Professor Fred Diamond
Telephone: +44 020 7848 1068
Title: Professor in Number Theory
Professor Diamond received his B.A. from the University of Michigan in 1984, and his Ph.D. from Princeton University in 1988 under the supervision of Andrew Wiles. He taught at several universities in the US, including Columbia, MIT, Rutgers and Brandeis, before moving to King's in 2006. He was awarded a Centennial Fellowship by the American Mathematical Society in 1997 and has held visiting positions at the Institute for Advanced Study in Princeton and the IHES in Paris. He is the author of numerous research and expository articles, as well as a textbook with Shurman on modular forms.
His main research interests are modular forms and Galois representations, and in particular the relations between them predicted by the Langlands Programme. To this end, some of his work further developed the techniques introduced by Wiles and Taylor in the course of Wiles' proof of Fermat's Last Theorem, and in 1999, together with Breuil, Conrad and Taylor, he completed the proof of the Shimura-Taniyama-Weil conjecture stating that every elliptic curve over rational numbers can be associated to a modular form. His current focus is on mod p and p-adic Langlands correspondences.
F. Diamond, The Taylor-Wiles construction and multiplicity one, Inventiones Mathematicae 128 (1997), 379–391.
C. Breuil, B. Conrad, F. Diamond, R. Taylor, On the modularity of elliptic curves over Q: Wild 3-adic exercises, Journal of the American Mathematical Society, 14 (2001), 843–939.
F. Diamond, J. Shurman, A First Course in Modular Forms, Graduate Texts in Mathematics 228, Springer, 2005.
K. Buzzard, F. Diamond, F. Jarvis, On Serre's conjecture for mod l Galois representations over totally real fields, Duke Math. J. 155 (2010), 105-161.
C. Breuil, F. Diamond, Formes modulaires de Hilbert modulo p et valeurs d'extensions entre caracteres galoisiennes, to appear in Ann. Sci. Ec. Norm. Sup., arXiv:1208.5367.