Laurent Lafforgue (; born 6 November 1966) is a French

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. He has made outstanding contributions to Langlands' program in the fields of

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

and

analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...

, and in particular proved the Langlands conjectures for the

automorphism group In mathematics, the automorphism group of an object ''X'' is the group consisting of automorphisms of ''X'' under composition of morphisms. For example, if ''X'' is a finite-dimensional vector space, then the automorphism group of ''X'' is the g ...

of a function field. The crucial contribution by Lafforgue to solve this question is the construction of compactifications of certain

moduli stack In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such space ...

s of

shtuka In mathematics, a Drinfeld module (or elliptic module) is roughly a special kind of module over a ring of functions on a curve over a finite field, generalizing the Carlitz module. Loosely speaking, they provide a function field analogue of comple ...

s. The proof was the result of more than six years of concentrated efforts. In 2002 at the 24th

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

Beijing } Beijing ( ; ; ), alternatively romanized as Peking ( ), is the capital of the People's Republic of China. It is the center of power and development of the country. Beijing is the world's most populous national capital city, with over 21 ...

China China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and ...

, he received the

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...

together with

Vladimir Voevodsky Vladimir Alexandrovich Voevodsky (, russian: Влади́мир Алекса́ндрович Воево́дский; 4 June 1966 – 30 September 2017) was a Russian-American mathematician. His work in developing a homotopy theory for algebraic var ...

Biography

Laurent Lafforgue has two brothers, Thomas and

Vincent Vincent ( la, Vincentius) is a male given name derived from the Roman name Vincentius, which is derived from the Latin word (''to conquer''). People with the given name Artists *Vincent Apap (1909–2003), Maltese sculptor *Vincent van Gogh ...

, both mathematicians. Thomas is now a teacher in a ''

classe préparatoire aux grandes écoles The ''classes préparatoires aux grandes écoles'' (CPGE) (English: Higher School Preparatory Classes), commonly called ''classes prépas'' or ''prépas'', are part of the French post-secondary education system. They consist of two years of stud ...

'' at Lycée Louis le Grand in

Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. S ...

and

CNRS The French National Centre for Scientific Research (french: link=no, Centre national de la recherche scientifique, CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 ...

directeur de recherches at the Institut Fourier in Grenoble. He won 2 silver medals at

International Mathematical Olympiad The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except i ...

(IMO) in 1984 and 1985. He entered the

École Normale Supérieure École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoi ...

in 1986. In 1994 he received his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

under the direction of Gérard Laumon in the

Arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...

and

Algebraic Geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

team at the

Université de Paris-Sud Paris-Sud University (French: ''Université Paris-Sud''), also known as University of Paris — XI (or as Université d'Orsay before 1971), was a French research university distributed among several campuses in the southern suburbs of Paris, in ...

. Currently he is a research director of

. He was detached as permanent professor of

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

at the

Institut des Hautes Études Scientifiques The Institut des hautes études scientifiques (IHÉS; English: Institute of Advanced Scientific Studies) is a French research institute supporting advanced research in mathematics and theoretical physics. It is located in Bures-sur-Yvette, just ...

(IHÉS) in

Bures-sur-Yvette Bures-sur-Yvette (, literally ''Bures on Yvette'') is a commune in the Essonne department in Île-de-France in northern France. Geography Bures-sur-Yvette is located in the Vallée de Chevreuse on the river Yvette, along which the RER line&nbs ...

, France, in 2000-2021. In 2021, he left his IHÉS position and moved to

Huawei Huawei Technologies Co., Ltd. ( ; ) is a Chinese multinational technology corporation headquartered in Shenzhen, Guangdong, China. It designs, develops, produces and sells telecommunications equipment, consumer electronics and various smar ...

. Laurent is a devout Catholic and never married.

Career

He received the

Clay Research Award __NOTOC__ The Clay Research Award is an annual award given by the Oxford-based Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research. The following mathematicians have received the award: {, class=" ...

in 2000, and the of the

French Academy of Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...

in 2001. His younger brother

Vincent Lafforgue Vincent Lafforgue (born 20 January 1974) is a French mathematician who is active in algebraic geometry, especially in the Langlands program, and a CNRS " Directeur de Recherches" at the Institute Fourier in Grenoble. He is the younger brother o ...

is also a notable mathematician. On 22 May 2011 Lafforgue was awarded an honorary Doctor of Science from the

University of Notre Dame The University of Notre Dame du Lac, known simply as Notre Dame ( ) or ND, is a private Catholic research university in Notre Dame, Indiana, outside the city of South Bend. French priest Edward Sorin founded the school in 1842. The main campu ...

Views

Lafforgue is a critic of what he calls the "pedagogically correct" in France's educational system. In 2005, he was forced to resign from the

Haut conseil de l'éducation The Haut Conseil de l'éducation is a French body set up in 2005, in a consultative capacity as regards essential knowledge, educational program An educational program is a program written by the institution or ministry of education which determin ...

after he expressed these views in a private letter that he sent to

Bruno Racine Bruno Racine (born 17 December 1951 in Paris) is a French civil servant and writer. Early life and education Racine is the son of Pierre Racine (a conseiller d'État) and Edwina Morgulis, Bruno Racine was born in Paris. He studied at the Éco ...

, president of the HCE, that later was made public..

Works

Expository articles * Lafforgue, L.
Chtoucas de Drinfeld et applications.
rinfelʹd shtukas and applications' Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998). Doc. Math. 1998, Extra Vol. II, 563–570. * Lafforgue, Laurent. ''Chtoucas de Drinfeld, formule des traces d'Arthur-Selberg et correspondance de Langlands. rinfelʹd shtukas, Arthur-Selberg trace formula and Langlands correspondence' Proceedings of the International Congress of Mathematicians, Vol. I (Beijing, 2002), 383–400, Higher Ed. Press, Beijing, 2002. Research articles * Lafforgue, Laurent. ''Chtoucas de Drinfeld et correspondance de Langlands. rinfelʹd shtukas and Langlands correspondence' Invent. Math. 147 (2002), no. 1, 1–241.

Notes

References

*Gérard Laumon
''The Work of Laurent Lafforgue''
Proceedings of the ICM, Beijing 2002, vol. 1, 91–97 *Gérard Laumon
''La correspondance de Langlands sur les corps de fonctions (d'après Laurent Lafforgue)''
Séminaire Bourbaki, 52e année, 1999–2000, no. 873

External links

Official home page
(in French) * * * * Lafforgue and education in Franc

(in Portuguese) {{DEFAULTSORT:Lafforgue, Laurent 1966 births Living people People from Antony, Hauts-de-Seine French Roman Catholics Members of the French Academy of Sciences 20th-century French mathematicians 21st-century French mathematicians Algebraic geometers Number theorists Paris-Sud University alumni École Normale Supérieure alumni Lycée Louis-le-Grand alumni Fields Medalists Clay Research Award recipients French National Centre for Scientific Research scientists Huawei people International Mathematical Olympiad participants Paris-Saclay University people Paris-Saclay University alumni Research directors of the French National Centre for Scientific Research