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Alain Connes

Alain Connes
Born April 1, 1947(1947-04-01) (age 61)
FranceResidence FranceCitizenship FrenchFields MathematicsInstitutions IHES, FranceAlma materÉcole Normale Supérieure, FranceDoctoraladvisor Jacques DixmierDoctoral students Alain Valette
Georges Skandalis
Benjamin Enriquez Known for Baum–Connes conjecture
Noncommutative geometry
Operator algebras
Notable awards Fields Medal(1982)
Crafoord Prize(2001)
CNRSGold Medal (2004)

Alain Connes (born April 1, 1947) is a French mathematician, currently Professor at the College de France, IHES and Vanderbilt University.

Contents

Work

Alain Connes is one of the leading specialists on operator algebras. In his early work on von Neumann algebras in the 1970s, he succeeded in obtaining the almost complete classification of injective factors. 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.

Connes has applied his work in areas of mathematics and theoretical physics, including number theory, differential geometry and particle physics.

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 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.

See also

External links

v • d • eFields Medalists

Lars Ahlfors / Jesse Douglas (1936) · Laurent Schwartz / Atle Selberg (1950) · Kunihiko Kodaira / Jean-Pierre Serre (1954) · Klaus Roth / René Thom (1958) · Lars Hörmander / John Milnor (1962) · Michael Atiyah / Paul Cohen / Alexander Grothendieck / Stephen Smale (1966) · Alan Baker / Heisuke Hironaka / Sergei Petrovich Novikov / John G. Thompson (1970) · Enrico Bombieri / David Mumford (1974) · Pierre Deligne / Charles Fefferman / Grigory Margulis / Daniel Quillen (1978) · Alain Connes / William Thurston / Shing-Tung Yau (1982) · Simon Donaldson / Gerd Faltings / Michael Freedman (1986) · Vladimir Drinfel'd / Vaughan Jones / Shigefumi Mori / Edward Witten (1990) · Efim Zelmanov / Pierre-Louis Lions / Jean Bourgain / Jean-Christophe Yoccoz (1994) · Richard Borcherds / William Timothy Gowers / Maxim Kontsevich / Curtis T. McMullen (1998) · Laurent Lafforgue / Vladimir Voevodsky (2002) · Andrei Okounkov / Grigori Perelman / Terence Tao / Wendelin Werner (2006)

Categories: 20th century mathematicians | Members of the National Academy of Sciences | 21st century mathematicians | Collège de France faculty | French mathematicians | Fields Medalists | Mathematical analysts | Differential geometers | Alumni of the École Normale Supérieure | Vanderbilt University faculty | Members of the Russian Academy of Sciences | 1947 births | Living people | Members of the French Academy of Sciences

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