**
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

**Description**

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 P.do 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.

**Prerequisites**

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.

**Organization**

Students who would like to sign up for the seminar should come to the organization meeting or send me an email (lee@mathi.uni-heidelberg.de) 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.

**Schedule**

Date | Time | Speaker | Title | Building | Room |

November 20 | 14:15 - 15:45 | Stephan & Sven | Differential Forms in R^{n} |
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 |

**Reference**

Manfredo P.do Carmo, Differential Forms and Applications, Springer-Verlag, 1994.

Shigeyuki Morita, Geometry of Differential Forms, American Mathematical Society, 2001.

Manfredo P.do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976.