ⓘ Alain Connes
Alain Connes is a French mathematician, currently Professor at the College de France, IHES, Ohio State University and Vanderbilt University. He was an Invited Professor at the Conservatoire national des arts et metiers.
1. Work
Alain Connes studies operator algebras. In his early work 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 Ktheory 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 has applied his work in areas of mathematics and theoretical physics, including number theory, differential geometry and particle physics.
2. 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 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.
3. Books
 Alain Connes and Matilde Marcolli, Noncommutative Geometry, Quantum Fields and Motives, Colloquium Publications, American Mathematical Society, 2007, ISBN 9780821842102
 Alain Connes, Noncommutative Geometry, Academic Press, 1994, ISBN 9780121858605
 JeanPierre Changeux, and Alain Connes, Conversations on Mind, Matter, and Mathematics, translated by M. B. DeBevoise, Princeton University Press, 1998, ISBN 9780691004051
 Alain Connes, Andre Lichnerowicz, and Marcel Paul Schutzenberger, Triangle of Thought, translated by Jennifer Gage, American Mathematical Society, 2001, ISBN 9780821826140
 notions were independently introduced by Boris Tsygan homology and Alain Connes cohomology in the 1980s. These invariants have many interesting relationships
 who pioneered the Hopf  algebraic approach to quantum field theory with Alain Connes and other co  authors. He is currently Humboldt professor at the department
 published counterexamples to a generalization of the Baum Connes conjecture i.e. Baum  Connes conjecture with coefficients in various special cases, based
 1988 agrege  preparateur teacher and worked under the direction of Alain Connes From 1988 he was charge de recherches and from 1993 directeur de recherches
 string theory Banks et al. 1997 BFSS matrix model in nLab Connes 1994, p. 1 Connes 1994 Connes Douglas, and Schwarz 1998 Nekrasov and Schwarz 1998 Seiberg
 of its role in M  theory made in 1997. Some of the theory developed by Alain Connes to handle noncommutative geometry at a technical level has roots in older
 He was a member and a leading figure of Nicolas Bourbaki. Along with Alain Connes he gave the 1975 1976 Peccot Lectures. He was an invited speaker at
 operators feature in the noncommutative geometry of French mathematician Alain Connes A compact operator A on an infinite dimensional separable Hilbert space
 several other mathematicians and physicists, among them Yuri I. Manin and Alain Connes Ten graduate students obtained their PhD under her supervision between
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