University of Oxford,
Woodstock Road, Oxford,
As of September 2021, I have moved to Oxford. My new webpage should be linked to from here, once it exists.
I am interested in algebraic number theory, particularly (p-adic) automorphic forms and Galois representations.
Papers and preprints:
- Symmetric power functoriality for holomorphic modular forms, II, with Jack Thorne
- Symmetric power functoriality for holomorphic modular forms, with Jack Thorne
- Adjoint Selmer groups of automorphic Galois representations of unitary type, with Jack Thorne
To appear in Journal of the EMS. Arxiv preprint.
- Automorphy lifting for residually reducible l-adic Galois representations, II, with Patrick Allen and Jack Thorne
To appear in Compositio Mathematica. Arxiv preprint.
- Monodromy for some rank two Galois representations over CM fields, with Patrick Allen
- Potential Automorphy over CM fields, with P. Allen, F. Calegari, A. Caraiani, T. Gee, D. Helm, B. Le Hung, P. Scholze, R. Taylor and J. Thorne
- Parallel weight 2 points on Hilbert modular eigenvarieties and the
parity conjecture, with Christian Johansson
Forum of Mathematics, Sigma, 2019 Arxiv preprint, journal version.
- Local Langlands correspondence in rigid families, with Christian Johansson and Claus Sorensen
Pacific J. Math., 2020. Arxiv preprint, journal version.
- Irreducible components of extended eigenvarieties and interpolating Langlands functoriality, with Christian Johansson
Math. Res. Lett., 2019 Arxiv preprint, journal version.
- Irreducible components of the eigencurve of finite degree are finite over the weight space, with Shin Hattori
J. Reine Angew. Math., 2020. Arxiv preprint, journal version.
- Patching and the completed homology of locally symmetric spaces, with Toby Gee
To appear in J. Inst. Math. Jussieu. Arxiv preprint, journal version.
- Extended eigenvarieties for overconvergent cohomology, with Christian Johansson
Algebra & Number Theory 2019. Arxiv preprint, journal version.
- Torsion Galois representations over CM fields and Hecke algebras in the derived category, with Jack Thorne
Forum of Mathematics, Sigma 2016. Arxiv preprint, journal version.
- Shimura curves, the Drinfeld curve and Serre weights, with Teruyoshi Yoshida
- Towards local-global compatibility for Hilbert modular forms of low weight
Algebra & Number Theory 2015. Arxiv preprint, journal version.
- Level raising for p-adic Hilbert modular forms
J. Théor. Nombres Bordeaux 2016. Arxiv preprint, journal version.
- An appendix to "Universal eigenvarieties, trianguline Galois representations, and p-adic Langlands functoriality" by David Hansen
J. Reine Angew. Math. 2017. Arxiv preprint, journal version.
- Serre weights and Shimura curves
Proceedings of the LMS, 2013. Preprint, journal version.
- Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence
Mathematische Annalen, 2012. Arxiv preprint (with a few fixes compared to the journal version), journal version.
- Level raising and completed cohomology
IMRN, 2011. Arxiv preprint, journal version.
- Geometric level raising for p-adic automorphic forms
Compositio Mathematica, 2011. Arxiv preprint, journal version.
Some minor corrections to this work can be found in the paper "Level raising for p-adic Hilbert modular forms" listed above.
2018 – present Ashwin Iyengar.
2018 – present Pol van Hoften.
2020 – present Lambert A'Campo.
I am also second supervisor for several students, including Hanneke Wiersema.
I lectured Introduction to Number theory at King's from 2016 to 2020. I am now teaching Linear Algebra and Geometry II. All course materials are on KEATS.
I lectured Group Representation Theory (M3/4/5P12) at Imperial College London in Spring 2016. The homepage for the course is here.
I lectured a Part III course in Cambridge on Modular Forms in Lent term 2014. The homepage for the course is here.
Details for the London Number Theory Seminar are here. I am hosting pages for the Summer 2020 (online) seminar and study group.