Alain Connes
This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. (February 2012)

Alain Connes  

Alain Connes in 2004


Born  Draguignan, France 
1 April 1947
Nationality  French 
Fields  Mathematics 
Institutions  IHÉS, France 
Alma mater  École Normale Supérieure, France 
Doctoral advisor  Jacques Dixmier 
Doctoral students  Georges Skandalis 
Known for  Baum–Connes conjecture Noncommutative geometry Operator algebras 
Notable awards  CNRS Silver Medal (1977) Prize Ampère (1980) Fields Medal (1982) Clay Research Award (2000) Crafoord Prize (2001) CNRS Gold medal (2004) 
Alain Connes (French: [alɛ̃ kɔn]; born 1 April 1947) is a French mathematician, currently Professor at the Collège de France, IHÉS, The Ohio State University and Vanderbilt University. He was an Invited Professor at the Conservatoire national des arts et métiers (2000).^{[1]}
Work
Alain Connes studies 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 Ktheory 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. He was a member of Bourbaki.^{[2]}
Connes has applied his work in areas of mathematics and theoretical physics, including number theory, differential geometry and particle physics.^{[3]}
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 was an invited speaker at the 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 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.
Books
 Alain Connes and Matilde Marcolli: Noncommutative Geometry, Quantum Fields and Motives, Colloquium Publications, American Mathematical Society, 2007, ISBN 9780821842102 [1]
 Alain Connes, Andre Lichnerowicz, Marcel Paul Schutzenberger, Jennifer Gage (translator): Triangle of Thought, American Mathematical Society, 2001, ISBN 9780821826140
 JeanPierre Changeux, Alain Connes, M. B. DeBevoise (translator): Conversations on Mind, Matter, and Mathematics, Princeton University Press, 1998, ISBN 9780691004051
 Alain Connes: Noncommutative Geometry, Academic Press, 1994, ISBN 9780121858605^{[4]}
See also
 Cyclic homology
 Factor (functional analysis)
 Higgs boson
 C*algebra
 M Theory
 Groupoid
 Criticism of nonstandard analysis
References
 ↑ Alain Connes, « Géométrie noncommutative », Université de tous les savoirs, 4, 175190, Editions Odile Jacob, 2001.
 ↑ Mashaal, Maurice (2006), Bourbaki: a secret society of mathematicians, American Mathematical Society, p. 18, ISBN 9780821839676<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>.
 ↑ Scientific Americain, The Geometer of Particle Physics, 24 July 2006
 ↑ Lua error in Module:Citation/CS1/Identifiers at line 47: attempt to index field 'wikibase' (a nil value).
External links
 Alain Connes Official Web Site containing downloadable papers, and his book Noncommutative geometry, ISBN 012185860X.
 Alain Connes in nLab
 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<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>.
 Alain Connes at the Mathematics Genealogy Project
 Use dmy dates from June 2013
 Articles lacking intext citations from February 2012
 1947 births
 Living people
 20thcentury mathematicians
 Members of the United States National Academy of Sciences
 21stcentury mathematicians
 Collège de France faculty
 French mathematicians
 Fields Medalists
 Mathematical analysts
 Differential geometers
 École Normale Supérieure alumni
 Vanderbilt University faculty
 Foreign Members of the Russian Academy of Sciences
 Members of the French Academy of Sciences
 Members of the Norwegian Academy of Science and Letters
 Members of the Royal Danish Academy of Sciences and Letters
 Clay Research Award recipients
 Participants in the Les Houches Physics Summer School