Alain Connes

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Alain Connes
Photo of the upper body of Alain Connes with vegetation, blue sky, and clouds in the background
Alain Connes in 2004
Born (1947-04-01) 1 April 1947 (age 75)
Draguignan, France
Alma materÉcole Normale Supérieure
Pierre and Marie Curie University
Known forBaum–Connes conjecture
Noncommutative geometry
Noncommutative standard model
Operator algebras
Thermal time hypothesis
AwardsCNRS Silver Medal (1977)
Prize Ampère (1980)
Fields Medal (1982)
Clay Research Award (2000)
Crafoord Prize (2001)
CNRS Gold medal (2004)
Scientific career
Particle physics
InstitutionsCollège de France
Ohio State University
Vanderbilt University
Doctoral advisorJacques Dixmier
Doctoral studentsJean-Benoît 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, Institut des Hautes Études Scientifiques, Ohio State University and Vanderbilt University. He was awarded the Fields Medal in 1982.



Academic career timeline:

(1966–1970) – Bachelor's degree from the École Normale Supérieure (now part of Paris Sciences et Lettres University).

(1973) – doctorate from Pierre and Marie Curie University, Paris, France

(1970–1974) – appointment at the French National Centre for Scientific Research, Paris

(1975) – Queen's University at Kingston, Ontario, Canada

(1976–1980) – the University of Paris VI

(1979 – present) – the Institute of Advanced Scientific Studies, Bures-sur-Yvette, France

(1981–1984) – the French National Centre for Scientific Research, Paris

(1984–2017) – the Collège de France, Paris

(2003–2011) – Vanderbilt University, Nashville, Tennessee

(2012–2020) – the Ohio State University, Columbus

Connes was an invited professor at the Conservatoire national des arts et métiers (2000).[2]


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 Nicolas Bourbaki.[3]

Connes has applied his work in areas of mathematics and theoretical physics, including number theory, differential geometry and particle physics.[4]

Awards and honours[edit]

Connes was awarded the Fields Medal in 1982,[5][6] the Crafoord Prize in 2001[7][8] and the gold medal of the French National Centre for Scientific Research in 2004. He was an invited speaker at the International Congress of Mathematicians (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 Royal Danish and Norwegian Academies of Science and Letters, and the Russian and US National Academies of Sciences.


  • Alain Connes and Matilde Marcolli, Noncommutative Geometry, Quantum Fields and Motives, Colloquium Publications, American Mathematical Society, 2007, ISBN 978-0-8218-4210-2 [1]
  • Alain Connes, André Lichnerowicz, and Marcel-Paul Schutzenberger, Triangle of Thought, translated by Jennifer Gage, American Mathematical Society, 2001, ISBN 978-0-8218-2614-0
  • Jean-Pierre Changeux, and Alain Connes, Conversations on Mind, Matter, and Mathematics, translated by M. B. DeBevoise, Princeton University Press, 1998, ISBN 978-0-691-00405-1
  • Alain Connes, Noncommutative Geometry, Academic Press, 1994, ISBN 978-0-12-185860-5[9]

See also[edit]


  1. ^ "Curriculum Vitae". Alain Connes. 22 April 2021. Retrieved 8 September 2022.
  2. ^ Alain Connes, « Géométrie non-commutative », Université de tous les savoirs, 4, 175–190, Editions Odile Jacob, 2001.
  3. ^ Mashaal, Maurice (2006). Bourbaki: a secret society of mathematicians. American Mathematical Society. p. 18. ISBN 978-0-8218-3967-6.
  4. ^ Alexander Hellemans, "The Geometer of Particle Physics" Scientific American, 24 July 2006
  5. ^ Albers, Donald J.; Alexanderson, G. L.; Reid, Constance (1986). "International mathematical congresses. An illustrated history 1893 – 1986". Springer-Verlag. Retrieved 2 December 2018.
  6. ^ IMU Secretariat. "Fields Medal – International Mathematical Union (IMU)". International Mathematical Union. Retrieved 2 December 2018.
  7. ^ "Crafoord Prize – Crafoord Prize Laureates". 2000. Retrieved 2 December 2018.
  8. ^ "Crafoord Prize to one of the world's foremost mathematicians". The Royal Swedish Academy of Sciences. 25 January 2001. Retrieved 2 December 2018.
  9. ^ 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/s0273-0979-96-00687-8. Archived (PDF) from the original on 9 October 2022.

External links[edit]