Alain Connes (; born 1 April 1947) is a French mathematician, and a theoretical physicist, 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.
Career
Connes was an Invited Professor at the Conservatoire national des arts et métiers (2000).Alain Connes, « Géométrie non-commutative », Université de tous les savoirs, 4, 175-190, Editions Odile Jacob, 2001.
Research
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 has applied his work in areas of mathematics and theoretical physics, including number theory, differential geometry and particle physics."
The Geometer of Particle Physics"  Scientific American, 24 July 2006 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.
Books
Alain Connes and Matilde Marcolli, Noncommutative Geometry, Quantum Fields and Motives, Colloquium Publications, American Mathematical Society, 2007,
Alain Connes, Andre Lichnerowicz, and Marcel Paul Schutzenberger, Triangle of Thought, translated by Jennifer Gage, American Mathematical Society, 2001,
Jean-Pierre Changeux, and Alain Connes, Conversations on Mind, Matter, and Mathematics, translated by M. B. DeBevoise, Princeton University Press, 1998,
Alain Connes, Noncommutative Geometry, Academic Press, 1994,
See also
Bost–Connes system
Cyclic category
Cyclic homology
Factor (functional analysis)
Higgs boson
C*-algebra
Noncommutative quantum field theory
M-theory
Groupoid
Spectral triple
Criticism of non-standard analysis
Riemann hypothesis
References
External links
Alain Connes Official Web Site containing downloadable papers, and his book Non-commutative geometry, .
Alain Connes' Standard Model
An interview with Alain Connes and a discussion about it
