| 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 |
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 $n \leq 6$.