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Alain Connes
Alain Connes in 2004
Born	1 April 1947 (1947-04-01) (age 62) France
Residence	France
Citizenship	French
Fields	Mathematics
Institutions	IHÉS, France
Alma mater	École Normale Supérieure, France
Doctoral advisor	Jacques Dixmier
Doctoral students	Alain Valette Georges Skandalis Benjamin Enriquez
Known for	Baum–Connes conjecture Noncommutative geometry Operator algebras
Notable awards	Fields Medal (1982) Crafoord Prize (2001) CNRS Gold Medal (2004)

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

Work

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
• Criticism of non-standard analysis

External links

• Alain Connes Official Web Site containing downloadable papers, and his book Non-commutative geometry, ISBN 0-12-185860-X.
• Alain Connes' Standard Model
• An interview with Alain Connes and a discussion about it
• O'Connor, John J.; Robertson, Edmund F., "Alain Connes", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Connes.html .
• Alain Connes at the Mathematics Genealogy Project