Academic Year 2015/2016 - Number Theory Seminars

The Algebra and Number Theory group of the University of Luxembourg hosts three seminars.

Unless announced otherwise, the seminars take place in the lecture room of the library in the G-building.

Everyone is invited to attend! For more information, please contact Gabor Wiese.

Luxembourg Number Theory Seminar

Date Speaker Title
07/10/2015, 16:00 François Legrand (Tel Aviv) Parametric Galois extensions
02/12/2015, 16:00 Matthias Wendt (Duisburg-Essen) New counterexamples to Quillen's conjecture
09/03/2016, 15:15 Piermarco Milione (Barcelona) Reduction of CM-points on Shimura curves

Work in Progress Seminar

Date Speaker Title
23/09/2015, 14:15 Chun Yin Hui Invariant dimensions and maximality of geometric monodromy action
21/10/2015, 15:30 Alexander Rahm On Bianchi modular forms
02/03/2016, 15:15 Panagiotis Tsaknias Base Change formulas for imaginary quadratic fields
16/03/2016, 15:15 Chun Yin Hui Abelian part of compatible systems and geometry of roots
20/04/2016, 15:15 Eduardo Soto

Summer Term 2016: Research Seminar: Some Topics Around Serre's Modularity Conjecture


Date Speaker Title
17/02/2016, 14:15 Gabor Wiese Introduction
02/03/2016, 13:30 Alexander Rahm Eichler-Shimura isomorphism
09/03/2016 Panagiotis Tsaknias The Galois representation attached to a Hecke eigenform
16/03/2016 Eduardo Soto Local representation theory
06/04/2016, 14:00 Laia Amorós Formulation of Serre's modularity conjecture
13/04/2016, 14:00 Jasper Van Hirtum Sketch of proof of Serre's modularity conjecture
20/04/2016, 13:30 Chun Yin Hui Statement of Buzzard-Diamond-Jarvis conjecture

Winter Term 2015: Research Seminar: p-adic Galois representations


Date Speaker Title
07/10/2015, 14/10/2015 Sara Arias-de-Reyna Talk 1: \ell-adic representations of local fields
21/10/2015 Chun Yin Hui Talk 2: B-representations and regular G-rings
28/10/2015 Panagiotis Tsaknias Talk 3: Mod p Galois representations of G_E with \Char E=p
04/11/2015 Gabor Wiese Talk 4: p-adic Galois representations of G_E with \Char E=p and the ring R
18/11/2015 Sara Arias-de-Reyna Talk 5: The action of G_K on \Frac R and (\phi,\Gamma)-modules}
25/11/2015 Sara Arias-de-Reyna Talk 6: The Ax-Sen Lemma
02/12/2015 Panagiotis Tsaknias Talk 7: C-representations I
04/12/2015, 14:00Chun Yin Hui Talk 8: C-representations II
09/12/2015 Gabor Wiese Talk 9: Sen's \Theta-operator and C-admissible representations
09/12/2015 Sara Arias-de-Reyna Talk 11: The period field B_dR
11/12/2015, 14:15 Panagiotis Tsaknias Talk 12: de Rham representations
16/12/2015 Chun Yin Hui Talk 13: The period rings B_cris and B_st
16/12/2015 Gabor Wiese Talk 14: Semi-stable representations and filtered (\phi,N)-modules
18/12/2015, 13:00 Sara Arias-de-Reyna Talk 15: Main Theorems

Collection of abstracts

François Legrand (Tel Aviv) Parametric Galois extensions
Given a finite group G and a number field k, the main topic of the talk will be parametric extensions, i.e. Galois extensions of k(T) with group G realizing all the Galois extensions of k with group G by specialization (with T an indeterminate). Although one may think that there are only a few parametric extensions, proving that a given finite Galois extension E/k(T) with group G is not parametric is in general a difficult problem and only a few examples are known. In the first part of the talk, I will explain how parametric extensions relate to some classical questions in Inverse Galois Theory (e.g. the Inverse Galois Problem, the Regular Inverse Galois Problem, the Beckmann-Black Problem...). In the second part, I will present a systematic approach to give more examples of finite Galois extensions E/k(T) with group G that are not parametric. The strategy will rest on a study of the local behavior of the specializations of E/k(T).

Matthias Wendt (Duisburg-Essen) New counterexamples to Quillen's conjecture
In the talk I will explain the computation of cohomology of GL_3 over function rings of affine elliptic curves. The computation is based on the study of the action of the group on its associated Bruhat-Tits building. It turns out that the equivariant cell structure can be described in terms of a graph of moduli spaces of vector bundles on the corresponding complete curve. The resulting spectral sequence computation of group cohomology provides very explicit counterexamples to Quillen's conjecture. I will also discuss a possible reformulation of the conjecture using a suitable rank filtration.

Last modification: 29 August 2016.