Fred Diamond

From Wikipedia, the free encyclopedia

This biography of a living person does not cite any references or sources. Please help by adding reliable sources. Contentious material about living persons that is unsourced or poorly sourced must be removed immediately, especially if potentially libelous or harmful. (April 2009) Find sources: (Fred Diamond – news, books, scholar)

Fred Diamond (born November 19, 1964) is an American mathematician, known for his role in proving the modularity theorem for elliptic curves. His research interest is in modular forms and Galois representations.

Diamond received his B.A. from the University of Michigan in 1983, and received his Ph.D. in mathematics from Princeton University in 1988 as a student of Andrew Wiles. He is currently a professor at Brandeis University, as well as a visiting professor at King's College London.

Diamond is the author of several research papers, and is a also a coauthor of A First Course in Modular Forms, a Springer-Verlag Graduate Text in Mathematics.

[edit] Publications

1. On congruence modules associated to Λ-adic forms, Compositio Mathematica 71 (1989), 49–83.
2. Congruence primes for cusp forms of weight k ≥ 2, Ast´erisque 196-197 (1991), 205–213.
3. (with R. Taylor) Non-optimal levels of mod l modular representations, Inventiones Mathematicae 115 (1994), 435–462.
4. Lifting modular mod l representations (with R. Taylor), Duke Mathematical Journal 74 (1994), 253–269.
5. The refined conjecture of Serre, in Elliptic Curves, Modular Forms & Fermat’s Last Theorem, J. Coates, S. T. Yau, eds., International Press (1995), 22–37.
6. Modularity of a family of elliptic curves (with K. Kramer), Mathematical Research Letters 2 (1995), 299–305.
7. Modular forms and modular curves (with J. Im), in Seminar on Fermat’s Last Theorem, V. K. Murty, ed., CMS Conference Proceedings 17 (1995), 39–133.
8. Fermat’s Last Theorem (with H. Darmon and R. Taylor), in Current Developments in Mathematics, 1995, R. Bott, A. Jaffe, M. Hopkins, I. Singer, D. Stroock, S. T. Yau, eds., International Press (1996), 1–154.
9. On deformation rings and Hecke rings, Annals of Mathematics 144 (1996), 137–166.
10. The Taylor-Wiles construction and multiplicity one, Inventiones Mathematicae 128 (1997), 379–391.
11. Congruences between modular forms: Raising the level and dropping Euler factors, Proceedings of the National Academy of Sciences 94 (1997), 11143–11146.
12. An extension of Wiles’ results, in Modular Forms and Fermat’s Last Theorem, G. Cornell, J. Silverman, G. Stevens, eds., Springer-Verlag (1997), 475–489.
13. l-adic modular deformations and Wiles’s “Main Conjecture” (with K. Ribet), in Modular Forms and Fermat’s Last Theorem, G. Cornell, J. Silverman, G. Stevens, eds., Springer-Verlag (1997), 357–371.
14. On the Hecke action on the cohomology of Hilbert-Blumenthal surfaces, in Number Theory, V. K. Murty, M. Waldschmidt, eds., Contemporary Mathematics, 210 (1998), 71–83.
15. Modularity of certain potentially Barsotti-Tate Galois representations (with B. Conrad and R. Taylor), Journal of the American Mathematical Society, 12 (1999), 521–567.
16. On the modularity of elliptic curves over Q: Wild 3-adic exercises (with C. Breuil, B. Conrad and R. Taylor), Journal of the American Mathematical Society, 14 (2001), 843–939.
17. The Bloch-Kato conjecture for adjoint motives of modular forms (withM. Flach and L. Guo), Mathematical Research Letters 8 (2001), 437–442.
18. The Tamagawa number conjecture of adjoint motives of modular forms (with M. Flach and L. Guo), Annales Scientifiques de l’Ècole Normale Sup´erieure 37 (2004), 663–727.
19. A First Course in Modular Forms (with J. Shurman), Graduate Texts in Mathematics 228, Springer, 2005.

[edit] External links

• Fred Diamond's web site
• Fred Diamond at the Mathematics Genealogy Project