Laurent Lafforgue

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Laurent Lafforgue, 2016

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

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

He proved the Langland correspondence for linear groups over function fields (from algebraic curves over finite fields ), which he worked on from 1994 to 2000 following his work on the Shtuka 's by Vladimir Drinfeld , which were an essential element of the proof. He achieved a major breakthrough in a central research area of ​​number theory and arithmetic algebraic geometry, on which many mathematicians had been working for 30 years. The goal is the proof for number fields , as in other cases, however, the proof in the simpler case for function fields is an important preliminary stage. The Langlands correspondence provides a bijection ( mapping the respective L-functions onto one another) between the l-adic r-dimensional irreducible representations of the Galois group of the function fields and the representations in the space of the automorphic peak forms of the linear group of rank r (with coefficients in Adele- Ring of the functional body). The case r = 1 corresponds to Artin 's law of reciprocity of number theory and corresponds to the commutative part of the Galois group. The case r = 2 was proven by Drinfeld in the 1970s.

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

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

He is the brother of mathematician Vincent Lafforgue .

Fonts

  • Chtoucas de Drinfeld et conjecture de Ramanujan-Petersson, Astérisque, vol. 243, 1997
  • Une compactification des champs classifiant les chtoucas de Drinfeld, Journal of the American Mathematical Society, Vol. 11, 1998, pp. 1001-1036
  • Chtoucas de Drinfeld et correspondance de Langlands, Inventiones Mathematicae, Vol. 147, 2002, pp. 1-241
  • Chirurgie des Grassmanniennes, CRM Monograph Series 19, American Mathematical Society 2003

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personal data
SURNAME Lafforgue, Laurent
BRIEF DESCRIPTION French mathematician
DATE OF BIRTH November 6, 1966
PLACE OF BIRTH Antony near Paris