Joaquim Serra: Catalogue data in Autumn Semester 2021 |
| Name | Prof. Dr. Joaquim Serra |
| Field | Mathematics |
| Address | Professur für Mathematik ETH Zürich, HG J 54 Rämistrasse 101 8092 Zürich SWITZERLAND |
| Telephone | +41 44 632 50 60 |
| joaquim.serra@math.ethz.ch | |
| Department | Mathematics |
| Relationship | Associate 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. In this case, you cannot change the category assignment by yourself in myStudies but must take contact with the Study Administration Office (www.math.ethz.ch/studiensekretariat) after having received the credits. | 10 credits | 4V + 1U | J. Serra | |
| 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 | Provide insightful knowledge about the classical theory of curves and surfaces (which is the precursor of modern differential geometry). Invite students to use and sharpen their geometric intuition. Introduce the language, basic tools, and some fundamental results in modern differential geometry. | ||||
| Lecture notes | Partial lecture notes are available from Prof. Lang's website https://people.math.ethz.ch/~lang/ | ||||
| Literature | - Manfredo P. do Carmo: Differential Geometry of Curves and Surfaces - John M. Lee: Introduction to Smooth Manifolds - S. Montiel, A. Ros: Curves and Surfaces - S. Kobayashi: Differential Geometry of Curves and Surfaces - Wolfgang Kühnel: Differentialgeometrie. Kurven-Flächen-Mannigfaltigkeiten - Dennis Barden & Charles Thomas: An Introduction to Differential Manifolds | ||||
| 401-5350-00L | Analysis Seminar | 0 credits | 1K | A. Carlotto, F. Da Lio, A. Figalli, N. Hungerbühler, M. Iacobelli, T. Ilmanen, L. Kobel-Keller, T. Rivière, J. Serra, University lecturers | |
| Abstract | Research colloquium | ||||
| Learning objective | |||||