Alain Connes
French mathematician (born 1947)
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Through Von Neumann algebra
Career
Alain Connes attended high school at Lycée Saint-Charles in Marseille, and was then a student of the classes préparatoires in Lycée Thiers. Between 1966 and 1970 he studied at École normale supérieure in Paris, and in 1973 he obtained a PhD from Pierre and Marie Curie University, under the supervision of Jacques Dixmier.
From 1970 to 1974 he was research fellow at the French National Centre for Scientific Research and during 1975 he held a visiting position at Queen's University at Kingston in Canada.
In 1976 he returned to France and worked as professor at Pierre and Marie Curie University until 1980 and at CNRS between 1981 and 1984. Moreover, since 1979 he holds the Léon Motchane Chair at IHES. From 1984 until his retirement in 2017 he held the chair of Analysis and Geometry at Collège de France.
In parallel, he was awarded a distinguished professorship at Vanderbilt University between 2003 and 2012, and at Ohio State University between 2012 and 2021.
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Research
Connes's main research interests revolved around operator algebras. He has applied his works in various areas of mathematics and number theory, differential geometry. Since the 1990s, he developed noncommutative geometry.
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. Over many years, he collaborated extensively with Henri Moscovici.
Family
Alain Connes is the middle-born of three sons. Both his parents lived to be 101 years old. He married in 1971.
Books
- Alain Connes and Matilde Marcolli, Noncommutative Geometry, Quantum Fields and Motives, Colloquium Publications, American Mathematical Society, 2007, ISBN 978-0-8218-4210-2
- 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