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{{Infobox Scientist
|name = Alain Connes
|box_width = 26em
|image = Replace this image male.svg
|image_width = 150px
|caption =
|birth_date = {{Birth date and age|1947|4|1}}
|birth_place = [[France]]
|death_date =
|death_place =
|residence = [[Image:Flag of France.svg|20px]] [[France]]
|citizenship = [[Image:Flag of France.svg|20px]] [[France|French]]
|nationality =
|ethnicity =
|field = [[Mathematics]]
|work_institutions = [[IHES]], [[France]]
|alma_mater = [[École Normale Supérieure]], [[France]]
|doctoral_advisor = [[Jacques Dixmier]]
|doctoral_students = Alain Valette<br/>Georges Skandalis<br/>Benjamin Enriquez
|known_for = [[Baum–Connes conjecture]]<br/>[[Noncommutative geometry]]<br/>[[Operator algebra]]s<br/>
|author_abbrev_bot =
|author_abbrev_zoo =
|prizes = [[Fields Medal]] (1982)<br/>[[Crafoord Prize ]] (2001)<br/>[[CNRS]] Gold Medal (2004)
|religion =
|footnotes =
}}

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

==Work==
Alain Connes is one of the leading specialists on [[operator algebra]]s. In his early work on [[von Neumann algebras]] in the 1970s, he succeeded in obtaining the almost complete classification of injective [[Von Neumann algebra#Factors|factor]]s. Following this he made contributions in [[K-theory|operator K-theory]] and [[index theory]], which culminated in the
[[Baum-Connes conjecture]]. He also introduced [[cyclic homology|cyclic cohomology]] in the early 1980s as a first step in the study of [[noncommutative geometry| 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 [[Royal Danish Academy of Sciences and Letters|Danish Academy of Sciences]], [[Norwegian Academy of Science and Letters|Norwegian Academy of Sciences]], [[Russian Academy of Sciences]], and [[United States National Academy of Sciences|US National Academy of Sciences]].

==See also==
* [[cyclic homology]]
* [[factor (functional analysis)]]
* [[Higgs boson]]
* [[C*-algebra]]
* [[M Theory]]
* [[Groupoid]]

==External links==

* [http://www.alainconnes.org/ Alain Connes Official Web Site] containing [http://www.alainconnes.org/downloads.html downloadable papers], and his book [ftp://ftp.alainconnes.org/book94bigpdf.pdf ''Non-commutative geometry''], ISBN 0-12-185860-X.
* {{MacTutor Biography|id=Connes}}
* {{MathGenealogy|id=34220}}

{{Fields medalists}}

{{DEFAULTSORT:Connes, Alain}}

[[Category:20th century mathematicians]]
[[Category:21st century mathematicians]]
[[Category:Collège de France faculty]]
[[Category:French mathematicians]]
[[Category:Fields Medalists]]
[[Category:Mathematical analysts]]
[[Category:Differential geometers]]
[[Category:Alumni of the École Normale Supérieure]]
[[Category:Vanderbilt University faculty]]
[[Category:Members and associates of the United States National Academy of Sciences]]
[[Category:Members of the Russian Academy of Sciences]]
[[Category:1947 births]]
[[Category:Living people]]
[[Category:Members of the French Academy of Sciences]]

[[ar:ألان كن]]
[[de:Alain Connes]]
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[[fr:Alain Connes]]
[[ko:알랭 콘느]]
[[it:Alain Connes]]
[[ja:アラン・コンヌ]]
[[pl:Alain Connes]]
[[fi:Alain Connes]]
[[zh:阿蘭·科納]]