Toby Gee

Toby Gee (born January 2, 1980 ) is a British mathematician who studies number theory.

Gee studied at the University of Cambridge (Trinity College), received his bachelor's degree and became Senior Wrangler in 2000, and received his PhD from Imperial College London in 2004 with Kevin Buzzard (Companion forms over totally real fields). As a post-doctoral student he was Benjamin Peirce Lecturer at Harvard University until 2010 and was Assistant Professor at Northwestern University in 2010/11 . He then went back to Imperial College in London as a Senior Lecturer and became a professor there in 2013.

From 2011 to 2013 he was a Sloan Research Fellow. In 2012 he received the Whitehead Prize and the Leverhulme Prize, and in 2014 he became a Fellow of the American Mathematical Society . In 2016 he received a Wolfson Research Merit Award from the Royal Society and in 2012 an ERC Starting Grant. In 2020 he received an ERC Advanced Grant (p-adic Langlands and the Emerton-Gee-Stack).

He deals with arithmetic geometry , automorphic forms and the p-adic Langlands program , which makes connections between p-adic Galois representations and automorphic forms. Here he introduced new geometric methods with Matthew Emerton ( Emerton-Gee-Stack ). With Mark Kisin he proved the Breuil-Mèzard conjecture for potential Barsotti-Tate representations and with Thomas Barnet-Lamb and David Geraghty the Sato - Tate conjecture for Hilbert modular forms .

Fonts (selection)

• Automorphic lifts of prescribed types , Mathematische Annalen, Volume 350, 2011, pp. 107-144, Arxiv
• On the weights of mod p Hilbert modular forms , Inventiones Mathematicae, Volume 184, 2011, pp. 1-46, Arxiv
• with Thomas Barnet-Lamb, David Geraghty: The Sato – Tate conjecture for Hilbert modular forms , Journal of the American Mathematical Society, Volume 24, 2011, pp. 411–469. Arxiv
• with M. Emerton: A geometric perspective on the Breuil – Mézard conjecture , Journal of the Institute of Mathematics of Jussieu, Volume 13, 2014, pp. 183–223, Arxiv
• with Mark Kisin : The Breuil – Mézard Conjecture For Potentially Barsotti – Tate Representations , Forum of Mathematics, Pi. 2, 2014, e1, Arxiv
• with T. Barnet-Lamb, D. Geraghty, R. Taylor: Potential automorphy and change of weight , Annals of Mathematics, Volume 179, 2014, pp. 501-609, Arxiv
• with K. Buzzard: The conjectural connections between automorphic representations and Galois representations, in: Automorphic Forms and Galois Representations, London Math. Soc. Lecture Note Series 414, 2015, pp. 135–187, Arxiv
• with Ana Caraiani , Matthew Emerton , D. Geraghty, V. Paskunas, SW Shin: Patching and the p-adic local Langlands correspondence , Cambridge Journal of Math., Volume 4, 2016, No. 2, pp. 197-287. Arxiv
• with A. Caraiani, M. Emerton, D. Geraghty, V. Paskunas, SW Shin: Patching and the p-adic Langlands program for GL2 (Qp) , Compositio Math., Volume 154, 2018, pp. 503-548. Arxiv
• with P. Allen, Frank Calegari , A. Caraiani, D. Helm, B. Le Hung, J. Newton, Peter Scholze , Richard Taylor , Jack Thorne : Potential automorphy over CM fields , Arxiv 2018

Web links

• Homepage at Imperial College

Individual evidence

1. ↑ Toby Gee in the Mathematics Genealogy Project (English)
2. ↑ Stephen Jones, Three Imperial academics win ERC Advanced Grants worth € 6.5m , March 31, 2020
3. ^ Description of Gee's project in the context of the ERC Advanced Grant