On the automorphy of l-adic Galois representations with small residual image.
To appear in the Journal of the Institute of Mathematics of Jussieu.
[pdf]
Adequate subgroups.
Appendix to the above paper. With Robert Guralnick, Florian Herzig and Richard Taylor.
[pdf]
On the Tate-Shafarevich groups of certain elliptic curves.
Journal of Number Theory (2010) 130, No. 9, pp. 2092-2098.
[pdf]
Notes for a summer tutorial in p-adic analysis. [pdf]