Urs Lang: Catalogue data in Autumn Semester 2019 |
| Name | Prof. Dr. Urs Lang |
| Field | Mathematik |
| Address | Professur für Mathematik ETH Zürich, HG G 27.3 Rämistrasse 101 8092 Zürich SWITZERLAND |
| Telephone | +41 44 632 60 11 |
| urs.lang@math.ethz.ch | |
| URL | http://www.math.ethz.ch/~lang |
| Department | Mathematics |
| Relationship | Full Professor |
| Number | Title | ECTS | Hours | Lecturers | |
|---|---|---|---|---|---|
| 401-3531-00L | Differential Geometry I  At most one of the three course units (Bachelor Core Courses) 401-3461-00L Functional Analysis I 401-3531-00L Differential Geometry I 401-3601-00L Probability Theory can be recognised for the Master's degree in Mathematics or Applied Mathematics. | 10 credits | 4V + 1U | U. Lang | |
| Abstract | Introduction to differential geometry and differential topology. Contents: Curves, (hyper-)surfaces in R^n, geodesics, curvature, Theorema Egregium, Theorem of Gauss-Bonnet. Hyperbolic space. Differentiable manifolds, immersions and embeddings, Sard's Theorem, mapping degree and intersection number, vector bundles, vector fields and flows, differential forms, Stokes' Theorem. | ||||
| Learning objective | |||||
| Lecture notes | Partial lecture notes are available from https://people.math.ethz.ch/~lang/ | ||||
| Literature | Differential geometry in R^n: - Manfredo P. do Carmo: Differential Geometry of Curves and Surfaces - Wolfgang Kühnel: Differentialgeometrie. Kurven-Flächen-Mannigfaltigkeiten - Christian Bär: Elementare Differentialgeometrie Differential topology: - Dennis Barden & Charles Thomas: An Introduction to Differential Manifolds - Victor Guillemin & Alan Pollack: Differential Topology - Morris W. Hirsch: Differential Topology | ||||
| 401-5530-00L | Geometry Seminar | 0 credits | 1K | M. Einsiedler, P. Feller, U. Lang, A. Sisto, University lecturers | |
| Abstract | Research colloquium | ||||
| Learning objective | |||||