Alain Connes

Alain Connes (; born 1 April 1947 in Draguignan) is a French mathematician, known for his contributions to the study of operator algebras and noncommutative geometry. He is a professor at the , , Ohio State University and Vanderbilt University. He was awarded the Fields Medal in 1982.

Career
Alain Connes attended high school at  in Marseille, and was then a student of the classes préparatoires in . Between 1966 and 1970 he studed 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.

In 2000 he was an invited professor at the Conservatoire national des arts et métiers.

Research 
Connes' main research interests revolved around operator algebras. Besides noncommutative geometry, he has applied his works in various areas of mathematics and theoretical physics, including number theory, differential geometry and particle physics.

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.

Awards and honours

Connes was awarded the Peccot-Vimont Prize in 1976, the Ampère Prize in 1980, the Fields Medal in 1982, the Clay Research Award in 2000 and the Crafoord Prize in 2001. The French National Centre for Scientific Research granted him the silver medal in 1977 and the gold medal in 2004.

He was an invited speaker at the International Congress of Mathematicians in 1974 at Vancouver and in 1986 at Berkeley, and a plenary speaker at the ICM in 1978 at Helsinki.

He was awarded honorary degrees from Queen's University at Kingston in 1979, University of Rome Tor Vergata in 1997, University of Oslo in 1999, University of Southern Denmark in 2009, Université Libre de Bruxelles in 2010 and Shanghai Fudan University in 2017.

Since 1982 he is a member of the French Academy of Sciences. He was elected member of several foreign academies and societies, including the Royal Danish Academy of Sciences and Letters in 1980, the Norwegian Academy of Science and Letters in 1983, the American Academy of Arts and Sciences in 1989, the London Mathematical Society in 1994, the Canadian Academy of Sciences in 1995 (incorporated since 2002 in the Royal Society of Canada), the US National Academy of Sciences in 1997, the Russian Academy of Science in 2003 and the Royal Academy of Science, Letters and Fine Arts of Belgium in 2016.

In 2001 he received (together with his co-authors André Lichnerowicz and Marco Schutzenberger) the Peano Prize for his work Triangle of Thoughts.

Books
 Alain Connes and Matilde Marcolli, Noncommutative Geometry, Quantum Fields and Motives, Colloquium Publications, American Mathematical Society, 2007,  
 Alain Connes, André 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
 
 

1947 births
Living people
People from Draguignan
20th-century French mathematicians
21st-century French mathematicians
Mathematical analysts
Differential geometers
Fields Medalists
Clay Research Award recipients
École Normale Supérieure alumni
Academic staff of the Collège de France
Institute for Advanced Study visiting scholars
Foreign associates of the National Academy of Sciences
Vanderbilt University faculty
Foreign Members of the Russian Academy of Sciences
Members of the French Academy of Sciences
Members of the Norwegian Academy of Science and Letters
Members of the Royal Danish Academy of Sciences and Letters
London Mathematical Society