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.
|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|
|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|
|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|
|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, 14:00||Chun 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|
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.