Alain Connes
Encyclopedia
Alain Connes is a French mathematician
, currently Professor at the Collège de France
, IHÉS, The Ohio State University and Vanderbilt University
.
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-theory
and index theory, 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
.
Connes has applied his work in areas of mathematics
and theoretical physics
, including number theory
, differential geometry and particle physics
.
in 1982, the Crafoord Prize
in 2001 and the gold medal of the CNRS in 2004. He is a member of the French Academy of Sciences
and several foreign academies and societies, including the Danish Academy of Sciences
, Norwegian Academy of Sciences
, Russian Academy of Sciences
, and US National Academy of Sciences
.
Mathematician
A 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 France
Collège de France
The 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 University
Vanderbilt University
Vanderbilt 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 algebraOperator algebra
In 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-theory
K-theory
In 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 cohomology
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...
in the early 1980s as a first step in the study of noncommutative differential geometry
Noncommutative geometry
Noncommutative 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 mathematics
Mathematics
Mathematics 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 physics
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
, including number theory
Number theory
Number 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 physics
Particle physics
Particle 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 MedalFields Medal
The 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 Prize
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...
in 2001 and the gold medal of the CNRS in 2004. He is a member of the French Academy of Sciences
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 research...
and several foreign academies and societies, including the Danish Academy of Sciences
Royal Danish Academy of Sciences and Letters
Royal 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 Sciences
Norwegian Academy of Science and Letters
The 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 Sciences
Russian Academy of Sciences
The 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 Sciences
United States National Academy of Sciences
The 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 homologyCyclic homologyIn 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 bosonHiggs bosonThe 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
- GroupoidGroupoidIn 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 analysisCriticism of non-standard analysisNon-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
- Alain Connes Official Web Site containing downloadable papers, and his book Non-commutative geometry, ISBN 0-12-185860-X.
- nlab about Alain Connes
- Alain Connes' Standard Model
- An interview with Alain Connes and a discussion about it