Permanent professor at the Institut des Hautes Études Scientifiques (IHÉS), Bures-sur-Yvette, France.
Thèmes de recherche : Laurent Lafforgue established the Langlands Correspondences for a much wider class of cases than previously known. These correspondences connect arithmetic properties to analytic properties of some special group representations called automorphic representations. It was formulated by Robert Langlands at the end of the 1960's. In rank 1, this conjecture is nothing other than the now traditional "class field theory" of Emil Artin. In rank 2 and for number fields, the first great confirmations of this conjecture were the proof of the conjecture of Ramanujan per Pierre Deligne and the proof by Langlands itself of the conjecture of Artin except for a case.At the beginning of the seventies, Vladimir Drinfeld attacked the conjectures in a more general algebraic context. For that purpose, he built varieties similar to modular curves and showed certain cases of the conjecture of Langlands in rank 2. Then, as these varieties did not make it possible to reach all desired representations, Drinfeld introduced the "chtoucas", a step which enabled him to prove the conjecture of Langlands in rank 2. This turned out to make the general case accessible, after formidable technical difficulties were surmounted.The crucial contribution by Laurent Lafforgue to solve this question is the construction of compactifications of certain varieties of modules. The proof, which is monumental, is the result of more than six years of concentrated efforts.
Prix et distinctions : 1996: Prix Peccot and Cours Peccot from the College of France
2000: Clay Research Award 2
2001: Jacques Herbrand Prize in Mathematics from the Academy of Sciences of Paris
2002: Fields Medal
Sélection de publications : (1) Sur la conjecture de Ramanujan-Petersson pour les corps de fonctions, I : étude géométrique,C. R. Acad. Sci. Paris, 322 (1996), 605-608 ; idem, II : étude spectrale, ibidem, 707-710.
(2) Sur la dégénérescence des chtoucas de Drinfeld,C. R. Acad. Sci. Paris, 323 (1996), 491-494.
(3) Compactification de l'isogénie de Lang et dégénérescence des structures du niveau simple des chtoucas de Drinfeld, C. R. Acad. Sci. Paris, 325 (1997), 1309-1312.
(4) Chtoucas de Drinfeld et conjecture de Ramanujan-Petersson,Astérisque, 243 (1997), 1-329.
(5) Chtoucas de Drinfeld et applications,Proc. Int. Congress Mathematicians, Berlin 1998, vol. II (1998), 563-570.
(6) Une compactification des champs classifiant les chtoucas de Drinfeld, J. of the Amer. Math. Soc. 11, 4 (1998), 1001-1036.
(7) Pavages des simplexes, schémas de graphes recollés et compactification des (PGLr)^n+1 /PGL_r,Inventiones Math., 136 (1999), 233-271.(N.B. : Cet article comporte une erreur très sérieuse ; un erratum est disponible à l'adresse électronique suivante : www.ihes.fr/PREPRINTS/M01/Resu/resu-M01-14.html ).
(8) Chtoucas de Drinfeld et correspondance de Langlands,A paraître dans Inventiones Math., 240 pages.
(9) Chirurgie des grassmanniennes, Prépublication IHÉS M/02/31, 267 pages.
LAFFORGUE, LAURENT 