature, Ricci curvature, and scalar curvature. Moreover, we will study some first global obstructions to curvature constraints. If all participants agree, this course can be held in German; solutions to the exercises can be handed in in German or English. Recommended previous knowledge All participants should have a firm background in Analysis I/II, in Linear Algebra I/II, in basic group theory (as covered in the lectures on Algebra), and in Analysis IV (e.g., as in Analysis auf Mannigfaltigkeiten; Prof. Ammann, SS 2020). Time/Date Wed 8:30--10:00, Thu 10:15--12:00 Location digital Course homepage http://www.mathematik.uni-r.de/loeh/teaching/diffgeo_ws2021 (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
BV, MV, MGAGeo ECTS 9 |