- Alain Connes
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Alain Connes 
Alain Connes in 2004Born 1 April 1947
Draguignan, FranceNationality 
FrenchFields Mathematics Institutions IHÉS, France Alma mater École Normale Supérieure, France Doctoral advisor Jacques Dixmier Doctoral students Benjamin Enriquez
Georges Skandalis
Alain ValetteKnown for Baum–Connes conjecture
Noncommutative geometry
Operator algebrasNotable awards Fields Medal (1982)
Crafoord Prize (2001)
CNRS Gold Medal (2004)Alain Connes (born 1 April 1947) is a French mathematician, currently Professor at the Collège de France, IHÉS, The Ohio State University and Vanderbilt University.
Contents
Work
Alain Connes is one of the leading specialists on 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.
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.
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.
- nlab about Alain Connes
- 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, http://www-history.mcs.st-andrews.ac.uk/Biographies/Connes.html.
- Alain Connes at the Mathematics Genealogy Project.
Categories:- 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
- Alumni of the École Normale Supérieure
- Vanderbilt University faculty
- Members of the Russian Academy of Sciences
- Members of the French Academy of Sciences
- Norwegian Academy of Science and Letters
- Members of the Royal Danish Academy of Sciences and Letters
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