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 "work place" MNO 6B in the 6th floor of the Maison du Nombre in Esch-Belval.

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

Date | Speaker | Title |

26/09/2019, 14:00h | Vlad Serban (Vienna) | Higher-dimensional distributions of Frobenius traces |

17/12/2019, all day | Luxembourg Number Theory Day 2019 | |

09/01/2020, 14:00 | Mladen Dimitrov (University of Lille) | Families of p-adic L-functions for conjugate-symplectic representations |

13/01/2020, 10:30 | Xiaoyu Zhang (Duisburg-Essen) | Hida theory for general spin Shimura varieties |

Date | Speaker | Title |

24/09/2019, 14:00 | Alexandre Maksoud | Iwasawa theory for weight one modular forms (I) |

01/10/2019, 14:00 | Alexandre Maksoud | Iwasawa theory for weight one modular forms (II) |

10/10/2019, 9:30 | Gabor Wiese | Integrality versus Ordinarity |

22/10/2019, 14:00 | Antonella Perucca | Kummer theory for number fields via entanglement groups |

29/10/2019, 14:00 | Andrea Conti | Symmetries of Galois representations (1) |

05/11/2019, 14:00 | Andrea Conti | Symmetries of Galois representations (2) |

26/11/2019, 14:00 | Daniel Berhanu | On Emerton-Gee Stacks |

03/12/2019, 14:00 | Luca Notarnicola | On Hidden Lattices |

14/01/2020, 14:00 | Emiliano Torti | Local Constancy Phenomena |

All references below are for Bosch: Lectures on Formal and Rigid Geometry, Springer.

Date | Speaker | Title |

01/10/2019, 11:00 | Emiliano Torti | Overview |

08/10/2019, 10:30 | Alexandre Maksoud | Tate Algebras |

22/10/2019, 10:30 | Andrea Conti | Affinoid Subdomains |

29/10/2019, 10:30 | Daniel Berhanu | Affinoid Functions (1) |

05/11/2019, 10:30 | Gabor Wiese | Affinoid Functions (2) |

12/11/2019, 10:30 | Emiliano Torti | Grothendieck topolodies |

19/11/2019, 10:30 | Alexandre Maksoud | Rigid Spaces |

26/11/2019, 10:30 | Andrea Conti | tba |

03/12/2019, 10:30 | Daniel Berhanu | tba |

10/12/2019, 10:30 | Fritz Hörmann | tba |

**Andrea Conti (uni.lu) ** * Symmetries of Galois representations *

The absolute Galois group of a local or global field can be better understood by studying its representations, important classes of which are constructed from geometric objects such as elliptic or modular curves. The results of a line of work initiated by Serre, Momose and Ribet suggest that certain symmetries of a Galois representation constructed this way, its so-called conjugate self-twists, are in bijection with the symmetries of the underlying geometric object. More precisely, one can show in many cases that the conjugate self-twists give an optimal bound for the image of the representation. We present a recent result in this direction, obtained in a joint work with J. Lang and A. Medvedovsky and relying on the Pink theory for generalised matrix algebras developed by J. Bellaïche, together with some open questions raised by this new development.

**Alexandre Maksoud (uni.lu) ** * Iwasawa theory for weight one modular forms *

In this talk we will first recall classical results in Iwasawa theory, then we will formulate and study an Iwasawa Main Conjecture in the context of classical newforms of weight one.

**Vlad Serban (Vienna) ** * Higher-dimensional distributions of Frobenius traces *

I will show how to extend the heuristics of Lang and Trotter on distributions of Frobenius traces for the Galois representation associated to elliptic curves to products of elliptic curves, highlighting the interesting features and the results motivating these predictions. I will also present some evidence for such conjectures. This is joint work with Hao Chen and Nathan Jones.

**Mladen Dimitrov (University of Lille)** *Families of p-adic L-functions for conjugate-symplectic representations*

We will explain how using automorphic cycles, one can attach p-adic L-functions to regular algebraic conjugate-symplectic cuspidal automorphic representations (RACSCAR) of GL(N) over a totally real number field. While in the ordinary case we recover those constructed by Ash-Ginzburg and by a previous work of the author with Januszewski and Raghuram, the more general (non-parabolically-critical) case relies on the full force of the overconvergent cohomology method. We further give the first variation of such p-adic L-functions in families, which had not previously been done even in the ordinary case. This is an ongoing joint work with Daniel Barrera and Chris Williams.

**Xiaoyu Zhang (University of Duisburg-Essen) *** Hida theory for general spin Shimura varieties*

The p-adic interpolation of modular forms started with Serre for Eisenstein series. Later Hida developed a theory of p-adic families of ordinary cuspidal modular forms. This theory has many interesting and important applications, such as modularity theorems, construction of p-adic L-functions, etc. In this talk, I will try to generalize this theory to general spin Shimura varieties where the ordinary locus may be empty. In this case, one can work with the mu-ordinary locus. I will talk about the construction of Hida families in this setting and give the control theorem on the dimension of such families.

Last modification: 13 January 2020.