| Alain Connes | |
 | |
| Born | April 1, 1947 France |
|---|---|
| Residence |  France |
| Citizenship | French |
| Fields | Mathematics |
| Institutions | IHES, France |
| Alma mater | École Normale Supérieure, France |
| Doctoral advisor | Jacques Dixmier |
| Doctoral students | Alain Valette Georges Skandalis Benjamin Enriquez |
| Known for | Baum–Connes conjecture Noncommutative geometry Operator algebras |
| Notable awards | Fields Medal (1982) Crafoord Prize (2001) CNRS Gold Medal (2004) |
Alain Connes (born April 1, 1947) is a French mathematician, currently Professor at the College de France, IHES and Vanderbilt University. Events 527 - Byzantine Emperor Justin I names his nephew Justinian I as co-ruler and successor to the throne Year 1947 ( MCMXLVII) was a Common year starting on Wednesday (link will display full 1947 calendar of the Gregorian calendar. This article is about the country For a topic outline on this subject see List of basic France topics. This article is about the country For a topic outline on this subject see List of basic France topics. This article is about the country For a topic outline on this subject see List of basic France topics. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and The Institut des Hautes Études Scientifiques ( IHÉS, en Institute of Advanced Scientific Studies is a French institute supporting advanced research in This article is about the country For a topic outline on this subject see List of basic France topics. Alma mater is Latin for "nourishing mother" It was used in Ancient Rome as a title for the mother Goddess, and in Medieval École Normale de Musique de ParisThe École normale supérieure (also known as Normale Sup’, Normale, ENS, ENS-Paris, ENS-Ulm or This article is about the country For a topic outline on this subject see List of basic France topics. A doctorate is an Academic degree that indicates the highest level of academic achievement Jacques Dixmier (born 1924 is a French mathematician He worked on Operator algebras and wrote several of the standard reference books on them In Mathematics, specifically in Operator K-theory, the Baum&ndashConnes conjecture suggests a link between the C*-algebra of a group and the Noncommutative geometry, or NCG, is a branch of Mathematics concerned with the possible spatial interpretations of Algebraic structures for which the In Functional analysis, an operator algebra is an algebra of continuous Linear operators on a Topological vector space with the multiplication The Fields Medal is a prize awarded to two three or four Mathematicians not over 40 years of age at each International Congress of the International Mathematical The annual Crafoord Prize is a science prize established in 1980 by Holger Crafoord, a Swedish industrialist and his wife Anna-Greta Crafoord Events 527 - Byzantine Emperor Justin I names his nephew Justinian I as co-ruler and successor to the throne Year 1947 ( MCMXLVII) was a Common year starting on Wednesday (link will display full 1947 calendar of the Gregorian calendar. This article is about the country For a topic outline on this subject see List of basic France topics. A mathematician is a person whose primary area of study and research is the field of Mathematics. The Collège de France is a higher education and research establishment ( Grand établissement) located in Paris, France, in the 5th arrondissement The Institut des Hautes Études Scientifiques ( IHÉS, en Institute of Advanced Scientific Studies is a French institute supporting advanced research in Vanderbilt University is a private, Nonsectarian, Coeducational Research University in Nashville, Tennessee,
Contents |
Work
Alain Connes is one of the leading specialists on operator algebras. In Functional analysis, an operator algebra is an algebra of continuous Linear operators on a Topological vector space with the multiplication In his early work on von Neumann algebras in the 1970s, he succeeded in obtaining the almost complete classification of injective factors. In Mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the In Mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the Following this he made contributions in operator K-theory and index theory, which culminated in the Baum-Connes conjecture. In Mathematics, K-theory is a tool used in several disciplines In the Mathematics of Manifolds and Differential operators the Atiyah–Singer index theorem states that for an elliptic differential operator In Mathematics, specifically in Operator K-theory, the Baum&ndashConnes conjecture suggests a link between the C*-algebra of a group and the He also introduced cyclic cohomology in the early 1980s as a first step in the study of noncommutative differential geometry. In Homological algebra, cyclic homology and cyclic cohomology are (cohomology theories for Associative algebras introduced by Alain Connes around Noncommutative geometry, or NCG, is a branch of Mathematics concerned with the possible spatial interpretations of Algebraic structures for which the
Connes has applied his work in areas of mathematics and theoretical physics, including number theory, differential geometry and particle physics. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Theoretical physics employs Mathematical models and Abstractions of Physics in an attempt to explain experimental data taken of the natural world Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes Differential geometry is a mathematical discipline that uses the methods of differential and integral Calculus to study problems in Geometry Particle physics is a branch of Physics that studies the elementary constituents of Matter and Radiation, and the interactions between them
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. The Fields Medal is a prize awarded to two three or four Mathematicians not over 40 years of age at each International Congress of the International Mathematical The annual Crafoord Prize is a science prize established in 1980 by Holger Crafoord, a Swedish industrialist and his wife Anna-Greta Crafoord 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. The French Academy of Sciences ( French: Académie des sciences) is a Learned society, founded in 1666 by Louis XIV at the Royal Danish Academy of Sciences and Letters ( Danish: Kongelige Danske Videnskabernes Selskab) is a Danish non-governmental science Academy founded November The Norwegian Academy of Science and Letters ( Det Norske Videnskaps-Akademi) was founded in Christiania in 1857 to "advance science and scholarship in Norway The Russian Academy of Sciences (Российская Академия Наук Rossi'iskaya Akade'miya Nau'k, shortened to PAH RAN) consists of the National The National Academy of Sciences (NAS is a corporation in the United States whose members serve Pro bono as "advisers to the nation on science
See also
External links
- Alain Connes Official Web Site containing downloadable papers, and his book Non-commutative geometry, ISBN 0-12-185860-X. In Homological algebra, cyclic homology and cyclic cohomology are (cohomology theories for Associative algebras introduced by Alain Connes around In Mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the The Higgs Boson is a hypothetical massive scalar Elementary particle predicted to exist by the Standard Model of Particle physics C*-algebras (pronounced "C-star" are an important area of research in Functional analysis, a branch of Mathematics. In Theoretical physics, M-theory is a new limit of String theory in which 11 dimensions of Spacetime may be identified In Mathematics, especially in Category theory and Homotopy theory
- Alain Connes' Standard Model
- An interview with Alain Connes and a discussion about it
- O'Connor, John J. & Robertson, Edmund F. , “Alain Connes”, MacTutor History of Mathematics archive
- Alain Connes at the Mathematics Genealogy Project
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