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Alain Connes (born April 1, 1947) is a French mathematician, currently Professor at the College de France, IHES and Vanderbilt University.


Alain Connes is one of the leading specialists on operator algebras. 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.

Awards and honours

Connes was awarded the Fields Medal 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.

See also

* cyclic homology

* factor (functional analysis)

* Higgs boson

* C*-algebra

* M Theory

* Groupoid


* Alain Connes Official Web Site containing downloadable papers, and his book Non-commutative geometry, ISBN 0-12-185860-X.

* O'Connor, John J; Edmund F. Robertson "Alain Connes". MacTutor History of Mathematics archive.

* Alain Connes at the Mathematics Genealogy Project

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