1 About me
|5||Matthew Emerton||Moduli stacks of étale (φ,Γ)-modules: a survey|
|4||Matthew Emerton||Moduli stacks of étale (φ,Γ)-modules and the existence of crystalline lifts|
|3||Ana Caraiani, Matthew Emerton and David Savitt||Moduli stacks of two-dimensional Galois representations|
|2||Patrick B. Allen, Frank Calegari, Ana Caraiani, David Helm, Bao V. Le Hung, James Newton, Peter Scholze, Richard Taylor, and Jack A. Thorne||Potential automorphy over CM fields|
|1||George Boxer, Frank Calegari and Vincent Pilloni||Abelian Surfaces over totally real fields are potentially modular|
|43||Frank Calegari and Matthew Emerton||Globally realizable components of local deformation rings||Journal de l'Institut de Mathématiques de Jussieu (to appear).|
|42||James Newton||Patching and the completed homology of locally symmetric spaces||Journal de l'Institut de Mathématiques de Jussieu (to appear).|
|41||Olivier Taïbi||Arthur's multiplicity formula for GSp(4) and restriction to Sp(4)||Journal de l’École polytechnique — Mathématiques 6 (2019), 469–535.|
|40||Matthew Emerton||`Scheme-theoretic images' of morphisms of stacks||Algebraic Geometry (to appear).|
|39||Rebecca Bellovin||G-valued local deformation rings and global lifts||Algebra and Number Theory 13.2 (2019), pp. 333–378.|
|38||Florian Herzig and David Savitt||General Serre weight conjectures||Journal of the European Math Society 20.12 (2018), 2859–2949.|
|37||Ana Caraiani, Matthew Emerton, David Geraghty, Vytautas Paškūnas and Sug Woo Shin||Patching and the p-adic Langlands program for GL(2, Qp)||Compositio Mathematica 154.3 (2018), 503–548.|
|36||Frank Calegari, Matthew Emerton and Lambros Mavrides||Explicit Serre weights for two-dimensional Galois representations||Compositio Mathematica 153.9 (2017), pp. 1893– 1907.|
|35||Florian Herzig, Tong Liu and David Savitt||Potentially crystalline lifts of certain prescribed types||Documenta Mathematica 22 (2017), 397–422.|
|34||Ana Caraiani, Matthew Emerton, David Geraghty, Vytautas Paškūnas and Sug Woo Shin||Patching and the p-adic local Langlands correspondence||Cambridge Journal of Mathematics 4.2 (2016), pp. 197–287.|
|33||Kevin Buzzard||Slopes of modular forms||Proceedings of the 2014 Simons symposium on the trace formula.|
|32||Matthew Emerton||p-adic Hodge-theoretic properties of étale cohomology with mod p coefficients, and the cohomology of Shimura varieties||Algebra and Number Theory 9 (2015), no. 5, 1035–1088.|
|31||David Geraghty||The Breuil-Mézard conjecture for quaternion algebras||Annales de l'Institut Fourier 64 (2015), no. 4, 1557-1575.|
|30||Thomas Barnet-Lamb and David Geraghty||Serre weights for U(n)||J. Reine Angew. Math. 735 (2018), 199–224.|
|29||Tong Liu and David Savitt||The weight part of Serre's conjecture for GL(2)||Forum of Math, Pi 3 (2015), e2, 52 pp.|
|28||Luis Dieulefait||Automorphy lifting for small l (Appendix B to Dieulefait's "Automorphy of Symm5(GL(2)) and base change")||J. Math. Pures et Appl. 104.4 (2015), 619–656.|
|27||Mark Kisin||The Breuil-Mézard conjecture for potentially Barsotti-Tate representations||Forum of Math, Pi 2 (2014), e1, 56 pp.|
|26||Matthew Emerton and David Savitt||Lattices in the cohomology of Shimura curves||Inventiones mathematicae 200 (2015), no. 1, 1–96.|
|25||Tong Liu and David Savitt||The Buzzard-Diamond-Jarvis Conjecture for Unitary Groups||J. Amer. Math. Soc. 27 (2014), no. 2, 389–435.|
|24||Thomas Barnet-Lamb, David Geraghty and Richard Taylor||Potential automorphy and change of weight||Annals of Mathematics (2) 179 (2014), no. 2, 501–609.|
|23||Thomas Barnet-Lamb and David Geraghty||Congruences betwen Hilbert modular forms: constructing ordinary lifts, II||Mathematical Research Letters 20 (2013), no. 1, 67–72.|
|22||Thomas Barnet-Lamb and David Geraghty||Serre weights for rank two unitary groups||Mathematische Annalen 356 (2013), no. 4, 1551–1598.|
|21||Matthew Emerton||A geometric perspective on the Breuil-Mézard conjecture||Journal de l'Institut de Mathématiques de Jussieu 13 (2014), no. 1, 183–223.|
|20||Kevin Buzzard||Explicit reduction modulo p of certain 2-dimensional crystalline representations, II||Bulletin of the LMS 45 (2013), no. 4, 779–788.|
|19||Matthew Emerton and Florian Herzig||Weight cycling and Serre-type conjectures for unitary groups||Duke Math. Journal 162 (2013), no. 9, 1649–1722.|
|18||Payman Kassaei||Companion forms in parallel weight one||Compositio Mathematica 149 (2013), no. 6, 903–913.|
|17||Frank Calegari||Irreducibility of automorphic Galois representations of GL(n), n at most 5||Annales de l'Institut Fourier 63 (2013), no. 5, 1881–1912.||pdf (including erratum)|
|16||Thomas Barnet-Lamb, David Geraghty and Richard Taylor||Local-global compatibility for l=p, II||Annales scientifiques de l'ENS (4) 47 (2014), no. 1, 165–179.|
|15||Kevin Buzzard||The conjectural connections between automorphic representations and Galois representations||Proceedings of the LMS Durham Symposium 2011.|
|14||Thomas Barnet-Lamb, David Geraghty and Richard Taylor||Local-global compatibility for l=p, I||Annales de Mathématiques de Toulouse Volume 21, Number 1, 57-92 (2012).|
|13||Thomas Barnet-Lamb and David Geraghty||Congruences betwen Hilbert modular forms: constructing ordinary lifts||Duke Math. Journal 161 (2012), Number 8, 1521-1580.|
|12||Tong Liu and David Savitt||Crystalline extensions and the weight part of Serre's conjecture||Algebra and Number Theory 6 (7), 1537-1559.|
|11||David Geraghty||Companion forms for unitary and symplectic groups||Duke Math. Journal 161 (2012), Number 2, 247-303.|
|10||Thomas Barnet-Lamb and David Geraghty||The Sato-Tate conjecture for Hilbert modular forms||J. Amer. Math. Soc. 24 (2011), 411-469.|
|9||David Savitt||Serre weights for mod p Hilbert modular forms: the totally ramified case||J. Reine Angew. Math. 2011:660, 1-26.|
|8||On the weights of mod p Hilbert modular forms||Inventiones mathematicae Volume 184, Number 1, 1-46 (2011).|
|7||David Savitt||Serre weights for quaternion algebras||Compositio Mathematica Volume 147, Issue 04, 1059-1086 (2011).|
|6||Automorphic lifts of prescribed types||Mathematische Annalen Volume 350, Number 1, 107-144 (2011).|
|5||The Sato-Tate conjecture for modular forms of weight 3||Documenta Mathematica 14 (2009) 771-800.|
|4||Kevin Buzzard||Explicit reduction modulo p of certain 2-dimensional crystalline representations||IMRN 2009, no. 12, 2303-2317.|
|3||A modularity lifting theorem for weight two Hilbert modular forms||Mathematical Research Letters Volume 13, Issue 5, September 2006, 805-811.||pdf Erratum|
|2||Companion forms over totally real fields, II||Duke Math. Journal 136 (2007), no. 2, 275-284.|
|1||Companion forms over totally real fields||Manuscripta Math. 125 (2008), no. 1, 1-41.|
Notes from my lectures at the 2019 Hausdorff School are here.
I taught a course on modularity lifting theorems at the 2013 Arizona Winter School; the current draft notes are here.
The preprint "Dimension theory and components of algebraic stacks" with Matthew Emerton is now completely incorporated into the Stacks project, so we do not intend to publish it. It is available here.
I am on the editorial board of Selecta Mathematica. Please see http://www.springer.com/birkhauser/mathematics/journal/29 for submission instructions.
I am on the academic advisory board of MathOA, which aims to persuade journals to convert to a "fair open access" model: http://www.mathoa.org
6 Accessibility on this site
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This statement was prepared on September 10 2020. It was last updated on September 12 2020.