# Luxembourg Number Theory Day 2023

The **Luxembourg Number Theory Day** will take place on December 20, 2023, on the Esch-Belval Campus of the University of Luxembourg.

### Speakers

Samuele Anni (Aix-Marseille Université)

Adel Betina (University of Copenhagen)

Wushi Goldring (Stockholm University)

Chun Yin Hui (University of Hong Kong)

### Contact

Andrea Conti, andrea.conti at uni.lu

### Location

All of the talks will take place in room **MNO 1.030** on the 1st floor of the Maison du Nombre at 6, Avenue de la Fonte, Esch-sur Alzette. You can see this on Google Maps or OpenStreetMap.

### Schedule

**Time** | **Speaker** | **Title** |

9:30-10:00 | *Coffee* | |

10:00-11:00 | tba | |

11:00-11:15 | *Coffee break* | |

11:15-12:15 | tba | |

12:15-13:45 | *Lunch break* | |

13:45-14:45 | tba | |

14:45-15:00 | *Coffee break* | |

15:00-16:00 | tba | |

A conference dinner will take place on the night of Tuesday, December 19.

### Abstracts

**Chun Yin Hui** *Monodromy of subrepresentations and irreducibility of low degree automorphic Galois representations*

Given a compatible system $\{\rho_\lambda : \Gal_K \to \GL_n(E_\lambda)\}_\lambda$ of semisimple $\lambda$-adic representations of a number field $K$ satisfying mild local conditions, we prove that for almost all $\lambda$ any type A irreducible subrepresentation of $\rho_\lambda\otimes\overline\Q_\ell$ is residually irreducible.
We apply this result and some potential automorphy theorem to prove that $\rho_\lambda\otimes\overline\Q_\ell$ is residually irreducible for almost all $\lambda$ if the compatible system is attached to a regular algebraic, polarized, cuspidal automorphic representation of $\GL_n(\A_\Q)$ and $n \leq 6$.