# Laurent Lafforgue

Laurent Lafforgue ( born November 6, 1966 in Antony, near Paris ) is a French mathematician and winner of the Fields Medal.

He won the first prize in the general competitions for admission to the elite universities in France ( Concours General ) and was then 1984-1986 in preparatory courses at the Lycée Louis- le -Grand. 1986 to 1990 he studied at the École Normale Supérieure, where in 1988 he earned his Agrégation in mathematics. 1988 to 1991, he conducted research there on Arakelov theory at Christophe Soulé, from 1990 as a scientist ( Chargé de Recherche ) of the CNRS at the University of Paris-Sud in Orsay. 1991/92 he did his military service as a teacher at the military academy Saint- Cyr. In 1994 he received his doctorate in the field of arithmetic algebraic geometry at the University of Paris-Sud with Gérard Laumon (D - chtoukas de Drinfeld ). Since 2000 he is Research Director of the CNRS and since 2000 professor of mathematics at the Institut des Hautes Études Scientifiques ( IHES ) in Bures -sur -Yvette.

He proved the Langlands correspondence for linear groups over function fields (of algebraic curves over finite fields ) to which he worked from 1994 to 2000 in connection to his work on the Shtuka 's of Vladimir Drinfeld, which were an essential element of proof. It is a major breakthrough came on a central area of research in number theory and arithmetic algebraic geometry, where for 30 years worked many mathematicians. The goal is the proof of a number field, as in other cases, however, the proof in the simpler case of function body as an important precursor. The Langlands correspondence provides a ( the respective L-functions successive imaging ) bijection between the l -adic r-dimensional irreducible representations of the Galois group of the function body and the representations in the space of automorphic cusp forms of the linear group of rank r ( with coefficients in Adele ring of the function body). The case r = 1 corresponds to the Artin'schen reciprocity theorem of number theory and corresponds to the commutative part of the Galois group. The case r = 2 was proved in the 1970s by Drinfeld.

From 2001, he worked on projective geometry and the configuration spaces of matroids, but then turned back to the Langlands program. Since 2004, he also deals with issues of mathematics education in France.

In 1996 he received the Prix Peccot the College de France in 1998 and the bronze medal of the CNRS. In 2000 he was awarded the Clay Price. In 1998 he was invited speaker at the International Congress of Mathematicians (ICM ) in Berlin ( Chtoucas de Drinfeld et applications ). In 2000 he was awarded the Clay Research Award. In 2002 he received the ICM in Beijing, People's Republic of China, the Fields Medal (next to Vladimir Vladislavovich Wojewodski ) for his outstanding contributions to the Langlands program in number theory. He also gave a plenary lecture ( Chtoucas de Drinfeld, Formule de trace d' Arthur - Selberg et correspondance de Langlands ). Since 2003 he is a member of the Académie des sciences, the Prix Jacques Herbrand he received in 2001. He holds honorary doctorates from the University of Notre Dame.

He is the brother of the mathematician Vincent Lafforgue.

## Writings

- Chtoucas de Drinfeld et conjecture de Ramanujan - Petersson, astérisque, Vol 243, 1997
- Compactification Une des champs classifiant les chtoucas de Drinfeld, Journal of the American Mathematical Society, Bd.11, 1998, S.1001 -1036
- Chtoucas de Drinfeld et correspondance de Langlands, Inventiones Mathematicae, Bd.147, 2002, p.1 -241
- Surgery of the Grassmanniennes, CRM Monograph Series 19, American Mathematical Society 2003