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Alain Connes in 2004
1 April 1947 |
|Alma mater||École Normale Supérieure, France|
|Doctoral advisor||Jacques Dixmier|
|Doctoral students||Georges Skandalis|
|Known for||Baum–Connes conjecture
|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).
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.
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.
- Alain Connes and Matilde Marcolli: Noncommutative Geometry, Quantum Fields and Motives, Colloquium Publications, American Mathematical Society, 2007, ISBN 978-0821842102 
- 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
- Cyclic homology
- Factor (functional analysis)
- Higgs boson
- M Theory
- Criticism of non-standard analysis
- Alain Connes, « Géométrie non-commutative », Université de tous les savoirs, 4, 175-190, Editions Odile Jacob, 2001.
- 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/s0273-0979-96-00687-8.
- 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
- 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