Let ff be a cuspidal Hecke eigenform of level 1. We prove the automorphy of the symmetric
power lifting Sym nf Sym^nf for every n≥ 1 n≧1. We establish the same result for a more …

We prove new potential modularity theorems for n-dimensional essentially self-dual l-adic
representations of the absolute Galois group of a totally real eld. Most notably, in the …

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math f</jats: tex-math>< mml: math xmlns: mml=" http://www. w3. org/1998/Math/MathML"> …

We prove an automorphy lifting theorem for l-adic representations where we impose a new
condition at l, which we call" potentential diagonalizability." This result allows for" change of …

Patching and the p-adic local Langlands correspondenceT1 Page 1 arXiv:1310.0831v5 [math.NT]
1 Jul 2016 Cambridge Journal of Mathematics Volume 0, Number 0, 1, 2014 Patching and the …

We prove new automorphy lifting theorems for essentially conjugate self-dual Galois
representations into GLn. Existing theorems require that the residual representation have …

We prove the Breuil–Mézard conjecture for two-dimensional potentially Barsotti–Tate
representations of the absolute Galois group (up to the question of determining precise …

For an abelian surface A over a number field k, we study the limiting distribution of the
normalized Euler factors of the L-function of A. This distribution is expected to correspond to …

A GEOMETRIC PERSPECTIVE ON THE BREUIL–MÉZARD CONJECTURE Page 1 J. Inst. Math.
Jussieu (2014) 13(1), 183–223 183 doi:10.1017/S147474801300011X c Cambridge University …

We consider certain families of automorphic representations over number fields arising from
the principle of functoriality of Langlands. Let GG be a reductive group over a number field …