Mathematics and Physics in Heidelberg Fakultät für Mathematik und Informatik Fakultät für Mathematik und Informatik Mathematisches Institut Karl-Theodor-Brücke Surprise Fakultät für Physik und Astronomie Fakultät für Physik und Astronomie Institut für Theoretische Physik Universität Heidelberg Universität Heidelberg Universität Heidelberg

Lecture course in the Summer Semester 2022 (Diese Veranstaltung findet in englischer Sprache statt!)

Lie groups and representation theory


Lecture

This course is taught in English.

Time and place: Monday & Wednesday, 9-11 am, SR A, INF 205 Mathematikon.
Recordings of the lecture are provided on MaMpf.

Instructor: Prof. J. Walcher, walcher@uni-heidelberg.de

Description: The course corresponds roughly to the learning content "Darstellungstheorie 1" of the module MM14 from the mathematics master program. In comparison to the current module description, a stronger emphasis is placed on the representation theory (of finite and compact topological groups over the real and complex numbers) that is most important for applications in physics.

Prerequisites: Linear algebra and elements of topology, basic notions of differential geometry and Hilbert spaces is advantageous for full benefit in the middle section of the course.

References: Within the enormous amount of literature on the subject, a modern classic is:
W. Fulton and J. Harris, Representation Theory: A first course, Springer GTM 129
I also like:
B. Simon, Representations of Finite and Compact Groups, AMS Graduate Studies in Mathematics, Vol. 10


Exercises

Important: Registration in MÜSLI and MaMpf.

Time and place: Tuesday, 14-16, SR 8, INF 205 Mathematikon and on Zoom.
Recordings of the exercises are provided on MaMpf.

Direction: Sebastian Nill

Routine: The weekly problem sets with two to four assignments become available in MaMpf on Monday, 1 pm. Solutions can be submitted until the following Monday, 12:00 through the digital homework box on MaMpf in groups of order two or three. Write all your names at the top of the first page. The file size of your PDF should not exceed 5 MB. The submissions will not be corrected and returned, but merely checked for completeness. Handing in 50% of the homework problems is sufficient to be admitted to the exam. Proposals for solutions are discussed in the tutorial on Tuesday. There is a thread on the MaMpf-Board for finding a submission group.


Exam

The written exam takes place in SR A on Monday, 25 July, 9:00-11:00. It will be a closed book exam. Additional materials, like a handwritten piece of paper or technical devices, are not allowed. Handing in 50% of the homework problems is sufficient to be admitted to the exam. Please register in MÜSLI for the exam, and bring your student ID. The exam review takes place in SR 1, INF 205 on Friday, 29 July Tuesday, 2 August, 10:00-10:45.