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

- The
**Luxembourg Number Theory Seminar**hosts invited speakers and takes place occasionally. - In the
**Research Seminar**the group members study a topic together; during term time the seminar takes place weekly. - In the
**Work in Progress Seminar**the group discusses its work in progress; during term time the seminar takes place weekly.

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.

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 |

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 |

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 |

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, 14:00 | 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.