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250008 SE Seminar: Advanced number theory (2018W)
Continuous assessment of course work
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Details
max. 25 participants
Language: English
Lecturers
Classes (iCal) - next class is marked with N
- Wednesday 03.10. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 10.10. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 17.10. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 24.10. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 31.10. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 07.11. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 14.11. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 21.11. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 28.11. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 05.12. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 12.12. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 09.01. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 16.01. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 23.01. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
- Wednesday 30.01. 11:30 - 13:00 Seminarraum 11 Oskar-Morgenstern-Platz 1 2.Stock
Information
Aims, contents and method of the course
This is an introduction into the local and global representation-theory of reductive groups over number fields. Special focus will be on jointly developing the basics of a theory of smooth automorphic representations with the guidance of the course instructor. To this end we will firstly present/recall the “local theory” (= representation-theory of local groups such as for instance GL(n,Q_p)) in a condensed way, followed by a more speculative “global part” of the course (= smooth automorphic representation-theory). This “global part” shall be held in form of an open discussion, in which various ideas and approaches will be presented and jointly discussed by the participants. The outcome of this course shall be collected in joint seminar lecture-notes.
Assessment and permitted materials
The assessment has two components: An oral one (by contributing to the general discussion, in particular during the "global part") and a written one (by compiling a part of the joint lecture-notes in LaTeX). You may use all of the literature, specific to the topic, as well as the internet (e.g., mathoverflow).
Minimum requirements and assessment criteria
The minimum requirements for a positive grade are: (i) an active contribution to the discussion during the "global part" of the seminar and (ii) writing notes of a part of the lectures. The contribution to the discussion will account for 60%, compiling some lecture-notes for 40%. Attendance is compulsory, but up to two absences without notice are permitted.
Examination topics
The contents of the lectures.
Reading list
Local part:
(i) Chapter 0, III.2.1 - III.2.4, III.7, IV from A. Borel, N. Wallach, Continuous cohomology, discrete subgroups and representations of reductive groups, Ann. of Math. Studies, Princeton Univ. Press, (2000)
(ii) W. Casselman, Introduction to admissible representations of p-adic groups, available online: https://www.math.ubc.ca/~cass/research/pdf/p-adic-book.pdfGlobal part:
(i) Lectures 2 -4 from J. Cogdell, "Lectures on L-functions, Converse Theorems, and Functoriality for GL(n)" in: Lectures on Automorphic L-functions, Fields Institute Monographs, AMS (2004) pp. 3-96; available online: https://people.math.osu.edu/cogdell.1/fields-www.pdf
(ii) E. Lapid, "A remark on Eisenstein series", in: Eisenstein series and applications, W.T. Gan, S.S. Kudla, Y. Tschinkel eds., Progr. Math., 258, Birkhäuser (2008) pp. 149--186
(iii) F. Shahidi, Eisenstein series and Automorphic L-functions, Colloquium publications, 58, AMS, (2010)
(i) Chapter 0, III.2.1 - III.2.4, III.7, IV from A. Borel, N. Wallach, Continuous cohomology, discrete subgroups and representations of reductive groups, Ann. of Math. Studies, Princeton Univ. Press, (2000)
(ii) W. Casselman, Introduction to admissible representations of p-adic groups, available online: https://www.math.ubc.ca/~cass/research/pdf/p-adic-book.pdfGlobal part:
(i) Lectures 2 -4 from J. Cogdell, "Lectures on L-functions, Converse Theorems, and Functoriality for GL(n)" in: Lectures on Automorphic L-functions, Fields Institute Monographs, AMS (2004) pp. 3-96; available online: https://people.math.osu.edu/cogdell.1/fields-www.pdf
(ii) E. Lapid, "A remark on Eisenstein series", in: Eisenstein series and applications, W.T. Gan, S.S. Kudla, Y. Tschinkel eds., Progr. Math., 258, Birkhäuser (2008) pp. 149--186
(iii) F. Shahidi, Eisenstein series and Automorphic L-functions, Colloquium publications, 58, AMS, (2010)
Association in the course directory
MALS
Last modified: Mo 07.09.2020 15:40