250113 VO Topics in Number Theory (2024S)
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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
- Friday 01.03. 11:30 - 14:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Friday 08.03. 11:30 - 14:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Friday 15.03. 11:30 - 14:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Friday 22.03. 11:30 - 14:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Friday 19.04. 11:30 - 14:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Friday 26.04. 11:30 - 14:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Friday 03.05. 11:30 - 14:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Friday 10.05. 11:30 - 14:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Friday 17.05. 11:30 - 14:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Friday 24.05. 11:30 - 14:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Friday 31.05. 11:30 - 14:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Friday 07.06. 11:30 - 14:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Friday 14.06. 11:30 - 14:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Friday 21.06. 11:30 - 14:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
- Friday 28.06. 11:30 - 14:00 Hörsaal 13 Oskar-Morgenstern-Platz 1 2.Stock
Information
Aims, contents and method of the course
This advanced course can be inscribed in one of the most exciting and active areas in Number Theory: the Langlands Program. This program is an expanding series of highly profound conjectures and theorems relating different objects in arithmetic, geometry and analysis, that would seem to be completely unrelated. At its core are the Langlands correspondences, relating the spectra of any reductive algebraic group G to some Galois theoretic data. We will focus in the case where G is the group GL(n,F), where F is a p-adic field, and just one side of the correspondence, the representation side.Therefore we will studying detail the representation theory of GL(n,F). Irreducible representations of this group are parametrised by the so-called multisegments some combinatorial avatars that are related to many interesting questions in combinatorics.
Assessment and permitted materials
Oral exam at the end of the lecture.
Minimum requirements and assessment criteria
Passing the exam.
Examination topics
The contents of the course.
Reading list
C. J. Bushnell, G. Henniart, "The Local Langlands Conjecture for GL(2)", Grundlehren der mathematischen Wissenschaften 335 (Springer, 2006)
D. Renard, Représentations des groupes réductifs p-adiques, Cours spécialisés, volume 17, SMF
A.V. Zelevinsky, Induced representations of reductive p-adic groups. II. On irreducible representations of GL(n), Ann. Sci. Éc. Norm. Supér. (4) 13 (2) (1980) 165–210.
Erez Lapid and Alberto Mínguez, On parabolic induction on inner forms of the general linear group over a non-archimedean local field, Selecta Math. (N.S.) 22 (2016), no. 4, 2347–2400.
Erez Lapid and Alberto Mínguez, Geometric conditions for -irreducibility of certain representations of the general linear group over a non-archimedean local field, Adv. Math. 339 (2018), 113–190.
D. Renard, Représentations des groupes réductifs p-adiques, Cours spécialisés, volume 17, SMF
A.V. Zelevinsky, Induced representations of reductive p-adic groups. II. On irreducible representations of GL(n), Ann. Sci. Éc. Norm. Supér. (4) 13 (2) (1980) 165–210.
Erez Lapid and Alberto Mínguez, On parabolic induction on inner forms of the general linear group over a non-archimedean local field, Selecta Math. (N.S.) 22 (2016), no. 4, 2347–2400.
Erez Lapid and Alberto Mínguez, Geometric conditions for -irreducibility of certain representations of the general linear group over a non-archimedean local field, Adv. Math. 339 (2018), 113–190.
Association in the course directory
MALV
Last modified: Tu 17.09.2024 14:26