Alain Connes in 2004
|Born||1 April 1947|
|Alma mater||École Normale Supérieure |
Pierre and Marie Curie University
|Known for||Baum-Connes conjecture|
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)
Ohio State University
|Doctoral advisor||Jacques Dixmier|
|Doctoral students||Jean-Benoît Bost|
Alain Connes (French: [al k?n]; born 1 April 1947) is a French mathematician known for his contributions to the study of operator algebras and noncommutative geometry. He is a Professor at the Collège de France, IHÉS, Ohio State University and Vanderbilt University. He was awarded the Fields Medal in 1982.
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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.
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.