250196 VO Locally Compact Groups (2021S)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik

Moodle

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

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

In case it should be impossible to teach on site, the course will take place digitally. A link to stream the talks will be available on the dedicated Moodle page.

Monday 01.03. 11:30 - 13:00 Digital
Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 08.03. 11:30 - 13:00 Digital
Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 15.03. 11:30 - 13:00 Digital
Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 22.03. 11:30 - 13:00 Digital
Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 12.04. 11:30 - 13:00 Digital
Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 19.04. 11:30 - 13:00 Digital
Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 26.04. 11:30 - 13:00 Digital
Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 03.05. 11:30 - 13:00 Digital
Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 10.05. 11:30 - 13:00 Digital
Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 17.05. 11:30 - 13:00 Digital
Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 31.05. 11:30 - 13:00 Digital
Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 07.06. 11:30 - 13:00 Digital
Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 14.06. 11:30 - 13:00 Digital
Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 21.06. 11:30 - 13:00 Digital
Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
Monday 28.06. 11:30 - 13:00 Digital
Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The topic of locally compact groups represents a joint cornerstone of algebra and analysis – a trait which will be apparent throughout the course. We will begin with an introduction to the general theory of topological groups, but with the aim of setting up the theory of integration on locally compact groups (keyword: Haar measure).
We will include several important case studies: locally compact fields (with close connections to number theory) and locally profinite groups (topologized generalizations of Galois groups and p-adic "localizations" of algebraic groups).
Introduction to the representation theory of locally compact groups, with special focus on the case of abelian groups, corresponding to abstract Fourier analysis, and on the case of locally profinite groups, corresponding to p-adic analysis.

Prerequisites: fundamental concepts from point-set topology, elementary algebraic structures, basic knowledge from real analysis in several dimensions.

Assessment and permitted materials

Oral exam at the end of the semester (online if necessary).

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) will be announced as the course progresses.

Reading list

• Gerald B. Folland, A Course in Abstract Harmonic Analysis, 1995
• Garth Warner, Harmonic Analysis on Semi-Simple Lie Groups, 1972
• Dinakar Ramakrishnan, Robert J. Valenza, Fourier Analysis on Number Fields, 1999
• Colin J. Bushnell, Guy Henniart, The Local Langlands Conjecture for GL(2), 2006

Association in the course directory

MALV; MANV;

Last modified: Tu 19.09.2023 00:22