Jack Thorne's homepage

Jack Thorne

I am a Clay Research Fellow and Reader in Number Theory at the University of Cambridge.

You can send me an e-mail: mylastname at dpmms dot cam dot ac dot uk.

Here are some of my papers. (Please note that these may not be final versions. In particular, they may not include changes made before publication.)

On the GL(n) eigenvariety and a conjecture of Venkatesh.
Preprint. With David Hansen. [pdf]

Elliptic curves over Q are modular.
Preprint. [pdf]

Torsion Galois representations over CM fields and Hecke algebras in the derived category.
Preprint. With James Newton. [pdf]

Automorphy of some residually S5 Galois representations.
Preprint. With Chandrashekhar Khare. [pdf]

A 2-adic automorphy lifting theorem for unitary groups over CM fields.
Preprint. [pdf]

Equidistribution of Frobenius eigenvalues.
To appear in IMRN. [pdf]

Potential automorphy and the Leopoldt conjecture.
Preprint. With Chandrashekhar Khare. [pdf]

On the 2-Selmer groups of plane quartic curves with a marked point.
Preprint. With an appendix by Tasho Kaletha. [pdf]

A remark on the arithmetic invariant theory of hyperelliptic curves.
Mathematical Research Letters, Vol. 21 (2014), No. 6, pp. 1451-1482. [pdf]

Automorphy of some residually dihedral Galois representations.
To appear in Math. Annalen. [pdf]

E6 and the arithmetic of a family of non-hyperelliptic curves of genus 3.
Forum of Mathematics, Π, Vol. 3 (2015), e1 [pdf]

Level-raising and symmetric power functoriality, III.
Preprint. With Laurent Clozel. [pdf]

On the rigid cohomology of certain Shimura varieties.
Preprint. With Michael Harris, Kai-Wen Lan, and Richard Taylor. [pdf]

On the φ-Selmer groups of the elliptic curves y2 = x3 - D x.
Preprint. With Daniel Kane. [pdf]

Level-raising and symmetric power functoriality, II.
Annals of Mathematics, Vol. 181 (2015), No. 1, pp. 303-359. With Laurent Clozel. [pdf]

Level-raising and symmetric power functoriality, I.
Compositio Mathematica, Vol. 150 (2014), No. 5, pp 729-748. With Laurent Clozel. [pdf]

Raising the level for GL(n).
Forum of Mathematics Σ, Vol. 2 (2014), e16. [pdf]

Automorphy lifting for residually reducible l-adic Galois representations.
J. Amer. Math. Soc. Vol. 28 (2015), pp. 785-870. [pdf]

Vinberg's representations and arithmetic invariant theory.
Algebra & Number Theory, Vol. 7 (2013), No. 9, 2331-2368. This is a revised version of my thesis, The Arithmetic of Simple Singularities. [pdf]

On the automorphy of l-adic Galois representations with small residual image.
Journal of the Inst. of Math. Jussieu, Vol. 11 (2012), No. 4, pp. 855-920. [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]