Seminar: Differential forms and their use

Wintersemester 2014/2015

Dr. Gye-Seon Lee

Time and Location
Thursdays 2 - 4 p.m. and INF 294, -111

Next meeting
February 6, at 4 p.m. in INF 288, HS 5

Office hours
Wednesdays 2 - 4 p.m. in INF 288, 108

Organization meeting
October 16, at 2 p.m. in INF 294, -111

In this seminar, we will introduce differential forms, develop the method of moving frames of Elie Cartan for surfaces, and finally prove the Gauss-Bonnet theorem for compact orientable surfaces. Our main reference is the book "Differential Forms and Applications" by Manfredo Carmo. After you skim over the book, you can choose one chapter (or project) you are interested in. There will be no regular meeting, however, during the semester you will give a presentation and hand in a short report.

This seminar is aimed at students interested in topology and geometry, but does not require any previous knowledge of them. We only assume an elementary knowledge of calculus. Interested students from physics are also welcome to attend. The seminar is open for bachelor (or master) students. The seminar will be taught in English.

Students who would like to sign up for the seminar should come to the organization meeting or send me an email ( and let me know what project you would like to carry out. Once you have agreed on the topic of your project with me, you should contact me to discuss the content of your project in more detail. Please let me help you during the preparation of your presentation.

Date Time Speaker Title Building Room
November 20 14:15 - 15:45 Stephan & Sven Differential Forms in Rn INF 294 -111
December 18 Danilo & Sandra Differentiable Manifolds
January 15 Benedetta & Pablo Integration on Manifolds
January 22 Ingolf & Phillpp Differential Geometry of Surfaces
January 29 14:15 - 15:15 Fabian Theorem of Gauss-Bonnet
February 5 Xiaoman Various operations on Differential forms
February 6 16:00 - 17:00 Vlora Fundamental theorem of the local theory of curves INF 288 HS 5
17:00 - 18:00 Andrea Frobenius Theorem

Manfredo Carmo, Differential Forms and Applications, Springer-Verlag, 1994.
Shigeyuki Morita, Geometry of Differential Forms, American Mathematical Society, 2001.
Manfredo Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976.

last updated: 6 February 2015