Toby Gee

I am a Professor in the mathematics department at Imperial College London.

Office 666
180 Queen's Gate
London
SW7 2RH
UK

My email address is toby dot gee at imperial dot ac dot uk.

My CV is here: pdf (updated October 2024)

Number	Coauthors	Title	Link
3	George Boxer, Frank Calegari and Vincent Pilloni	Modularity theorems for abelian surfaces	pdf
2	Matthew Emerton and Eugen Hellmann	An introduction to the categorical p-adic Langlands program	pdf
1	Andrea Dotto and Matthew Emerton	Localization of smooth p-power torsion representations of GL2(Qp)	pdf

Number	Coauthors	Title	Journal	Link
53	George Boxer, Frank Calegari, James Newton and Jack A. Thorne	The Ramanujan and Sato-Tate conjectures for Bianchi modular forms	Forum of Math, Pi (2025), Vol. 13:e10 1–65.	pdf
52	George Boxer and Frank Calegari	Cuspidal cohomology classes for GLn(Z)	J. Amer. Math. Soc. (to appear)	pdf
51	Ana Caraiani, Matthew Emerton and David Savitt	The geometric Breuil–Mézard conjecture for two-dimensional potentially Barsotti-Tate Galois representations	Algebra and Number Theory (to appear)	pdf
50	Ana Caraiani, Matthew Emerton and David Savitt	Components of moduli stacks of two-dimensional Galois representations	Forum of Mathematics, Sigma 12 (2024), e31	pdf
49		Modularity lifting theorems	Essential Number Theory (to appear)	pdf
48	Matthew Emerton	Moduli stacks of étale (φ,Γ)-modules: a survey	Proceedings of the International Colloquium on `Arithmetic Geometry', TIFR Mumbai, Jan. 6-10, 2020 (to appear)	pdf
47	Ana Caraiani, Matthew Emerton and David Savitt	Local geometry of moduli stacks of two-dimensional Galois representations	Proceedings of the International Colloquium on `Arithmetic Geometry', TIFR Mumbai, Jan. 6-10, 2020 (to appear)	pdf
46	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	Annals of Mathematics (to appear)	pdf
45	Matthew Emerton	Moduli stacks of étale (φ,Γ)-modules and the existence of crystalline lifts	Annals of Math. Studies (to appear)	pdf errata
44	George Boxer, Frank Calegari and Vincent Pilloni	Abelian Surfaces over totally real fields are potentially modular	Publ. Math. de l'IHES (to appear)	pdf
43	Frank Calegari and Matthew Emerton	Globally realizable components of local deformation rings	Journal de l'Institut de Mathématiques de Jussieu (to appear)	pdf
42	James Newton	Patching and the completed homology of locally symmetric spaces	Journal de l'Institut de Mathématiques de Jussieu (to appear)	pdf
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.	pdf
40	Matthew Emerton	`Scheme-theoretic images' of morphisms of stacks	Algebraic Geometry (to appear)	pdf
39	Rebecca Bellovin	G-valued local deformation rings and global lifts	Algebra and Number Theory 13.2 (2019), pp. 333–378.	pdf
38	Florian Herzig and David Savitt	General Serre weight conjectures	Journal of the European Math Society 20.12 (2018), 2859–2949.	pdf
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.	pdf
36	Frank Calegari, Matthew Emerton and Lambros Mavrides	Explicit Serre weights for two-dimensional Galois representations	Compositio Mathematica 153.9 (2017), pp. 1893– 1907.	pdf
35	Florian Herzig, Tong Liu and David Savitt	Potentially crystalline lifts of certain prescribed types	Documenta Mathematica 22 (2017), 397–422.	pdf
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.	pdf
33	Kevin Buzzard	Slopes of modular forms	Proceedings of the 2014 Simons symposium on the trace formula.	pdf
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.	pdf
31	David Geraghty	The Breuil-Mézard conjecture for quaternion algebras	Annales de l'Institut Fourier 64 (2015), no. 4, 1557-1575.	pdf
30	Thomas Barnet-Lamb and David Geraghty	Serre weights for U(n)	J. Reine Angew. Math. 735 (2018), 199–224.	pdf
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.	pdf
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.	pdf
27	Mark Kisin	The Breuil-Mézard conjecture for potentially Barsotti-Tate representations	Forum of Math, Pi 2 (2014), e1, 56 pp.	pdf
26	Matthew Emerton and David Savitt	Lattices in the cohomology of Shimura curves	Inventiones mathematicae 200 (2015), no. 1, 1–96.	pdf
25	Tong Liu and David Savitt	The Buzzard-Diamond-Jarvis Conjecture for Unitary Groups	J. Amer. Math. Soc. 27 (2014), no. 2, 389–435.	pdf
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.	pdf
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.	pdf
22	Thomas Barnet-Lamb and David Geraghty	Serre weights for rank two unitary groups	Mathematische Annalen 356 (2013), no. 4, 1551–1598.	pdf
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.	pdf
20	Kevin Buzzard	Explicit reduction modulo p of certain 2-dimensional crystalline representations, II	Bulletin of the LMS 45 (2013), no. 4, 779–788.	pdf
19	Matthew Emerton and Florian Herzig	Weight cycling and Serre-type conjectures for unitary groups	Duke Math. Journal 162 (2013), no. 9, 1649–1722.	pdf
18	Payman Kassaei	Companion forms in parallel weight one	Compositio Mathematica 149 (2013), no. 6, 903–913.	pdf
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.	pdf
15	Kevin Buzzard	The conjectural connections between automorphic representations and Galois representations	Proceedings of the LMS Durham Symposium 2011.	pdf
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).	pdf
13	Thomas Barnet-Lamb and David Geraghty	Congruences betwen Hilbert modular forms: constructing ordinary lifts	Duke Math. Journal 161 (2012), Number 8, 1521-1580.	pdf
12	Tong Liu and David Savitt	Crystalline extensions and the weight part of Serre's conjecture	Algebra and Number Theory 6 (7), 1537-1559.	pdf
11	David Geraghty	Companion forms for unitary and symplectic groups	Duke Math. Journal 161 (2012), Number 2, 247-303.	pdf
10	Thomas Barnet-Lamb and David Geraghty	The Sato-Tate conjecture for Hilbert modular forms	J. Amer. Math. Soc. 24 (2011), 411-469.	pdf
9	David Savitt	Serre weights for mod p Hilbert modular forms: the totally ramified case	J. Reine Angew. Math. 2011:660, 1-26.	pdf
8		On the weights of mod p Hilbert modular forms	Inventiones mathematicae Volume 184, Number 1, 1-46 (2011).	pdf
7	David Savitt	Serre weights for quaternion algebras	Compositio Mathematica Volume 147, Issue 04, 1059-1086 (2011).	pdf
6		Automorphic lifts of prescribed types	Mathematische Annalen Volume 350, Number 1, 107-144 (2011).	pdf
5		The Sato-Tate conjecture for modular forms of weight 3	Documenta Mathematica 14 (2009) 771-800.	pdf
4	Kevin Buzzard	Explicit reduction modulo p of certain 2-dimensional crystalline representations	IMRN 2009, no. 12, 2303-2317.	pdf
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.	pdf
1		Companion forms over totally real fields	Manuscripta Math. 125 (2008), no. 1, 1-41.	pdf

The preprint "Dimension theory and components of algebraic stacks" with Matthew Emerton is now incorporated into the Stacks project, so we do not intend to publish it. It is available here.

I am an editor at Duke Mathematical Journal. Please see https://www.dukeupress.edu/Duke-Mathematical-Journal/ for submission instructions.

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