Fachbereich Mathematik

Geometry in Physics


The lecture will be held online. I will record the lectures and share the link via ILIAS. Additionally, there will be a weekly question hour on Monday, 12:30-1:30 pm, via zoom. The first question hour is on Nov 3. I will follow Stefan Teufel's lecture notes of this course held in the winter term 2018/19.

Schedule of the Lecture:

Date Video sections
02/11/2020 00.00 - 01.05
06/11/2020 01.06 - 02.02
09/11/2020 02.02 - 02.07
12/11/2020 02.08 - 02.12
16/11/2020 03.01 - 03.06
20/11/2020 04.01 - 04.05
23/11/2020 04.06 - 04.09
26/11/2020 05.01 - 05.04
30/11/2020 05.05 - 05.09
03/12/2020 06.01 - 06.06
07/12/2020 06.07 - 06.09
10/12/2020 07.01 - 07.05
14/12/2020 07.06 - 07.09
17/12/2020 08.01 - 08.04

Exercise class:

The exercise class will be held online as well, until further notice. I will put an exercise sheet online every Monday, which has to be submitted on Monday 12:00 am in the week after. Some solutions will be presented in videos, while others will be discussed in an exercise class, held by Stephen Lynch via zoom on Friday, 9:30-10:30 am. Participation in the exercise class via zoom will be made possible, if nessecary.

Sheets can be submitted as a single person or as a group of two people. In order to do the exam, 50% of the total amount of points need to be achieved by the end of the term.

via ILIAS, until Friday, November 13, 12:00 am.

Course Language:

This course is the module G1 of the Master in Mathematical Physics Program but is open to all degree programs.

Math: Analysis 1 and 2 and linear algebra.
Physics: Prior knowledge is sometimes helpful but not required.

The course provides an introduction to fundamental methods of differential geometry and their relevance for physics. Particular topics are manifolds, differential forms, Riemannian metrics and associated notions of curvature, Riemannian geometry of submanifolds, real and complex vector bundles, and connections. Applications of these concepts in Physics are discussed. 

Learning goals:
Students obtain knowledge, understanding, and acquaintance with the use of the listed notions of differential geometry. They develop, in particular, a deeper understanding of differential and integral calculus and experience through examples how the mathematical notions are naturally applied within physical theories.