V5A6 Selected Topics in Representation Theory: The Arithmetic of the Langlands program - Sommersemester 2020
Time and Place
First Lecture: 23.4.2020.
Due to the Corona crisis the lectures will be delivered via Zoom. Meeting number and password will appear on eCampus. In case of any questions or problems contact me via e-mail.
Content of the course
Originally, the aim of this course was to provide its participants with more background material for the parallel trimester program The Arithmetic of the Langlands program at the HIM, so that they could more easily profit from the lectures and talks presented there. As the trimester program was cancelled due to the Corona crisis, the aim of this course has slightly changed and is now a general introduction to the Langlands program, in particular to the local Langlands program. The material of this course can still include topics such as a (very) general introduction to the Langlands program, the construction of Galois representations associated to modular forms, examples of Shimura varieties, p-adic modular forms and so on. In particular, the lectures will probably provide more of an overview than a detailed exposition and the lectures may, to some extent, be independent of each other. Participants can moreover express interest in particular aspects of the Langlands program and their suggestions can be taken up during the semester.
The precise prerequisites for the different lectures will vary drastically. General prerequisites include (étale) cohomology theory, scheme theory, Galois theory and algebraic number theory. However, as the lectures give more of an overview it will be possible to profit from the courses even if the prerequisites are not met.
There exists a revised version of the notes, which were presented in the lectures. Use these carefully, as they are presumably not free from mistakes!
- Bernstein, Joseph; Gelbart, Steve : An Introduction to the Langlands program, ISBN 978-0-8176-8226-2.
- Getz, Jayce R.; Hahn, Heekyoung: An Introduction to Automorphic representations with a view toward Trace formulae, a draft is available here .
There will be no exercise session accompanying the lecture.
Contact me if you want to take an oral exams. The first day for oral exams will be on 31.7.2020.