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Alain Connes  

Alain Connes in 2004  
Born  Draguignan, France  1 April 1947
Nationality  French 
Alma mater  École Normale Supérieure Pierre and Marie Curie University 
Known for  Baum–Connes conjecture Noncommutative geometry Operator algebras Thermal time hypothesis 
Awards  CNRS Silver Medal (1977) Prize Ampère (1980) Fields Medal (1982) Clay Research Award (2000) Crafoord Prize (2001) CNRS Gold medal (2004) 
Scientific career  
Fields  Mathematics Particle physics 
Institutions  Collège de France IHÉS Ohio State University Vanderbilt University 
Doctoral advisor  Jacques Dixmier 
Doctoral students  JeanBenoît Bost Georges Skandalis 
Alain Connes (French: [alɛ̃ kɔn]; born 1 April 1947) is a French mathematician, and a theoretical physicist, known for his contributions to the study of operator algebras and noncommutative geometry. He is a Professor at the Collège de France, IHÉS, Ohio State University and Vanderbilt University. He was awarded the Fields Medal in 1982.
Career
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Connes was an Invited Professor at the Conservatoire national des arts et métiers (2000).^{[1]}
Research
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. He also formulated the Connes embedding problem. 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,^{[4]}^{[5]} the Crafoord Prize in 2001^{[6]}^{[7]} 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^{[8]}
See also
 Bost–Connes system
 Cyclic homology
 Factor (functional analysis)
 Higgs boson
 C*algebra
 Mtheory
 Groupoid
 Criticism of nonstandard analysis
 Riemann hypothesis
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.
 ^ "The Geometer of Particle Physics" Scientific American, 24 July 2006
 ^ Albers, Donald J.; Alexanderson, G. L.; Reid, Constance (1986). "International mathematical congresses. An illustrated history 1893  1986". SpringerVerlag. Retrieved 2 December 2018.
 ^ IMU Secretariat. "Fields Medal  International Mathematical Union (IMU)". International Mathematical Union. Retrieved 2 December 2018.
 ^ "Crafoord Prize  Crafoord Prize Laureates". crafoordprize.se. 2000. Retrieved 2 December 2018.
 ^ "Crafoord Prize to one of the world's foremost mathematicians". The Royal Swedish Academy of Sciences. 25 January 2001. Retrieved 2 December 2018.
 ^ Segal, Irving (1996). "Book Review: Noncommutative Geometry, by Alan Connes" (PDF). Bulletin of the American Mathematical Society. New Series. 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