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	Current Fellows: Marie-France Vigneras
		Initially proposed by Robert Langlands in 1967, the Langlands program unifies number theory and automorphic representations of groups.
		The Langlands program has invaded a large part of mathematics and is popping up in physics.
		The geometric Langlands program is related to electric-magnetic duality in physics.
	www.radcliffe.edu /fellowships/current/bio.php?id=235&year=2006-2007 (191 words)

	NationMaster - Encyclopedia: Langlands program (Site not responding. Last check: )
		In mathematics, the Langlands program is a web of far-reaching and influential conjectures that connect number theory and the representation theory of certain groups.
		Robert Langlands (born 1936 in Canada) is one of the most significant mathematicians of the 20th century, with profound insights in number theory and representation theory.
		Langlands attached L-functions to these automorphic representations, and conjectured that every Artin L-function arising from a finite-dimensional representation of the Galois group of a number field is equal to one arising from an automorphic cuspidal representation.
	www.nationmaster.com /encyclopedia/Langlands-program (2549 words)

	Langlands program
		In mathematics, the Langlands program is a web of far-reaching and influential conjectures that connect number theory and the representation theory of certain groups.
		Langlands then generalized these to automorphic cuspidal representations, which are certain infinite dimensional irreducible representations of the general linear group over the adele ring of Q.
		Langlands attached L-functions to these automorphic cuspidal representations, and conjectured that every L-function arising from finite-dimensional representations of the Galois group is equal to one arising from an automorphic cuspidal representation.
	www.ebroadcast.com.au /lookup/encyclopedia/la/Langlands_program.html (660 words)

	Robert Langlands Biography
		Robert Langlands (born 1936 in Canada) is one of the most significant mathematicians of the 20th century, with profound insights in number theory and representation theory.
		Langlands is the author of the Langlands program, a deep web of conjectures connecting number theory and representation theory.
		Langlands understood that the theory of automorphic forms gives a generalization of class field theory, a central topic in algebraic number theory.
	www.biographybase.com /biography/Langlands_Robert.html (0 words)

	Langlands program - Definition, explanation
		Artin's law applies to an algebraic number field whose Galois group over Q is abelian, assigns L-functions to the one-dimensional representations of this Galois group; and states that these L-functions are identical to certain Dirichlet L-series (that is, the analogues of the Riemann Zeta function constructed from Dirichlet characters).
		Langlands attached L-functions to these automorphic representations, and conjectured that every L-function arising from finite-dimensional representations of the Galois group is equal to one arising from an automorphic cuspidal representation.
		In a very broad context, the program built on existing ideas: the philosophy of cusp forms formulated a few years earlier by Gel'fand, the work and approach of Harish-Chandra on semisimple Lie groups, and in technical terms the trace formula of Selberg and others.
	www.calsky.com /lexikon/en/txt/l/la/langlands_program.php (836 words)

	Robert Langlands Summary
		Langlands attended the University of British Columbia as an undergraduate and received his PhD from Yale University in 1960.
		Langlands understood that the theory of automorphic representation offers a generalization of class field theory, a central topic in algebraic number theory.
		Langlands received the Wolf Prize in 1996 and the Nemmers Prize in Mathematics in 2006 for his work on the Langlands program.
	www.bookrags.com /Robert_Langlands (0 words)

	More Information
		The Langlands Program, launched by Robert Langlands in the late 60's, ties together seemingly unrelated objects in number theory, algebraic geometry, and the theory of automorphic functions.
		The Langlands conjecture predicts that there is a correspondence between n-dimensional representations of the Galois group of a number field and automorphic representations of the group GL(n) over the ring of adeles of this field.
		Moreover, the Langlands dual group that is essential in the formulation of the Langlands correspondence also plays a prominent role in the S-dualities that are ubiquitous in physics (and was in fact rediscovered by physicists P. Goddard, J. Nuyts and D. Olive).
	www2.math.northwestern.edu /langlands/index_moreinfo.htm (0 words)

	NSERC - 1999 Laureate - Canada Gold Medal for Science and Engineering
		Developed some 30 years ago by Canadian-born mathematician Robert Langlands, the model's ultimate goal is to link two great streams of classical mathematics: analysis, which deals with how phenomena such as planetary motion vary with respect to time; and algebra, which deals with the unchanging world of integers and prime numbers.
		When it is finally achieved, the knowledge that comes from the Langlands program will represent a fundamental ordering principle in mathematics and beyond.
		Arthur and others have been able to complete part of the Langlands program by using the geometric side of the trace formula to illuminate the spectral side.
	www.nserc.ca /news/1999/arthur_e.htm (639 words)

	Previous Recipients, Nemmers Prizes, Office of the Provost, Northwestern University
		Langlands is best known for the fundamental research program that bears his name.
		Langlands’ numerous distinguished awards include the La Grande Medaille d’or de l’Academie (2000), the Wolf Prize in Mathematics (1995-96), the National Academy of Sciences Medal (1993) and the Cole Prize (1982).
		Langlands is the author or co-author of numerous articles and the editor, with D. Ramakrishnan, of “The Zeta Functions of Picard Modular Surfaces,” Les Publications CRM, Montreal (1992).
	www.northwestern.edu /provost/awards/nemmers/nemprmath.html (0 words)

	Study group on the Langlands program
		The aim is to prepare the ground for a reading of the papers from last year by Witten and collaborators on the connection between S-duality of topologically twisted, Euclidean quantum field theory and the geometric Langlands program.
		Kapustin and E. Witten, "Electric-Magnetic Duality and the Geometric Langlands Program".
		Gukov and E. Witten, "Gauge Theory, Ramification, and the Geometric Langlands Program".
	fy.chalmers.se /~mans/langlands.html (0 words)

	[No title]
		Date: 26 Mar 94 16:05:43 EST The Langlands program is a system of conjectures connecting number theory and the representation theory of Lie groups.
		Standard references for the Langlands program are: Stephen Gelbart, "An Elementary Introduction to the Langlands Program", Bulletin of the AMS v.10 no. 2 April 1984.
		This is the proceedings of a conference on the Langlands conjectures, including expository articles on the Langlands program and some of the background.
	www.math.niu.edu /~rusin/known-math/94/langlands (0 words)

	Background on 2002 Fields and Nevanlinna Awardees
		The Langlands Program, formulated by Robert P. Langlands for the first time in a famous letter to Andre Weil in 1967, is a set of far-reaching conjectures that make precise predictions about how certain disparate areas of mathematics might be connected.
		The roots of the Langlands program are found in one of the deepest results in number theory, the Law of Quadratic Reciprocity, which goes back to the time of Fermat in the 17th century and was first proved by Carl Friedrich Gauss in 1801.
		One of the original motivations behind the Langlands Program was to provide a complete understanding of reciprocity laws that apply in even more general situations.
	www.ams.org /ams/fields2002-background.html (0 words)

	Math luminary to show old masters' modern magic-Mumbai-Cities-NEWS-The Times of India (Site not responding. Last check: )
		Thanks to Langlands' own unifying insights, two vibrant mathematical areasâ” representation theory of Lie groups and number theoryâ” are now seen as intimately entwined, resulting in a burst of creative research.
		In 2002, the proof of another piece of the Langlands Program by the French mathematician Laurent Lafforgue won the Fields Medal, which is often called the Nobel Prize of Mathematics.
		Langlands is visiting the Tata Institute of Fundamental Research and is to deliver a public lecture on Wednesday at the Homi Bhabha auditorium on âDescartes and Fermat: Reading the Ancients as Moderns'.
	timesofindia.indiatimes.com /articleshow/1015552.cms (627 words)

	Open Questions: The Langlands Program (Site not responding. Last check: )
		This is an archive of many of Langlands' papers and writings, which indicates the general topics of concern in his "program".
		Part of the Langlands program is to make general statements about such series.
		The relationship of these conjectures to the Langlands program is discussed.
	www.openquestions.com /oq-ma016.htm (372 words)

	TGD diary: Langlands Program and TGD
		Number theoretic Langlands program can be seen as an attempt to unify number theory on one hand and theory of representations of reductive Lie groups on the other hand.
		Geometric Langlands program tries to achieve a similar conceptual unification in the case of function fields.
		Finite-dimensional representations of Gal(\overline{Q}/Q) are crucial for Langlands program.
	matpitka.blogspot.com /2007/02/langlands-program-and-tgd.html (0 words)

	Robert Langlands' work - main page
		Robert P. Langlands was born in New Westminster, British Columbia, in 1936.
		He has won several awards recognizing his outstanding contributions to the theory of automorphic forms, among them an honorary degree from the University of British Columbia in 1985.
		Looking forward to eventual publication of his collected works, Professor Langlands is cooperating with us in providing on our site a large selection from his professional correspondence and previously unpublished work, as well as an almost complete collection of all of his published work.
	sunsite.ubc.ca /DigitalMathArchive/Langlands/intro.html (552 words)

	Not Even Wrong » Blog Archive » Langlands on Langlands
		While this inspired the “Geometric Langlands Program” that I’ve written about here recently, it’s a quite different subject, one that is very much central to research in number theory.
		Langlands ironically characterizes his own review as “the pedantry of… one priggish mathematician” and I have to say that is pretty accurate.
		Langlands some good to take a little time off from the Institute for Advanced Study and teach a precalculus course at a large state university.
	www.math.columbia.edu /~woit/wordpress/?p=494 (0 words)

	News: Math Department, WCAS, Northwestern University
		This program postulates a deep relationship between two different areas of mathematics, number theory and automorphic forms via a study of their symmetries.
		Since its initiation about 40 years ago the Langlands program has served as a unifying principle in mathematics and has guided research in number theory, automorphic forms, and representation theory.
		The Geometric Langlands Program is supported by grants from DARPA and the National Science Foundation that are administered through Northwestern.
	www.math.northwestern.edu /news (0 words)

	Robert Langlands' work - main page
		Robert P. Langlands was born in New Westminster, British Columbia, in 1936.
		He has won several awards recognizing his outstanding contributions to the theory of automorphic forms, among them an honorary degree from the University of British Columbia in 1985.
		Looking forward to eventual publication of his collected works, Professor Langlands is cooperating with us in providing on our site a large selection from his professional correspondence and previously unpublished work, as well as an almost complete collection of all of his published work.
	www.sunsite.ubc.ca /DigitalMathArchive/Langlands/intro.html (0 words)

	Fields Medals 2002
		He made his contribution to proving the Langlands correspondence between 1990 and 2000 when he was a CNRS chargé de recherche.
		The so-called Langlands correspondence owes its name to Canadian mathematician Robert P. Langlands who, in 1967, in a famous letter to French mathematician André Weil, put forward a set of ideas and conjectures at the crossroads of number theory and analysis and the theory of group representations.
		This correspondence was to become a research program in and of itself and became the basis for a number of works in fundamental mathematics.
	www.cnrs.fr /cw/en/pres/compress/FieldsLafforgue.htm (0 words)

	MIT hep-th/0604151 Seminar
		The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N=4 super Yang-Mills theory in four dimensions.
		Seemingly esoteric notions of the geometric Langlands program, such as Hecke eigensheaves and D-modules, arise naturally from the physics.
		The purpose of the first half of the talk is to introduce the affine Grassmannian of a reductive group G and explain its connection to the Langlands dual group G as well to moduli spaces of G-bundles on an algebraic curve.
	www-math.mit.edu /hepth0604151/hepth0604151-fall06.html (0 words)

	An Introduction to the Langlands Program
		For the past several decades the theory of automorphic forms has become a major focal point of development in number theory and algebraic geometry, with applications in many diverse areas, including combinatorics and mathematical physics.
		The twelve chapters of this monograph present a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics.
		A variety of areas in number theory from the classical zeta function up to the Langlands program are covered.
	www.xmlwriter.net /books/viewbook/An_Introduction_to_the_Langlands_Program-0817632115.html (465 words)

	info: Langlands_program (Site not responding. Last check: )
		Geometric Langlands ProgramThis program is dedicated to the investigation of the geometric Langlands, its relationship to other areas of mathematics, and its relationship to physics; more
		GRASP: Introduction to Geometric LanglandsA three-part introduction to the geometric Langlands program I gave in 2002 is available on streaming video courtesy of MSRI: Geometric Class Field Theory, Quantization of Hitchin's Hamiltonians, and...
		Edward Frenkel's homepageI am involved in running a Research Project dedicated to the investigation of the geometric Langlands Program, its relationship to other areas of mathematics, and its relationship to physics.
	www.napoli-pizza.net /Langlands_program.html (260 words)

	Fields Institute - Conference on automorphic forms and the trace formula
		The trace formula is a powerful tool and one of the main techniques in attacking Langlands' Functoriality Conjecture and related problems in the Langlands program.
		James Arthur has almost single handedly developed this very complicated machinery since the begining of his career in the early 1970's and his contribution to the modern theory of automorphic forms may be considered as one of the most important.
		The aim of this conference is to report on recent progress made on the Langlands Program with some emphasis on the trace formula approach, celebrating Arthur's contributions.
	www.fields.utoronto.ca /programs/scientific/04-05/arthurconf (0 words)

	Math = beauty + truth / (really hard) - Salon
		Robert Langlands conjectured that two very different animals are intimately connected.
		Langlands' conjecture, described as a "Rosetta stone" of mathematics, was formalized into the Langlands Program, a quest that has happily occupied scores of mathematicians for more than 30 years.
		At the same time it gave mathematicians confidence that the Langlands Program would succeed in other areas where work proceeds on the conjecture.
	dir.salon.com /story/tech/feature/2002/09/05/math_prizes/index1.html (728 words)

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