Toby Gee

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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.

I am an editor for Mathematische Annalen. Please submit papers via the online system at https://www.editorialmanager.com/maan/.

I am also on the editorial board of Selecta Mathematica. Please see http://www.springer.com/birkhauser/mathematics/journal/29 for submission instructions.

My CV is here: pdf (updated January 2017)

Teaching

I taught a course on modularity lifting theorems at the 2013 Arizona Winter School; the current draft notes are here.

Preprints

  Coauthors Title Link
5 Rebecca Bellovin G-valued local deformation rings and global lifts pdf
4 Matthew Emerton Dimension theory and components of algebraic stacks pdf
3 James Newton Patching and the completed homology of locally symmetric spaces pdf
2 Florian Herzig and David Savitt General Serre weight conjectures pdf
1 Matthew Emerton `Scheme-theoretic images' of morphisms of stacks pdf

Publications

  Coauthors Title Journal Link    
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 (to appear). pdf    
36 Frank Calegari, Matthew Emerton and Lambros Mavrides Explicit Serre weights for two-dimensional Galois representations Compositio Mathematica (to appear). pdf    
35 Florian Herzig, Tong Liu and David Savitt Potentially crystalline lifts of certain prescribed types Documenta Mathematica (to appear). 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 (to appear). pdf    
33 Kevin Buzzard Slopes of modular forms Proceedings of the 2014 Simons symposium on the trace formula (to appear). 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. (to appear). 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. (to appear). 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