Alain Connes is a French
mathematicianA mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, currently Professor at the
Collège de FranceThe Collège de France is a higher education and research establishment located in Paris, France, in the 5th arrondissement, or Latin Quarter, across the street from the historical campus of La Sorbonne at the intersection of Rue Saint-Jacques and Rue des Écoles...
, IHÉS, The Ohio State University and
Vanderbilt UniversityVanderbilt University is a private research university located in Nashville, Tennessee, United States. Founded in 1873, the university is named for shipping and rail magnate "Commodore" Cornelius Vanderbilt, who provided Vanderbilt its initial $1 million endowment despite having never been to the...
.
Work
Alain Connes is one of the leading specialists on
operator algebraIn functional analysis, an operator algebra is an algebra of continuous linear operators on a topological vector space with the multiplication given by the composition of mappings...
s. In his early work on von Neumann algebras in the 1970s, he succeeded in obtaining the almost complete classification of injective factors. Following this he made contributions in
operator K-theoryIn mathematics, K-theory originated as the study of a ring generated by vector bundles over a topological space or scheme. In algebraic topology, it is an extraordinary cohomology theory known as topological K-theory. In algebra and algebraic geometry, it is referred to as algebraic K-theory. It...
and index theory, which culminated in the
Baum-Connes conjecture. He also introduced
cyclic cohomologyIn homological algebra, cyclic homology and cyclic cohomology are homology theories for associative algebras introduced by Alain Connes around 1980, which play an important role in his noncommutative geometry...
in the early 1980s as a first step in the study of
noncommutative differential geometryNoncommutative geometry is a branch of mathematics concerned with geometric approach to noncommutative algebras, and with construction of spaces which are locally presented by noncommutative algebras of functions...
.
Connes has applied his work in areas of
mathematicsMathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and
theoretical physicsTheoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
, including
number theoryNumber theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, differential geometry and
particle physicsParticle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...
.
Awards and honours
Connes was awarded the
Fields MedalThe Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
in 1982, the
Crafoord PrizeThe Crafoord Prize is an annual science prize established in 1980 by Holger Crafoord, a Swedish industrialist, and his wife Anna-Greta Crafoord...
in 2001 and the gold medal of the CNRS in 2004. He is a member of the
French Academy of SciencesThe 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 research...
and several foreign academies and societies, including the
Danish Academy of SciencesRoyal Danish Academy of Sciences and Letters is a Danish non-governmental science Academy, founded 13 November 1742 by permission of the King Christian VI, as a historical Collegium Antiquitatum...
,
Norwegian Academy of SciencesThe Norwegian Academy of Science and Letters is a learned society based in Oslo, Norway.-History:The University of Oslo was established in 1811. The idea of a learned society in Christiania surfaced for the first time in 1841. The city of Throndhjem had no university, but had a learned...
,
Russian Academy of SciencesThe Russian Academy of Sciences consists of the national academy of Russia and a network of scientific research institutes from across the Russian Federation as well as auxiliary scientific and social units like libraries, publishers and hospitals....
, and
US National Academy of SciencesThe National Academy of Sciences is a corporation in the United States whose members serve pro bono as "advisers to the nation on science, engineering, and medicine." As a national academy, new members of the organization are elected annually by current members, based on their distinguished and...
.
See also
- Cyclic homology
In homological algebra, cyclic homology and cyclic cohomology are homology theories for associative algebras introduced by Alain Connes around 1980, which play an important role in his noncommutative geometry...
- Factor (functional analysis)
- Higgs boson
The Higgs boson is a hypothetical massive elementary particle that is predicted to exist by the Standard Model of particle physics. Its existence is postulated as a means of resolving inconsistencies in the Standard Model...
- C*-algebra
- M Theory
- Groupoid
In mathematics, especially in category theory and homotopy theory, a groupoid generalises the notion of group in several equivalent ways. A groupoid can be seen as a:...
- Criticism of non-standard analysis
Non-standard analysis and its offshoot, non-standard calculus, have been criticized by several authors. The evaluation of non-standard analysis in the literature has varied greatly...
External links