Alain Connes (; born 1 April 1947) is a French mathematician, known for his contributions to the study of

operator algebra In functional analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication given by the composition of mappings. The results obtained in the study o ...

s and

noncommutative geometry Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of ''spaces'' that are locally presented by noncommutative algebras of functions, possibly in some g ...

. He was a professor at the , ,

Ohio State University The Ohio State University (Ohio State or OSU) is a public university, public Land-grant university, land-grant research university in Columbus, Ohio, United States. A member of the University System of Ohio, it was founded in 1870. It is one ...

and

Vanderbilt University Vanderbilt University (informally Vandy or VU) is a private university, private research university in Nashville, Tennessee, United States. Founded in 1873, it was named in honor of shipping and railroad magnate Cornelius Vanderbilt, who provide ...

. He was awarded 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 ...

in 1982.

Career

Alain Connes attended high school at in Marseille, and was then a student of the classes préparatoires in . Between 1966 and 1970 he studied at

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 Paris, and in 1973 he obtained a PhD from

Pierre and Marie Curie University Pierre and Marie Curie University ( , UPMC), also known as Paris VI, was a public research university in Paris, France, from 1971 to 2017. The university was located on the Jussieu Campus in the Latin Quarter of the 5th arrondissement of Paris, ...

, under the supervision of

Jacques Dixmier Jacques Dixmier (born 24 May 1924) is a French mathematician. He worked on operator algebras, especially C*-algebras, and wrote several of the standard reference books on them, and introduced the Dixmier trace and the Dixmier mapping. Biogra ...

. From 1970 to 1974 he was research fellow at the

French National Centre for Scientific Research 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 engi ...

and during 1975 he held a visiting position at

Queen's University at Kingston Queen's University at Kingston, commonly known as Queen's University or simply Queen's, is a public university, public research university in Kingston, Ontario, Kingston, Ontario, Canada. Queen's holds more than of land throughout Ontario and ...

in Canada. In 1976 he returned to France and worked as professor at Pierre and Marie Curie University until 1980 and at

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 ...

between 1981 and 1984. Moreover, since 1979 he holds the Léon Motchane Chair at IHES. From 1984 until his retirement in 2017 he held the chair of Analysis and Geometry at

Collège de France The (), formerly known as the or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment () in France. It is located in Paris near La Sorbonne. The has been considered to be France's most ...

. In parallel, he was awarded a distinguished professorship at

between 2003 and 2012, and at

between 2012 and 2021.

Research

Connes' main research interests revolved around

s. Besides

, he has applied his works in various areas of mathematics and

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 ...

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

. Since the 1990s, he developed

. In his early work on

von Neumann algebra In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. It is a special type of C*-algebra. Von Neumann al ...

s in the 1970s, he succeeded in obtaining the almost complete classification of injective

factor Factor (Latin, ) may refer to: Commerce * Factor (agent), a person who acts for, notably a mercantile and colonial agent * Factor (Scotland), a person or firm managing a Scottish estate * Factors of production, such a factor is a resource used ...

s. He also formulated the Connes embedding problem. Following this, he made contributions in operator K-theory and

index theory Index (: indexes or indices) may refer to: Arts, entertainment, and media Fictional entities * Index (''A Certain Magical Index''), a character in the light novel series ''A Certain Magical Index'' * The Index, an item on the Halo Array in the ...

, which culminated in the Baum–Connes conjecture. He also introduced cyclic cohomology in the early 1980s as a first step in the study of noncommutative differential geometry. He was a member of

Nicolas Bourbaki Nicolas Bourbaki () is the collective pseudonym of a group of mathematicians, predominantly French alumni of the École normale supérieure (Paris), École normale supérieure (ENS). Founded in 1934–1935, the Bourbaki group originally intende ...

. Over many years, he collaborated extensively with Henri Moscovici.

Awards and honours

Connes was awarded the Peccot-Vimont Prize in 1976, the Ampère Prize in 1980, the

in 1982, the Clay Research Award in 2000 and the

Crafoord Prize The Crafoord Prize () is an annual science prize established in 1980 by Holger Crafoord, a Swedish industrialist, and his wife Anna-Greta Crafoord following a donation to the Royal Swedish Academy of Sciences. It is awarded jointly by the Acade ...

in 2001. The

granted him the

silver medal A silver medal, in sports and other similar areas involving competition, is a medal made of, or plated with, silver awarded to the second-place finisher, or runner-up, of contests or competitions such as the Olympic Games, Commonwealth Games, ...

in 1977 and the

gold medal A gold medal is a medal awarded for highest achievement in a non-military field. Its name derives from the use of at least a fraction of gold in form of plating or alloying in its manufacture. Since the eighteenth century, gold medals have b ...

in 2004. He was an invited speaker at the

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 ...

in 1974 at Vancouver and in 1986 at Berkeley, and a plenary speaker at the ICM in 1978 at Helsinki. He was awarded

honorary degree An honorary degree is an academic degree for which a university (or other degree-awarding institution) has waived all of the usual requirements. It is also known by the Latin phrases ''honoris causa'' ("for the sake of the honour") or '' ad hon ...

s from

in 1979, University of Rome Tor Vergata in 1997,

University of Oslo The University of Oslo (; ) is a public university, public research university located in Oslo, Norway. It is the List of oldest universities in continuous operation#Europe, oldest university in Norway. Originally named the Royal Frederick Univ ...

in 1999,

University of Southern Denmark The University of Southern Denmark (, SDU) has campuses located in Southern Denmark and on Zealand. It offers a number of joint programmes in co-operation with the University of Flensburg and the University of Kiel. Contacts with regional indu ...

in 2009,

Université libre de Bruxelles The (French language, French, ; lit. Free University of Brussels; abbreviated ULB) is a French-speaking research university in Brussels, Belgium. It has three campuses: the ''Solbosch'' campus (in the City of Brussels and Ixelles), the ''Plain ...

in 2010 and Shanghai Fudan University in 2017. Since 1982 he is a member 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 ...

. He was elected member of several foreign academies and societies, including the

Royal Danish Academy of Sciences and Letters The Royal Danish Academy of Sciences and Letters ({{Langx, da, Det Kongelige Danske Videnskabernes Selskab or ''Videnskabernes Selskab'') is a Danish academy of science. The Royal Danish Academy was established on 13 November 1742, and was create ...

in 1980, the

Norwegian Academy of Science and Letters The Norwegian Academy of Science and Letters (, DNVA) is a learned society based in Oslo, Norway. Its purpose is to support the advancement of science and scholarship in Norway. History The Royal Frederick University in Christiania was establis ...

in 1983, the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...

in 1989, the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's Learned society, learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh ...

in 1994, the Canadian Academy of Sciences in 1995 (incorporated since 2002 in the

Royal Society of Canada The Royal Society of Canada (RSC; , SRC), also known as the Academies of Arts, Humanities, and Sciences of Canada (French: ''Académies des arts, des lettres et des sciences du Canada''), is the senior national, bilingual council of distinguishe ...

), the US National Academy of Sciences in 1997, the Russian Academy of Science in 2003 and the

Royal Academy of Science, Letters and Fine Arts of Belgium The Royal Academy of Science, Letters and Fine Arts of Belgium ( , sometimes referred to as ' ) is the independent learned society of science and arts of the French Community of Belgium. One of Belgium's numerous academies, it is the French-speak ...

in 2016. In 2001 he received (together with his co-authors

André Lichnerowicz André Lichnerowicz (; January 21, 1915, Bourbon-l'Archambault – December 11, 1998, Paris) was a French differential geometer and mathematical physicist. He is considered the founder of modern Poisson geometry. Biography His grandfather Jan f ...

and Marco Schutzenberger) the Peano Prize for his work ''Triangle of Thoughts.''

Family

Alain Connes is the middle-born of three sons – born to parents both of whom lived to be 101 years old. He married in 1971.

Books

* Alain Connes and Matilde Marcolli, ''Noncommutative Geometry, Quantum Fields and Motives'', Colloquium Publications,

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

, 2007,

* Alain Connes,

, and Marcel-Paul Schützenberger, Marcel-Paul Schutzenberger, ''Triangle of Thought'', translated by Jennifer Gage, American Mathematical Society, 2001, *

Jean-Pierre Changeux Jean-Pierre Changeux (; born 6 April 1936) is a French neuroscientist known for his research in several fields of biology, from the structure and function of proteins (with a focus on the allosteric proteins), to the early development of the ner ...

and Alain Connes, ''Conversations on Mind, Matter, and Mathematics'', translated by M. B. DeBevoise,

Princeton University Press Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial ...

, 1998, * Alain Connes, ''Noncommutative Geometry'',

Academic Press Academic Press (AP) is an academic book publisher founded in 1941. It launched a British division in the 1950s. Academic Press was acquired by Harcourt, Brace & World in 1969. Reed Elsevier said in 2000 it would buy Harcourt, a deal complete ...

, 1994,

Career

Research

Awards and honours

Family

Books

See also

References

External links