Toby Gee

picture2018.jpg

1 About me

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 August 2019)

2 Preprints

Number Coauthors Title Link
5 Matthew Emerton Moduli stacks of étale (φ,Γ)-modules: a survey pdf
4 Matthew Emerton Moduli stacks of étale (φ,Γ)-modules and the existence of crystalline lifts pdf
3 Ana Caraiani, Matthew Emerton and David Savitt Moduli stacks of two-dimensional Galois representations pdf
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 pdf
1 George Boxer, Frank Calegari and Vincent Pilloni Abelian Surfaces over totally real fields are potentially modular pdf

3 Publications

Number Coauthors Title Journal Link
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

4 Notes

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.

5 Journals

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

We want as many people as possible to be able to use this website. For example, that means you should be able to use all screen sizes, skip to main content links, and there is colour contrast.

We work to achieve and maintain WCAG 2.1 AA standards, but it is not always possible for all our content to be accessible. Where content is not accessible, we will state a reason, warn users and offer alternatives.

Technical information about this website’s accessibility

Imperial College London is committed to making its website accessible in accordance with the Public Sector Bodies (Websites and Mobile Applications) (No. 2) Accessibility Regulations 2018.

This website is partially compliant with the Web Content Accessibility Guidelines version 2.1 AA standard, due to the most of the material being in the form of PDFs, because it consists of scientific papers.  

Reporting accessibility issues

If you need information on this website in a different format or if you have any issues accessing the content then please contact toby.gee at imperial.ac.uk. I will reply as soon as possible.

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Last updated

This statement was prepared on September 10 2020. It was last updated on September 12 2020.