Toby Gee

Toby Gee is a British mathematician specializing in number theory, algebraic geometry, and the theory of automorphic forms. He is known for work on modularity lifting theorems, the Fontaine–Mazur conjecture, and the p-adic Langlands program, collaborating with prominent figures in arithmetic geometry and representation theory. His research has influenced developments connected to the Langlands correspondence, Galois representations, and the arithmetic of automorphic forms.

Early life and education

Born in the United Kingdom, Gee completed undergraduate and graduate studies at the University of Cambridge under the supervision of Richard Taylor. During his doctoral training he engaged with problems related to the Taniyama–Shimura conjecture, the Fontaine–Mazur conjecture, and p-adic Hodge theory, interacting with researchers at institutes such as the Isaac Newton Institute and the Clay Mathematics Institute. He received his PhD in the context of the broader revolution following the proof of the Modularity theorem and the proof of Fermat's Last Theorem.

Academic career

Gee held research and teaching posts at institutions including Imperial College London, the University of Cambridge faculty, and the University of Oxford, contributing to postgraduate training in mathematics and supervising students who later joined departments such as the University of Chicago and Princeton University. He has been involved with collaborative research groups at the Hausdorff Center for Mathematics, the American Institute of Mathematics, and European networks connected to the European Research Council. Gee has been an invited speaker at conferences organized by the International Congress of Mathematicians, the European Mathematical Society, and the London Mathematical Society.

Research and contributions

Gee's research addresses the interaction between Galois representations and automorphic representations, developing modularity lifting techniques alongside collaborators including Mark Kisin, Christophe Breuil, Fred Diamond, and Richard Taylor. He has worked on potential modularity theorems linked to the Sato–Tate conjecture and on local-global compatibility in the Langlands program. His contributions include advances in understanding deformation rings, R=T theorems, and the application of p-adic local Langlands correspondence to questions about cohomology of Shimura varieties and the arithmetic of Hilbert modular forms and Siegel modular forms. Through papers and lecture series he has influenced work on the Fontaine–Laffaille theory, Breuil–Mézard conjecture, and the modularity of elliptic curves and higher-dimensional motives, often collaborating with researchers at the Simons Foundation and the Royal Society.

Awards and honours

Gee's work has been recognized by invitations to deliver lectures at major venues including the International Congress of Mathematicians and the European Congress of Mathematics, and by fellowships and research grants from institutions such as the Royal Society and the European Research Council. He has held prizes and positions that reflect prominence within organizations like the London Mathematical Society and national research councils in the United Kingdom. His students and collaborators have received awards from bodies including the American Mathematical Society and the Royal Society of Edinburgh.

Selected publications

- Gee, T.; Kisin, M.; Taylor, R. — Papers on modularity lifting and R=T results addressing deformations of Galois representations and implications for the Langlands correspondence published in leading journals and presented at the International Congress of Mathematicians. - Gee, T.; Breuil, C.; Diamond, F. — Collaborative articles on the Breuil–Mézard conjecture, local-global compatibility, and applications to Hilbert modular forms and Shimura varieties. - Gee, T. — Expository and research monographs on modularity, p-adic Hodge theory, and deformation theory circulated through seminars at the Isaac Newton Institute and workshops at the Hausdorff Center for Mathematics.

Category:British mathematicians Category:Number theorists