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
9:30-10:00Coffee
10:00-11:00tba
11:00-11:15Coffee break
11:15-12:15tba
12:15-13:45Lunch break
13:45-14:45tba
14:45-15:00Coffee break
15:00-16:00tba

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 $n \leq 6$.