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| | The author's title is Christy. Distributing manufacturing is where her primary earnings arrives from. To play lacross is something I truly enjoy doing. Ohio is where his home is and his family enjoys it.<br><br>Also visit my web-site: cheap psychic readings ([http://www.caelumen.com/JSKTC try this out www.caelumen.com]) |
| {{Infobox scientist
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| |name = Robert Langlands
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| |image = Langlands2.jpg
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| |image_size = 230px
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| |caption =
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| |birth_date = {{birth date and age|1936|10|06}}
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| |birth_place = [[New Westminster]], [[British Columbia]], [[Canada]]
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| |death_date =
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| |death_place =
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| |nationality = [[Canada|Canadian]]
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| |fields = [[Mathematics]]
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| |workplaces = [[Princeton University]], <br /> [[Yale University]], <br />[[Institute for Advanced Study]]
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| |alma_mater = [[University of British Columbia]],<br />[[Yale University]]
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| |doctoral_advisor = [[Cassius Ionescu-Tulcea]]
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| |doctoral_students = [[James Arthur (mathematician)|James Arthur]]<br>[[Thomas Callister Hales]]<br>[[Baris Kendirli]]<br>[[Jonathan Rogawski]]<br>[[Diana Shelstad]]<br>[[Rajat Tandon]]
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| |known_for = [[Langlands program]]
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| |awards = [[Jeffery–Williams Prize]] (1980)<br>[[Wolf Prize]] (1995/96)<br>[[Leroy P. Steele Prize#The Leroy P. Steele Prize for Seminal Contribution to Research|Steele Prize]] (2005)<br>[[Nemmers Prize in Mathematics|Nemmers Prize]] (2006)<br>[[Shaw Prize]] (2007)
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| }}
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| '''Robert Phelan Langlands''' (born October 6, 1936) is a [[Canadian]] [[mathematician]] best known as the founder of the [[Langlands program]], a vast web of conjectures and results connecting [[representation theory]] and [[automorphic form]]s to the study of Galois groups in [[number theory]]. He is an [[emeritus]] [[professor]] at the [[Institute for Advanced Study]]. | |
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| ==Career==
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| Langlands received an undergraduate degree from the [[University of British Columbia]] in 1957, and continued on there to receive an M. Sc. in 1958. He then went to [[Yale University]] where he received a Ph.D. in 1960. His academic positions since then include the years 1960-67 at Princeton University, ending up as Associate Professor, and the years 1967-72 at Yale University. He was appointed Hermann Weyl Professor at the [[Institute for Advanced Study]] in 1972, becoming Professor Emeritus in January 2007.
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| ==Research==
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| His Ph.D. thesis was on the analytical theory of semi-groups, but he soon moved into representation theory, adapting the methods of [[Harish-Chandra]] to the theory of automorphic forms. His first accomplishment in this field was a formula for the dimension of certain spaces of automorphic forms, in which particular types of Harish-Chandra's discrete series appeared.
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| He next constructed an analytical theory of [[Eisenstein series]] for reductive groups of rank greater than one, thus extending work of Maass, Roelcke and [[Atle Selberg|Selberg]] from the early 1950s for rank one groups such as <math>SL(2)</math>. This amounted to describing in general terms the continuous spectra of arithmetic quotients, and showing that all automorphic forms arise in terms of cusp forms and the residues of Eisenstein series induced from cusp forms on smaller subgroups. As a first application, he proved the [[Weil conjecture on Tamagawa numbers]] for the large class of arbitrary simply connected Chevalley groups defined over the rational numbers. Previously this had been known only in a few isolated cases and for certain classical groups where it could be shown by induction.
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| As a second application of this work, he was able to show meromorphic continuation for a large class of [[L-function|<math>L</math>-functions]] arising in the theory of automorphic forms, not previously known to have them. These occurred in the constant terms of Eisenstein series, and meromorphicity as well as a weak functional equation were a consequence of functional equations for Eisenstein series. This work led in turn, in the winter of 1966/67, to the now well known conjectures making up what is often called the [[Langlands program]]. Very roughly speaking, they propose a huge generalization of previously known examples of reciprocity, including (a) classical [[class field theory]], in which characters of local and arithmetic abelian [[Galois group]]s are identified with characters of local multiplicative groups and the idele quotient group, respectively; (b) earlier results of Eichler and Shimura in which the Hasse-Weil zeta functions of arithmetic quotients of the upper half plane are identified with <math>L</math>-functions occurring in Hecke's theory of holomorphic automorphic forms. These conjectures were first posed in relatively complete form in a famous letter to Weil, written in January 1967. It was in this letter that he introduced what has since become known as the <math>L</math>-group and along with it, the notion of functoriality.
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| Functoriality, the <math>L</math>-group, the rigorous introduction of adele groups, and the consequent application of the representation theory of reductive groups over local fields changed drastically the way research in automorphic forms was carried out. Langlands's introduction of (or in cases where others had done previous work, emphasis on) these notions broke up large and to some extent intractable problems into smaller and more manageable pieces. For example, they made the infinite-dimensional representation theory of reductive groups into a major field of mathematical activity.
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| Functoriality is the conjecture that automorphic forms on different groups should be related in terms of their <math>L</math>-groups. As one example of this conjecture the letter to Weil raised the possibility of solving the well known conjecture of [[Emil Artin]] regarding the behaviour of Artin's <math>L</math>-functions, a hope partly realized in Langlands' later work on base change. In its application to Artin's conjecture, functoriality associated to every <math>N</math>-dimensional representation of a [[Galois group]] an automorphic representation of the adelic group of <math>GL(N)</math>. In the theory of Shimura varieties it associates automorphic representations of other groups to certain <math>l</math>-adic Galois representations as well.
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| The book by [[Hervé Jacquet]] and Langlands on <math>GL(2)</math> presented a theory of automorphic forms for the [[general linear group]] <math>GL(2)</math>, establishing among other things the [[Jacquet–Langlands correspondence]] showing that functoriality was capable of explaining very precisely how automorphic forms for <math>GL(2)</math> related to those for quaternion algebras. This book applied the adelic [[Selberg trace formula|trace formula]] for <math>GL(2)</math> and quaternion algebras to do this. Subsequently [[James Arthur (mathematician)|James Arthur]], a student of Langlands while he was at Yale, successfully developed the trace formula for groups of higher rank. This has become a major tool in attacking functoriality in general, and in particular has been applied to demonstrating that the [[Hasse-Weil zeta function]]s of certain [[Shimura variety|Shimura varieties]] are among the <math>L</math>-functions arising from automorphic forms.
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| The functoriality conjecture is far from proved, but a special case (the octahedral [[Emil Artin|Artin conjecture]], proved by Langlands and Tunnell) was the starting point of [[Andrew Wiles]]' attack on the [[Taniyama–Shimura conjecture]] and [[Fermat's last theorem]].
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| In the mid-1980s Langlands turned his attention to [[physics]], particularly the problems of percolation and conformal invariance.
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| In recent years he has turned his attention back to automorphic forms, working in particular on a theme he calls `beyond endoscopy'.
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| In 1995 Langlands started a collaboration with Bill Casselman at the University of British Columbia with the aim of posting nearly all of his writings—including publications, preprints, as well as selected correspondence—on the Internet. The correspondence includes a copy of the original letter to Weil that introduced the <math>L</math>-group.
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| ==Awards and honors==
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| Langlands has received the 1996 [[Wolf Prize]] (which he shared with [[Andrew Wiles]]),<ref>[http://www.ams.org/notices/199602/people.pdf AMS Notices]</ref> the 2005 AMS [[Steele Prize]], the 1980 [[Jeffery-Williams Prize]], the 1988 [[NAS Award in Mathematics]] from the [[United States National Academy of Sciences|National Academy of Sciences]],<ref name=NASMath>{{cite web|title=NAS Award in Mathematics|url=http://www.nasonline.org/site/PageServer?pagename=AWARDS_mathematics|publisher=National Academy of Sciences|accessdate=13 February 2011}}</ref> the 2006 [[Nemmers Prize in Mathematics]], and the 2007 [[Shaw Prize]] in Mathematical Sciences (with [[Richard Taylor (mathematician)|Richard Taylor]]) for his work on automorphic forms.
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| He was elected a [[Fellow of the Royal Society]] of London in 1981. In 2012, he became a fellow of the [[American Mathematical Society]].<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-01-27.</ref>
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| ==Personal life==
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| Langlands spent a year in [[Turkey]] in 1967/68, where his office at the [[Middle East Technical University]] was next to that of [[Cahit Arf]]'s. He speaks Turkish.<ref>[http://www.sunsite.ubc.ca/DigitalMathArchive/Langlands/miscellaneous.html The work of Robert Langlands - Miscellaneous items], Digital Mathematics Archive, UBC SunSITE, last accessed 2013-12-10.</ref>
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| ==Publications==
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| *{{Citation |title=Euler products |year=1967 |location=New Haven |publisher=Yale University Press |isbn=0-300-01395-7 }}
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| *{{Citation |title=On the Functional Equations Satisfied by Eisenstein Series |year=1976 |location=Berlin |publisher=Springer |isbn=3-540-07872-X }}
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| *{{Citation |title=Base Change for GL(2) |year=1980 |location=Princeton |publisher=Princeton University Press |isbn=0-691-08272-3 }}
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| ==See also==
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| *[[Langlands classification]]
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| *[[Langlands decomposition]]
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| *[[Langlands–Deligne local constant]]
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| *[[Langlands dual]]
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| *[[Langlands group]]
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| *[[Langlands program]]
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| ==References==
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| {{Reflist}}
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| ==External links==
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| *{{MacTutor Biography|id=Langlands}}
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| *{{MathGenealogy |id=31056 }}
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| *[http://publications.ias.edu/rpl/ The work of Robert Langlands (a nearly complete archive)]
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| *[http://www.math.ias.edu/people/faculty/rpl Faculty page at IAS]
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| {{Wolf Prize in Mathematics}}
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| {{Shaw Prize}}
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| {{Authority control |VIAF=108958415 |LCCN=n/80/02435 }}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME =Langlands, Robert
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = Canadian mathematician
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| | DATE OF BIRTH =October 6, 1936
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| | PLACE OF BIRTH =[[New Westminster]], [[British Columbia]], [[Canada]]
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| | DATE OF DEATH =
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| | PLACE OF DEATH =
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| }}
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| {{DEFAULTSORT:Langlands, Robert}}
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| [[Category:1936 births]]
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| [[Category:Living people]]
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| [[Category:Members of the United States National Academy of Sciences]]
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| [[Category:Canadian mathematicians]]
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| [[Category:20th-century mathematicians]]
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| [[Category:Institute for Advanced Study faculty]]
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| [[Category:Number theorists]]
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| [[Category:People from New Westminster]]
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| [[Category:Princeton University faculty]]
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| [[Category:University of British Columbia alumni]]
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| [[Category:Wolf Prize in Mathematics laureates]]
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| [[Category:Yale University alumni]]
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| [[Category:Fellows of the Royal Society]]
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| [[Category:Fellows of the American Mathematical Society]]
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| [[Category:National Academy of Sciences laureates]]
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| [[Category:Alexander von Humboldt Fellows]]
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The author's title is Christy. Distributing manufacturing is where her primary earnings arrives from. To play lacross is something I truly enjoy doing. Ohio is where his home is and his family enjoys it.
Also visit my web-site: cheap psychic readings (try this out www.caelumen.com)