Alain Connes

Alain Connes 2004

Alain Connes (born April 1, 1947 in Draguignan near Cannes , France ) is a French mathematician and recipient of the Fields Medal .

life and career

Connes is the son of a police chief in Marseille . After his studies from 1966 to 1970 at the elite university Ecole Normale Supérieure (ENS) doctorate he in 1973 Jacques Dixmier ( A Classification of Factors of Type III ). From 1970 he did research for the CNRS . In 1975 he was visiting scholar at Queen's University in Kingston . In 1976 he was appointed assistant professor (Maître de conférences) at the University of Paris VI and later professor, which he remained until 1980. 1978/1979 he was at the Institute for Advanced Study in Princeton . From 1979 he held the Léon Motchane chair at the Institut des Hautes Études Scientifiques (IHES) and from 1981 he was research director at the CNRS for eight years. Since 1984 he has been Professor of Analysis and Geometry at the Collège de France . Since 2003 he has also been a professor at Vanderbilt University .

For example, he worked on Von Neumann algebras . The classification of the type III factors of these algebras was also the dissertation topic for Jacques Dixmier in 1973. He is known as the founder of non-commutative geometry , a synthesis essentially created by him, in which one considers the function rings defined on them instead of the underlying spaces . If these are non-commutative, they can be used to examine the underlying non-commutative spaces that are otherwise difficult to access. He applied his theory to a wide variety of areas, from the Riemann Hypothesis of number theory to the standard model of elementary particle physics .

As a hobby he plays the piano.

Prizes, awards and memberships

• Invited Speaker at the International Congress of Mathematicians (ICM) 1974 in Vancouver (Structure Theory of Type III Factors)
• Peccot-Vimont Prize of the College de France (1976)
• Silver medal of the CNRS 1977
• Ampère Prize of the Academie des Sciences (1980)
• Aimé Berthé Prize of the Academie des Sciences (1982)
• Plenary lecture at the ICM 1978 in Helsinki (Von Neumann Algebras)
• Fields Medal (1982)
• Invited Speaker at the ICM 1986 in Berkeley (Cyclic cohomology and noncommutative differential geometry)
• Clay Research Award (2000)
• Crafoord Prize (2001)
• CNRS Gold Medal (2004)
• Member of the Académie des sciences (corresponding member since 1980, full member since 1983)
• Foreign member of the Royal Danish Academy of Sciences (1980)
• Foreign member of the Norwegian Academy of Sciences (1993)
• Member of the American Academy of Arts and Sciences (1989)
• Member of the National Academy of Sciences (1997)
• Foreign Corresponding Member of the Russian Academy of Sciences (2003)
• Fellow of the Royal Society of Canada (1996)
• He has multiple honorary doctorates: Queen's University in Kingston (1979), Rome ( Tor Vergata ) (1997), University of Oslo (1999), University of South Denmark (2009), Free University of Brussels (2010)

Fonts

• Connes: Noncommutative geometry (PDF; 4.3 MB) Academic Press, 1994
• Connes, André Lichnerowicz , Marcel Schutzenberger: Triangle of thought . American Mathematical Society, 2001
• Connes, Matilde Marcolli: A walk in the noncommutative garden . 2006, arxiv : math.QA/0601054
• Connes: Noncommutative Geometry Year 2000 . 2000, arxiv : math.QA/0011193
• Advice to a young mathematician . In: Timothy Gowers , June Barrow-Green , Imre Leader (Editor): The Princeton Companion to Mathematics . Princeton University Press, 2008, pp. 1011-1013
• Some of his essays (mostly in French) can be found online at numdam.org . a. A new proof of Morley's theorem . In :: Pub.Math.IHES , 1998 (the sentence from triangular geometry) and Une classification des facteurs de type III . In: Annales scientifiques de l'École Normale Supérieure , Sér. 4, Volume 6, No. 2, 197, pp. 133-252 (his dissertation)

Web links

• Literature by and about Alain Connes in the catalog of the German National Library
• Homepage Alain Connes, with a number of his essays
• Institut des hautes études scientifiques
• Alain Connes in the Mathematics Genealogy Project (English)
• John J. O'Connor, Edmund F. Robertson :  Alain Connes. In: MacTutor History of Mathematics archive .
• Author profile Alain Connes in the database zbMATH
• Connes: The flashes of insight never came for free . (PDF) Nieuw Archief voor Wiskunde; Interview 2010

Individual evidence

1. ^ Smolin: The trouble with physics . Mariner Book, 2007, p. 245.
2. ↑ Alain Connes in the Mathematics Genealogy Project (English)
3. ↑ See, for example, Lesniewski Noncommutative geometry , Notices AMS 1997