Alain Connes
Title: Alain Connes
Subject: Noncommutative standard model, Fields Medal, Von Neumann algebra, Matilde Marcolli, Michael Atiyah
Collection: 1947 Births, 20Th-Century Mathematicians, 21St-Century Mathematicians, Clay Research Award Recipients, Collège De France Faculty, Differential Geometers, École Normale Supérieure Alumni, Fields Medalists, Foreign Members of the Russian Academy of Sciences, French Mathematicians, Living People, Mathematical Analysts, 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, Members of the United States National Academy of Sciences, Participants in the Les Houches Physics Summer School, Vanderbilt University Faculty
Alain Connes in 2004
(1947-04-01) 1 April 1947
Draguignan, France
IHÉS, France
École Normale Supérieure, France
Jacques Dixmier
Georges Skandalis
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: ; 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]
Awards and honours 2
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 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. 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]
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.
Alain Connes and Matilde Marcolli: Noncommutative Geometry, Quantum Fields and Motives, Colloquium Publications, American Mathematical Society, 2007, ISBN 978-0821842102 [1]
Alain Connes, Andre Lichnerowicz, Marcel Paul Schutzenberger, Jennifer Gage (translator): Triangle of Thought, American Mathematical Society, 2001, ISBN 978-0821826140
Jean-Pierre Changeux, Alain Connes, M. B. DeBevoise (translator): Conversations on Mind, Matter, and Mathematics, Princeton University Press, 1998, ISBN 978-0691004051
Alain Connes: Noncommutative Geometry, Academic Press, 1994, ISBN 978-0121858605[4]
Cyclic homology
Factor (functional analysis)
C*-algebra
M Theory
Groupoid
Criticism of non-standard analysis
^ Alain Connes, « Géométrie non-commutative », Université de tous les savoirs, 4, 175-190, Editions Odile Jacob, 2001.
^ .
^ , 24 July 2006The Geometer of Particle PhysicsScientific Americain,
Alain Connes Official Web Site containing downloadable papers, and his book Non-commutative geometry, ISBN 0-12-185860-X.
Alain Connes in nLab
Alain Connes' Standard Model
An interview with Alain Connes and a discussion about it
Alain Connes at the Mathematics Genealogy Project
Fields Medalists
1936 Ahlfors
1950 Schwartz
Selberg
1954 Kodaira
1958 Roth
1962 Hörmander
1966 Atiyah
Grothendieck
Smale
1970 Baker
Hironaka
Novikov
1974 Bombieri
Mumford
1978 Deligne
Fefferman
Margulis
Quillen
1982 Connes
1986 Donaldson
Faltings
Freedman
1990 Drinfeld
1994 Bourgain
Yoccoz
Zelmanov
1998 Borcherds
Gowers
Kontsevich
McMullen
2002 Lafforgue
Voevodsky
2006 Okounkov
Perelman
2010 Lindenstrauss
Ngô
Villani
2014 Avila
Hairer
Mirzakhani
Mathematics portal
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Articles lacking in-text citations from February 2012
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20th-century mathematicians
Members of the United States National Academy of Sciences
21st-century mathematicians
Collège de France faculty
French mathematicians
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
Logic, Set theory, Statistics, Number theory, Mathematical logic
University of Cambridge, Institute for Advanced Study, Princeton University, University of California, Berkeley, University of Oxford
Mathematics, Topology, Number theory, Hausdorff space, Duality (mathematics)
Texas A&M University, Duke University, University of Florida, Tulane University, University of Texas at Austin
Computer science, Cryptography, Statistics, Discrete mathematics, Numerical analysis
Noncommutative standard model
Noncommutative geometry, Standard Model, General relativity, Riemannian geometry, Pi
Von Neumann algebra
Mathematics, Ergodic theory, Quantum mechanics, Crossed product, Representation theory
Matilde Marcolli
Amsterdam, Authority control, Mumbai, Number theory, University of Chicago
Trinity College, Cambridge, University of Oxford, University of Leicester, Royal Society, University of Edinburgh