Joaquim Serra: Catalogue data in Autumn Semester 2021

Name Prof. Dr. Joaquim Serra
Professur für Mathematik
ETH Zürich, HG J 54
Rämistrasse 101
8092 Zürich
Telephone+41 44 632 50 60
RelationshipAssistant Professor

401-3531-00LDifferential Geometry I Information
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 (Link) after having received the credits.
10 credits4V + 1UJ. Serra
AbstractIntroduction 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.
ObjectiveProvide 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 notesPartial lecture notes are available from Prof. Lang's website
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
401-5350-00LAnalysis Seminar Information 0 credits1KA. Carlotto, F. Da Lio, A. Figalli, N. Hungerbühler, M. Iacobelli, T. Ilmanen, L. Kobel-Keller, T. Rivière, J. Serra, University lecturers
AbstractResearch colloquium