We study irreducible odd mod p Galois representations ρ¯: Gal (F‾∕ F)→ G (F‾ p), for F a
totally real number field and G a general reductive group. For p≫ G, F 0, we show that any …

We construct a Langlands parameterization of supercuspidal representations of $ G_2 $
over a $ p $-adic field. More precisely, for any finite extension $ K/\QQ_p $ we will construct …

A note on Galois representations with big image Page 1 L’Enseignement Mathématique (2) 65
(2019), 271–301 DOI . /LEM/ - / - A note on Galois representations with big image Nicholas M …

Up to isomorphism, there is a unique connected semisimple algebraic group over $\mathbb
{Q} $ of Lie type $\mathrm {F} _ {4} $, with compact real points and split over $\mathbb {Q} …

We study irreducible mod p representations, valued in general reductive groups, of the
Galois group of a number field. When the number field is totally real, we show that odd …

We prove a potential automorphy theorem for suitable Galois representations Γ F+→ GSpin
2 n+ 1 (F¯ p) and Γ F+→ GSpin 2 n+ 1 (Q¯ p), where Γ F+ is the absolute Galois group of a …

In this paper, we prove new instances of the inverse Galois problem over global function
fields for finite groups of Lie type. This is done by constructing compatible systems of ℓ-adic …

For a Shimura variety $(G, X) $ in the superrigid regime and neat level subgroup $ K_0 $,
we show that the canonical family of $\ell $-adic representations associated to a number …

These are lectures given at the 2022 Arizona Winter School. It gives an introduction to the
rigidity method for constructing automorphic forms for semisimple groups over function …

Let m be an integer such that m≥ 7 and m≡ 0, 1, 7 mod8. We construct strictly compatible
systems of representations of ΓQ→ Spinm (Ql) spin−−→ GLN (Ql) that are potentially …