Alain Connes
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Alain Connes  

Alain Connes in 2004


Born 
Draguignan, France 
1 April 1947
Nationality  French 
Fields  Mathematics 
Institutions  IHÉS, France 
Alma mater 
École Normale Supérieure Pierre and Marie Curie University 
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, and Marcel Paul Schutzenberger, Triangle of Thought, translated by Jennifer Gage, American Mathematical Society, 2001, ISBN 9780821826140
 JeanPierre Changeux, and Alain Connes, Conversations on Mind, Matter, and Mathematics, translated by M. B. DeBevoise, 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.
 ^ Scientific Americain, The Geometer of Particle Physics, 24 July 2006
 ^ Segal, Irving (1996). "Review: Noncommutative geometry, by Alain Connes" (PDF). Bull. Amer. Math. Soc. (N.S.). 33 (4): 459–465. doi:10.1090/s0273097996006878.
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.
 Alain Connes at the Mathematics Genealogy Project
 1947 births
 Living people
 20thcentury French mathematicians
 Members of the United States National Academy of Sciences
 21stcentury mathematicians
 Collège de France faculty
 Institute for Advanced Study visiting scholars
 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