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, mathematical structure, structure, space, Mathematica ...

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

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

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 (mathematics), scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of suc ...

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 Proof most often refers to: * Proof (truth), argument or sufficient evidence for the truth of a proposition * Alcohol proof, a measure of an alcoholic drink's strength Proof may also refer to: Mathematics and formal logic * Formal proof, a co ...

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 IMU Abacus Medal (known before ...

Beijing Beijing, Chinese postal romanization, previously romanized as Peking, is the capital city of China. With more than 22 million residents, it is the world's List of national capitals by population, most populous national capital city as well as ...

China China, officially the People's Republic of China (PRC), is a country in East Asia. With population of China, a population exceeding 1.4 billion, it is the list of countries by population (United Nations), second-most populous country after ...

, 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 Mathematicians, International Congress of the International Mathematical Union (IMU), a meeting that takes place e ...

together with

Vladimir Voevodsky Vladimir Alexandrovich Voevodsky (, ; 4 June 1966 – 30 September 2017) was a Russian-American mathematician. His work in developing a homotopy theory for algebraic varieties and formulating motivic cohomology led to the award of a Fields Medal ...

Biography

Laurent Lafforgue has two brothers, Thomas and

Vincent Vincent (Latin: ''Vincentius'') is a masculine given name originating from the Roman name ''Vincentius'', which itself comes from the Latin verb ''vincere'', meaning "to conquer." People with the given name Artists *Vincent Apap (1909–2003) ...

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

classe préparatoire aux grandes écoles The ''Classes préparatoires aux grandes écoles'' (, ''Higher school preparatory classes'', abbr. CPGE), commonly called ''classes prépas'' or ''prépas'', are part of the French post-secondary education system. They consist of two years of s ...

'' at Lycée Louis le Grand in

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...

and

CNRS The French National Centre for Scientific Research (, , CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 staff, including 11,137 tenured researchers, 13,415 eng ...

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. It is widely regarded as the most prestigious mathematical competition in the wor ...

(IMO) in 1984 and 1985. He entered the

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

in 1986. In 1994 he received his Ph.D. under the direction of Gérard Laumon in the

Arithmetic Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. ...

and

Algebraic Geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

team at the

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

. Currently he is a research director of

. He was detached as permanent professor of

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

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 (also with a small theoretical biology g ...

(IHÉS) in

Bures-sur-Yvette Bures-sur-Yvette (, "Bures-on- Yvette") is a commune in the Essonne department in the Île-de-France region in Northern France. It is a southern Parisian outer suburb in the Vallée de Chevreuse, with a population of 9,254 as of 2021. Geograp ...

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

Huawei Huawei Technologies Co., Ltd. ("Huawei" sometimes stylized as "HUAWEI"; ; zh, c=华为, p= ) is a Chinese multinational corporationtechnology company in Longgang, Shenzhen, Longgang, Shenzhen, Guangdong. Its main product lines include teleco ...

. His goal there is to apply

topos theory In mathematics, a topos (, ; plural topoi or , or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally, on a site). Topoi behave much like the category of sets and possess a notion ...

to the area of

artificial intelligence Artificial intelligence (AI) is the capability of computer, computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of re ...

Career

He received the Clay Research Award in 2000, and the of the

French Academy of Sciences The French Academy of Sciences (, ) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefron ...

in 2001 and was awarded the Fields Medal in 2002. 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 of ...

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; ; ND) is a Private university, private Catholic research university in Notre Dame, Indiana, United States. Founded in 1842 by members of the Congregation of Holy Cross, a Cathol ...

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 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 Écol ...

, president of the HCE, that later was made public. Laurent is a devout Catholic and never married. He opposed

same-sex marriage in France Same-sex marriage has been legal in France since 18 May 2013, making France the Legal status of same-sex marriage, thirteenth country in the world and the ninth in Europe to allow same-sex couples to marry. The legislation applies to metropolita ...

, and supported the . In 2024, he declared that he was “full of admiration for Huawei”, which would supposedly be suffering a campaign of criticism from the USA.

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
''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 French 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