# Alain Connes

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**Alain Connes** (Template:IPA-fr; born 1 April 1947) is a French mathematician, currently Professor at the Collège de France, IHÉS, The Ohio State University and Vanderbilt University.

## 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.

Connes has applied his work in areas of mathematics and theoretical physics, including number theory, differential geometry and particle physics.^{[1]}

## 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.

## Books

- 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

## See also

- Cyclic homology
- Factor (functional analysis)
- Higgs boson
- C*-algebra
- M Theory
- Groupoid
- Criticism of non-standard analysis

## External links

- Alain Connes Official Web Site containing downloadable papers, and his book
*Non-commutative geometry*, ISBN 0-12-185860-X. - Template:Nlab
- Alain Connes' Standard Model
- An interview with Alain Connes and a discussion about it
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- 1947 births
- Living people
- 20th-century mathematicians
- Members of the United States National Academy of Sciences
- 21st-century mathematicians
- Collège de France faculty
- French mathematicians
- Fields Medalists
- 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