Alain Connes (; born 1 April 1947) is a French mathematician, and a theoretical physicist, 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 of ...

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 ge ...

. He is a professor at the , ,

Ohio State University The Ohio State University, commonly called Ohio State or OSU, is a public land-grant research university in Columbus, Ohio. A member of the University System of Ohio, it has been ranked by major institutional rankings among the best publ ...

and

Vanderbilt University Vanderbilt University (informally Vandy or VU) is a private research university in Nashville, Tennessee. Founded in 1873, it was named in honor of shipping and rail magnate Cornelius Vanderbilt, who provided the school its initial $1-million ...

. 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 the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award ho ...

in 1982.

Career

Source: Academic career timeline: (1966–1970) – Bachelor's degree from the École Normale Supérieure (now part of

Paris Sciences et Lettres University Paris Sciences et Lettres University (PSL University or simply PSL) is a public research university based in Paris, France. It was established in 2010 and formally created as a university in 2019. It is a collegiate university with 11 constituen ...

). (1973) – doctorate from

Pierre and Marie Curie University Pierre and Marie Curie University (french: link=no, Université Pierre-et-Marie-Curie, UPMC), also known as Paris 6, was a public university, public research university in Paris, France, from 1971 to 2017. The university was located on the Jussi ...

, Paris, France (1970–1974) – appointment at the

French National Centre for Scientific Research 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 ...

, Paris (1975) –

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

, Ontario, Canada (1976–1980) – the University of Paris VI (1979 – present) – the Institute of Advanced Scientific Studies,

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 (1981–1984) – the French National Centre for Scientific Research, Paris (1984–2017) – the , Paris (2003–2011) – Vanderbilt University, Nashville, Tennessee (2012–2020) – the Ohio State University, Columbus Connes was an invited professor at the (2000).

Research

Connes studies

s. 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 algeb ...

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

factor Factor, a Latin word meaning "who/which acts", 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, suc ...

s. He also formulated the

Connes embedding problem Connes' embedding problem, formulated by Alain Connes in the 1970s, is a major problem in von Neumann algebra theory. During that time, the problem was reformulated in several different areas of mathematics. Dan-Virgil Voiculescu, Dan Voiculescu de ...

. Following this, he made contributions in

operator K-theory In mathematics, operator K-theory is a noncommutative analogue of topological K-theory for Banach algebras with most applications used for C*-algebras. Overview Operator K-theory resembles topological K-theory more than algebraic K-theory. In pa ...

and

index theory Index (or its plural form 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 a Halo megastru ...

, which culminated in the

Baum–Connes conjecture In mathematics, specifically in operator K-theory, the Baum–Connes conjecture suggests a link between the operator K-theory, K-theory of the reduced C*-algebra of a group theory, group and the K-homology of the classifying space of proper act ...

. He also introduced

cyclic cohomology In noncommutative geometry and related branches of mathematics, cyclic homology and cyclic cohomology are certain (co)homology theories for associative algebras which generalize the de Rham (co)homology of manifolds. These notions were independent ...

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 - PSL (ENS). Founded in 1934–1935, the Bourbaki group originally in ...

. Connes has applied his work in areas of mathematics and

theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...

, including

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� ...

differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

and

particle physics Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...

Awards and honours

Connes was awarded the

in 1982, 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. The Prize is awarded in partnership between the Royal Swedish Academy of Sciences and the Crafoord Foun ...

in 2001 and the gold medal of the

in 2004. He was an

invited speaker at the International Congress of Mathematicians This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." ...

(ICM) in 1974 at Vancouver and in 1986 at Berkeley, and a plenary speaker at the ICM in 1978 at Helsinki. He is a member 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 ...

and several foreign academies and societies, including the Royal Danish and Norwegian Academies of Science and Letters, and the

Russian Russian(s) refers to anything related to Russia, including: *Russians (, ''russkiye''), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries *Rossiyane (), Russian language term for all citizens and peo ...

and US National Academies of Sciences.

Books

* Alain Connes and

Matilde Marcolli Matilde Marcolli is an Italian and American mathematical physicist. She has conducted research work in areas of mathematics and theoretical physics; obtained the Heinz Maier-Leibnitz-Preis of the Deutsche Forschungsgemeinschaft, and the Sofia Kov ...

, ''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,

André Lichnerowicz André Lichnerowicz (January 21, 1915, Bourbon-l'Archambault – December 11, 1998, Paris) was a noted France, French Differential geometry and topology, differential geometer and Mathematical physics, mathematical physicist of Poland, Polish desc ...

, and Marcel-Paul Schutzenberger, ''Triangle of Thought'', translated by Jennifer Gage, American Mathematical Society, 2001, * Jean-Pierre Changeux, 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 su ...

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

Academic Press Academic Press (AP) is an academic book publisher founded in 1941. It was acquired by Harcourt, Brace & World in 1969. Reed Elsevier bought Harcourt in 2000, and Academic Press is now an imprint of Elsevier. Academic Press publishes reference ...

, 1994,

Career

Research

Awards and honours

Books

See also

References

External links