Papers

"Computing weight 1 modular forms over C and F_p-bar". pdf. Last modified late May 2012.

"Explicit reduction modulo $p$ of certain 2-dimensional crystalline Galois representations, II", with Toby Gee. pdf. Last modified May 2012.

"Potential modularity---a survey". I was asked to write this paper because there were some talks on potential modularity of elliptic curves by myself and others in Cambridge at the Newton Institute in 2009. dvi or pdf. Last modified April 2011.

"The conjectural connections between automorphic representations and Galois representations", with Toby Gee. dvi or pdf. Last modified Sept 2011 (definition of C-group added).

"On Serre's conjecture for mod ell Galois representations over totally real fields", with Fred Diamond and Frazer Jarvis, Duke Math Journal Vol 55 no. 1, 2010, pp105--161, dvi or pdf. Last modified April 2010.

"Explicit reduction modulo p of certain crystalline representations", with Toby Gee, IMRN 2009, no. 12, 2303--2317. dvi or pdf. Last modified Feb 2009.

"Eigenvarieties", in "$L$-functions and Galois representations", 59--120, London Math. Soc. Lecture Note Ser., 320, Cambridge Univ. Press, Cambridge, 2007. dvi or pdf (last updated 02/08/06).

"The 2-adic eigencurve is proper", with F. Calegari, dvi or pdf, Documenta Mathematica 2006, Extra Vol., 211--232 (last updated 05/07/05). That version assumes some standard facts about the 2-adic eigencurve. A slightly longer version of the paper, containing proofs of these facts, is here: dvi or pdf (also last updated 05/07/05).

"The 2-adic eigencurve at the boundary of weight space", with L. Kilford, Compositio Math. 141 (2005), 605--619, dvi or pdf, (last updated 04/06/04).

"Slopes of overconvergent 2-adic modular forms", with F. Calegari, Compositio Math. 141 (2005), 591--604, dvi or pdf,

"A counterexample to the Gouvea-Mazur conjecture", with F. Calegari, Comptes rendus - Mathematiques, Vol 338/10 (2004), pp 751--753, dvi or pdf, (last updated 28 Aug 03).

"On p-adic families of automorphic forms", pp23--44 of "Modular Curves and Abelian Varieties", Progress in Maths 224, Birkhauser, dvi or pdf (last updated 12 Oct 2004).

"Questions about slopes of modular forms", pp1--15 of "Formes Automorphes (I)", Asterisque 298, dvi or pdf. Computer programs related to this paper are here.

"Analytic continuation of overconvergent eigenforms", Journal of the American Math. Society 16 (2003), pp29--55. dvi or pdf

"A mod 5 approach to the modularity of icosahedral Galois representations", with W. Stein, Pacific Journal of Mathematics Vol 203 No 2 (2002), pp265-282, dvi or pdf.

"On icosahedral Artin representations", with M. Dickinson, N. Shepherd-Barron and R. Taylor, Duke Math Journal Vol 109 No 2 (2001), pp283-318, dvi or pdf.

"Families of modular forms", Journal de Th\'eorie des Nombres de Bordeaux, Vol 13 Fasc. 1 (2001), pp43--52, dvi or pdf.

"A mod l multiplicity one result", appendix to "Lectures on Serre's Conjectures" by K. Ribet and W. Stein, Arithmetic Algebraic Geometry, B. Conrad and K. Rubin, eds., IAS/Park City Mathematics Series vol. 9, AMS, dvi or pdf.

"On level lowering for mod 2 representations", Mathematical Research Letters 7, pp95--110 (2000), dvi or pdf.

"Companion forms and weight 1 forms" (with Richard Taylor), Annals of Maths Vol.149 (1999), 905--919, dvi or pdf.

"Integral models of certain Shimura curves", Duke Math Journal, Vol.87,No.3, 1997, dvi or pdf.

"On the eigenvalues of the Hecke operator T_2", Journal of Number Theory, Vol 57 No.1, March 1996, dvi or pdf.