CONNES, ALAIN

born April 1, 1947, Darguignan, France French mathematician who won the Fields Medal in 1983 for his work in operator theory. Connes received his doctorate from the University of Paris VI in 1973. He held appointments at the National Centre for Scientific Research, Paris (197074); Queen's University at Kingston in Canada (197475); the University of Paris VI (197577); the Institute for Advanced Study, Princeton, N.J., U.S. (197879); and the Institute of Advanced Scientific Studies, Bures-sur-Yvette, France (1979 ). Connes received the Fields Medal at the International Congress of Mathematicians in Warsaw in 1983. The study of von Neumann algebrasi.e., special algebras of all bounded linear operators on a Hilbert spacebegan in the 1930s, when their factors were classified, although technical problems remained open until the late '60s, when there was a resurgence of interest. Connes unified a number of concepts in the area that had earlier been considered disparate. He also worked on the application of operator algebras to differential geometry, developing an index theorem analogous to the well-known Atiyah-Singer index theorem. Connes's later work had significant and deep implications in ergodic theory. Connes's publications include Gomtrie non commutative (1990; Noncommutative Geometry) and Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory (1990).