ⓘ Alain Connes


ⓘ 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 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.


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 978-0821842102
  • Alain Connes, Noncommutative Geometry, Academic Press, 1994, ISBN 978-0121858605
  • Jean-Pierre Changeux, and Alain Connes, Conversations on Mind, Matter, and Mathematics, translated by M. B. DeBevoise, Princeton University Press, 1998, ISBN 978-0691004051
  • Alain Connes, Andre Lichnerowicz, and Marcel Paul Schutzenberger, Triangle of Thought, translated by Jennifer Gage, American Mathematical Society, 2001, ISBN 978-0821826140