Alain Connes | |
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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 |

Institutions | IHÉS, France |

Doctoral advisor | Jacques Dixmier |

Doctoral students | Georges Skandalis |

**Alain Connes** (French: [alɛ̃ kɔn]; born 1 April 1947) is a French mathematician, currently Professor at the Collège de France, IHÉS, 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. He also formulated the Connes embedding problem. 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,^{[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 978-0821842102 [1] - Alain Connes, Andre Lichnerowicz, and Marcel Paul Schutzenberger,
*Triangle of Thought*, translated by Jennifer Gage, American Mathematical Society, 2001, ISBN 978-0821826140 - Jean-Pierre Changeux, and Alain Connes,
*Conversations on Mind, Matter, and Mathematics*, translated by M. B. DeBevoise, Princeton University Press, 1998, ISBN 978-0691004051 - Alain Connes,
*Noncommutative Geometry*, Academic Press, 1994, ISBN 978-0121858605^{[8]}

## See also

- Bost–Connes system
- Cyclic homology
- Factor (functional analysis)
- Higgs boson
- C*-algebra
- M-theory
- Groupoid
- Criticism of non-standard analysis

## References

**^**Alain Connes, « Géométrie non-commutative »,*Université de tous les savoirs*,**4**, 175-190, Editions Odile Jacob, 2001.**^**Mashaal, Maurice (2006),*Bourbaki: a secret society of mathematicians*, American Mathematical Society, p. 18, ISBN 978-0-8218-3967-6.**^**"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". Springer-Verlag. Retrieved 2 December 2018.**^**IMU Secretariat. "Fields Medal - International Mathematical Union (IMU)". International Mathematical Union. Retrieved 2 December 2018.**^**"Crafoord Prize - Crafoord Prize Laureates". www.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). "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.

## 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
- 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