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Alain Connes

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Title: Alain Connes  
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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
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Alain Connes

Alain Connes
Alain Connes in 2004
Born (1947-04-01) 1 April 1947
Draguignan, France
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: ; 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]

Contents

  • Work 1
  • Awards and honours 2
  • Books 3
  • See also 4
  • References 5
  • External links 6

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 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]

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 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]

See also

References

  1. ^ Alain Connes, « Géométrie non-commutative », Université de tous les savoirs, 4, 175-190, Editions Odile Jacob, 2001.
  2. ^ .
  3. ^ , 24 July 2006The Geometer of Particle PhysicsScientific Americain,
  4. ^

External links

  • 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
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