Fachbereich Mathematik

Geometry in Physics

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

Class begins on October 18

Please register here for the exercise classes: URM

All further information including lecture notes, lecture recordings, and homework assignments will be provided on ILIAS. 

You can log in to both pages with your university access data.

Course Language:

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. 

The two weekly 90-minute lectures are accompanied by one weekly 90-minute exercise class, held by Paul Hege, where the weekly homework assignments will be discussed. Participants need to register here for the exercises.

In addition to the lecture notes, the following text books could be helpful.

- John Lee, Introduction to smooth manifolds

- John Lee, Riemannian manifolds: An introduction

- Chris Isham, Modern differential geometry for physicists

- M. Nakahara, Geometry, Topology and Physics