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 ...
in
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
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 ...
a
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
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 ...
. 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