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250087 VO Advanced topics in global number theory (2024S)
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Registration/Deregistration
Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).
Details
max. 25 participants
Language: English
Examination dates
Lecturers
Classes (iCal) - next class is marked with N
- Wednesday 06.03. 13:15 - 14:45 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
- Wednesday 13.03. 13:15 - 14:45 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
- Wednesday 20.03. 13:15 - 14:45 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
- Wednesday 10.04. 13:15 - 14:45 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
- Wednesday 17.04. 13:15 - 14:45 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
- Wednesday 24.04. 13:15 - 14:45 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
- Wednesday 08.05. 13:15 - 14:45 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
- Wednesday 15.05. 13:15 - 14:45 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
- Wednesday 22.05. 13:15 - 14:45 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
- Wednesday 29.05. 13:15 - 14:45 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
- Wednesday 05.06. 13:15 - 14:45 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
- Wednesday 12.06. 13:15 - 14:45 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
- Wednesday 19.06. 13:15 - 14:45 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
- Wednesday 26.06. 13:15 - 14:45 Seminarraum 6 Oskar-Morgenstern-Platz 1 1.Stock
Information
Aims, contents and method of the course
This course is an introduction into the theory of unitary representations of GL(n) over the ring of adeles and their eminent role in modern number theory.We will start with basic concepts (e.g., What is the ring of adeles?), explain fundamental notions of representation theory of locally compact groups and we will then focus on the case of our interest, the group GL(n) over the adeles.A prominent role will take the cuspidal spectrum of GL(n) - a unitary representation on a certain space of square-integrable functions, which is of highest number-theoretical importance. We will see - by analogy to GL(1) - that the cuspidal spectrum of GL(n) decomposes over irreducible unitary representations: The cuspidal “automorphic” representations of GL(n).However, these global automorphic „building blocks“ decompose even further: Namely, they are the infinite tensor product of local irreducible unitary representations, one for each place of the field of rational numbers! This final observation, which will be one of the main objectives of the lecture, will close the loop back to modern number theory.
Assessment and permitted materials
Oral exam at the end of the semester on appointment.
Minimum requirements and assessment criteria
Good knowledge of the central concepts presented in the course, as well as the ability to apply them in certain examples. We apply the usual standards for exams of Master's courses.
Examination topics
The contents presented in the course. Exceptions (if any) would be announced as the course progresses.
Reading list
J. Neukirch "Algebraic Number Theory" Springer (1999)
D. Goldfeld, J. Hundley, "Automorphic Representations and L-Functions for the General Linear Group" I & II, Cambridge Univ. Press (2011)
D. Bumb, "Automorphic Forms and Representations" Cambridge Univ. Press (1998)
D. Goldfeld, J. Hundley, "Automorphic Representations and L-Functions for the General Linear Group" I & II, Cambridge Univ. Press (2011)
D. Bumb, "Automorphic Forms and Representations" Cambridge Univ. Press (1998)
Association in the course directory
MALV
Last modified: Th 09.01.2025 14:26