Lectures on the Langlands Program and Conformal Field Theory
Identifieur interne : 000078 ( Istex/Corpus ); précédent : 000077; suivant : 000079Lectures on the Langlands Program and Conformal Field Theory
Auteurs : Edward FrenkelSource :
Abstract
Abstract : These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. It has long been suspected that the Langlands duality should somehow be related to various dualities observed in quantum field theory and string theory. Indeed, both the Langlands correspondence and the dualities in physics have emerged as some sort of non-abelian Fourier transforms. Moreover, the so-called Langlands dual group introduced by R. Langlands in [1] that is essential in the formulation of the Langlands correspondence also plays a prominent role in the study of S-dualities in physics and was in fact also introduced by the physicists P. Goddard, J. Nuyts and D. Olive in the framework of four-dimensional gauge theory [2].
Url:
DOI: 10.1007/978-3-540-30308-4_11
Links to Exploration step
ISTEX:043EEDC3726A102FC937D808A5B7E2CF24419D3ALe document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Lectures on the Langlands Program and Conformal Field Theory</title><author><name sortKey="Frenkel, Edward" sort="Frenkel, Edward" uniqKey="Frenkel E" first="Edward" last="Frenkel">Edward Frenkel</name><affiliation><mods:affiliation>Department of Mathematics, University of California, 94720, Berkeley, CA, USA</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:043EEDC3726A102FC937D808A5B7E2CF24419D3A</idno><date when="2007" year="2007">2007</date><idno type="doi">10.1007/978-3-540-30308-4_11</idno><idno type="url">https://api.istex.fr/document/043EEDC3726A102FC937D808A5B7E2CF24419D3A/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">000078</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000078</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Lectures on the Langlands Program and Conformal Field Theory</title><author><name sortKey="Frenkel, Edward" sort="Frenkel, Edward" uniqKey="Frenkel E" first="Edward" last="Frenkel">Edward Frenkel</name><affiliation><mods:affiliation>Department of Mathematics, University of California, 94720, Berkeley, CA, USA</mods:affiliation></affiliation></author></analytic><monogr></monogr></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract : These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. It has long been suspected that the Langlands duality should somehow be related to various dualities observed in quantum field theory and string theory. Indeed, both the Langlands correspondence and the dualities in physics have emerged as some sort of non-abelian Fourier transforms. Moreover, the so-called Langlands dual group introduced by R. Langlands in [1] that is essential in the formulation of the Langlands correspondence also plays a prominent role in the study of S-dualities in physics and was in fact also introduced by the physicists P. Goddard, J. Nuyts and D. Olive in the framework of four-dimensional gauge theory [2].</div></front></TEI><istex><corpusName>springer-ebooks</corpusName><editor><json:item><name>Pierre Cartier</name><affiliations><json:string>I.H.E.S., 35 route de Chartres, F-91440, Bures-sur-Yvette, France</json:string><json:string>E-mail: cartier@ihes.fr</json:string></affiliations></json:item><json:item><name>Pierre Moussa</name><affiliations><json:string>Service de Physique Théorique, CEA/Saclay, F-91191, Gif-sur-Yvette, France</json:string><json:string>E-mail: moussa@spht.saclay.cea.fr</json:string></affiliations></json:item><json:item><name>Bernard Julia</name><affiliations><json:string>LPTENS, 24 rue Lhomond, F-75005, Paris, France</json:string><json:string>E-mail: Bernard.Julia@lpt.ens.fr</json:string></affiliations></json:item><json:item><name>Pierre Vanhove</name><affiliations><json:string>Service de Physique Théorique, CEA/Saclay, 24 rue Lhomond, F-91191, Gif-sur-Yvette, France</json:string><json:string>E-mail: pierre.vanhove@cern.ch</json:string></affiliations></json:item></editor><author><json:item><name>Edward Frenkel</name><affiliations><json:string>Department of Mathematics, University of California, 94720, Berkeley, CA, USA</json:string></affiliations></json:item></author><arkIstex>ark:/67375/HCB-12X4CPXF-9</arkIstex><language><json:string>eng</json:string></language><originalGenre><json:string>chapter</json:string></originalGenre><abstract>Abstract : These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. It has long been suspected that the Langlands duality should somehow be related to various dualities observed in quantum field theory and string theory. Indeed, both the Langlands correspondence and the dualities in physics have emerged as some sort of non-abelian Fourier transforms. Moreover, the so-called Langlands dual group introduced by R. Langlands in [1] that is essential in the formulation of the Langlands correspondence also plays a prominent role in the study of S-dualities in physics and was in fact also introduced by the physicists P. Goddard, J. Nuyts and D. Olive in the framework of four-dimensional gauge theory [2].</abstract><qualityIndicators><score>8.488</score><pdfWordCount>67595</pdfWordCount><pdfCharCount>319361</pdfCharCount><pdfVersion>1.4</pdfVersion><pdfPageCount>147</pdfPageCount><pdfPageSize>439.455 x 666.283 pts</pdfPageSize><refBibsNative>false</refBibsNative><abstractWordCount>124</abstractWordCount><abstractCharCount>796</abstractCharCount><keywordCount>0</keywordCount></qualityIndicators><title>Lectures on the Langlands Program and Conformal Field Theory</title><chapterId><json:string>11</json:string><json:string>Chap11</json:string></chapterId><genre><json:string>chapter</json:string></genre><host><title>Frontiers in Number Theory, Physics, and Geometry II</title><language><json:string>unknown</json:string></language><copyrightDate>2007</copyrightDate><doi><json:string>10.1007/978-3-540-30308-4</json:string></doi><eisbn><json:string>978-3-540-30308-4</json:string></eisbn><bookId><json:string>978-3-540-30308-4</json:string></bookId><isbn><json:string>978-3-540-30307-7</json:string></isbn><pages><first>387</first><last>533</last></pages><genre><json:string>book</json:string></genre><editor><json:item><name>Pierre Cartier</name><affiliations><json:string>I.H.E.S., 35 route de Chartres, F-91440, Bures-sur-Yvette, France</json:string><json:string>E-mail: cartier@ihes.fr</json:string></affiliations></json:item><json:item><name>Pierre Moussa</name><affiliations><json:string>Service de Physique Théorique, CEA/Saclay, F-91191, Gif-sur-Yvette, France</json:string><json:string>E-mail: moussa@spht.saclay.cea.fr</json:string></affiliations></json:item><json:item><name>Bernard Julia</name><affiliations><json:string>LPTENS, 24 rue Lhomond, F-75005, Paris, France</json:string><json:string>E-mail: Bernard.Julia@lpt.ens.fr</json:string></affiliations></json:item><json:item><name>Pierre Vanhove</name><affiliations><json:string>Service de Physique Théorique, CEA/Saclay, 24 rue Lhomond, F-91191, Gif-sur-Yvette, France</json:string><json:string>E-mail: pierre.vanhove@cern.ch</json:string></affiliations></json:item></editor><subject><json:item><value>Mathematics and Statistics</value></json:item><json:item><value>Mathematics</value></json:item><json:item><value>Number Theory</value></json:item><json:item><value>Algebraic Geometry</value></json:item><json:item><value>Theoretical, Mathematical and Computational Physics</value></json:item></subject></host><ark><json:string>ark:/67375/HCB-12X4CPXF-9</json:string></ark><publicationDate>2007</publicationDate><copyrightDate>2007</copyrightDate><doi><json:string>10.1007/978-3-540-30308-4_11</json:string></doi><id>043EEDC3726A102FC937D808A5B7E2CF24419D3A</id><score>1</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/document/043EEDC3726A102FC937D808A5B7E2CF24419D3A/fulltext/pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/document/043EEDC3726A102FC937D808A5B7E2CF24419D3A/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/043EEDC3726A102FC937D808A5B7E2CF24419D3A/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">Lectures on the Langlands Program and Conformal Field Theory</title><respStmt><resp>Références bibliographiques récupérées via GROBID</resp><name resp="ISTEX-API">ISTEX-API (INIST-CNRS)</name></respStmt></titleStmt><publicationStmt><authority>ISTEX</authority><publisher scheme="https://publisher-list.data.istex.fr">Springer Berlin Heidelberg</publisher><pubPlace>Berlin, Heidelberg</pubPlace><availability><licence><p>Springer, 2007</p></licence><p scheme="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-3XSW68JL-F">springer</p></availability><date>2007</date></publicationStmt><notesStmt><note type="chapter" scheme="https://content-type.data.istex.fr/ark:/67375/XTP-CGT4WMJM-6">chapter</note><note type="book" scheme="https://publication-type.data.istex.fr/ark:/67375/JMC-5WTPMB5N-F">book</note></notesStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">Lectures on the Langlands Program and Conformal Field Theory</title><author xml:id="author-0000"><persName><forename type="first">Edward</forename><surname>Frenkel</surname></persName><affiliation>Department of Mathematics, University of California, 94720, Berkeley, CA, USA</affiliation></author><editor xml:id="author-0001"><persName><forename type="first">Pierre</forename><surname>Cartier</surname></persName><email>cartier@ihes.fr</email><affiliation>I.H.E.S., 35 route de Chartres, F-91440, Bures-sur-Yvette, France</affiliation></editor><editor xml:id="author-0002"><persName><forename type="first">Pierre</forename><surname>Moussa</surname></persName><email>moussa@spht.saclay.cea.fr</email><affiliation>Service de Physique Théorique, CEA/Saclay, F-91191, Gif-sur-Yvette, France</affiliation></editor><editor xml:id="author-0003"><persName><forename type="first">Bernard</forename><surname>Julia</surname></persName><email>Bernard.Julia@lpt.ens.fr</email><affiliation>LPTENS, 24 rue Lhomond, F-75005, Paris, France</affiliation></editor><editor xml:id="author-0004"><persName><forename type="first">Pierre</forename><surname>Vanhove</surname></persName><email>pierre.vanhove@cern.ch</email><affiliation>Service de Physique Théorique, CEA/Saclay, 24 rue Lhomond, F-91191, Gif-sur-Yvette, France</affiliation></editor><idno type="istex">043EEDC3726A102FC937D808A5B7E2CF24419D3A</idno><idno type="ark">ark:/67375/HCB-12X4CPXF-9</idno><idno type="DOI">10.1007/978-3-540-30308-4_11</idno><idno type="ChapterID">11</idno><idno type="ChapterID">Chap11</idno></analytic><monogr><title level="m">Frontiers in Number Theory, Physics, and Geometry II</title><title level="m" type="sub">On Conformal Field Theories, Discrete Groups and Renormalization</title><idno type="DOI">10.1007/978-3-540-30308-4</idno><idno type="pISBN">978-3-540-30307-7</idno><idno type="eISBN">978-3-540-30308-4</idno><idno type="book-title-id">112476</idno><idno type="book-id">978-3-540-30308-4</idno><idno type="book-chapter-count">16</idno><idno type="PartChapterCount">6</idno><editor xml:id="book-author-0000"><persName><forename type="first">Pierre</forename><surname>Cartier</surname></persName><email>cartier@ihes.fr</email><affiliation>I.H.E.S., 35 route de Chartres, F-91440, Bures-sur-Yvette, France</affiliation></editor><editor xml:id="book-author-0001"><persName><forename type="first">Pierre</forename><surname>Moussa</surname></persName><email>moussa@spht.saclay.cea.fr</email><affiliation>Service de Physique Théorique, CEA/Saclay, F-91191, Gif-sur-Yvette, France</affiliation></editor><editor xml:id="book-author-0002"><persName><forename type="first">Bernard</forename><surname>Julia</surname></persName><email>Bernard.Julia@lpt.ens.fr</email><affiliation>LPTENS, 24 rue Lhomond, F-75005, Paris, France</affiliation></editor><editor xml:id="book-author-0003"><persName><forename type="first">Pierre</forename><surname>Vanhove</surname></persName><email>pierre.vanhove@cern.ch</email><affiliation>Service de Physique Théorique, CEA/Saclay, 24 rue Lhomond, F-91191, Gif-sur-Yvette, France</affiliation></editor><imprint><publisher>Springer Berlin Heidelberg</publisher><pubPlace>Berlin, Heidelberg</pubPlace><date type="published" when="2007"></date><biblScope unit="page" from="387">387</biblScope><biblScope unit="page" to="533">533</biblScope></imprint></monogr></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2007</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract : These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. It has long been suspected that the Langlands duality should somehow be related to various dualities observed in quantum field theory and string theory. Indeed, both the Langlands correspondence and the dualities in physics have emerged as some sort of non-abelian Fourier transforms. Moreover, the so-called Langlands dual group introduced by R. Langlands in [1] that is essential in the formulation of the Langlands correspondence also plays a prominent role in the study of S-dualities in physics and was in fact also introduced by the physicists P. Goddard, J. Nuyts and D. Olive in the framework of four-dimensional gauge theory [2].</p></abstract><textClass><keywords scheme="Book-Subject-Collection"><list><label>SUCO11649</label><item><term>Mathematics and Statistics</term></item></list></keywords></textClass><textClass><keywords scheme="Book-Subject-Group"><list><label>SCM</label><label>SCM25001</label><label>SCM11019</label><label>SCP19005</label><item><term>Mathematics</term></item><item><term>Number Theory</term></item><item><term>Algebraic Geometry</term></item><item><term>Theoretical, Mathematical and Computational Physics</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2007">Published</change><change xml:id="refBibs-istex" who="#ISTEX-API" when="2017-11-28">References added</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/043EEDC3726A102FC937D808A5B7E2CF24419D3A/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="corpus springer-ebooks not found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="UTF-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//Springer-Verlag//DTD A++ V2.4//EN" URI="http://devel.springer.de/A++/V2.4/DTD/A++V2.4.dtd" name="istex:docType"></istex:docType><istex:document><Publisher><PublisherInfo><PublisherName>Springer Berlin Heidelberg</PublisherName><PublisherLocation>Berlin, Heidelberg</PublisherLocation></PublisherInfo><Book Language="En"><BookInfo BookProductType="Collection of essays" ContainsESM="No" Language="En" MediaType="eBook" NumberingStyle="ChapterContent" TocLevels="0"><BookID>978-3-540-30308-4</BookID><BookTitle>Frontiers in Number Theory, Physics, and Geometry II</BookTitle><BookSubTitle>On Conformal Field Theories, Discrete Groups and Renormalization</BookSubTitle><BookDOI>10.1007/978-3-540-30308-4</BookDOI><BookTitleID>112476</BookTitleID><BookPrintISBN>978-3-540-30307-7</BookPrintISBN><BookElectronicISBN>978-3-540-30308-4</BookElectronicISBN><BookChapterCount>16</BookChapterCount><BookCopyright><CopyrightHolderName>Springer</CopyrightHolderName><CopyrightYear>2007</CopyrightYear></BookCopyright><BookSubjectGroup><BookSubject Code="SCM" Type="Primary">Mathematics</BookSubject><BookSubject Code="SCM25001" Priority="1" Type="Secondary">Number Theory</BookSubject><BookSubject Code="SCM11019" Priority="2" Type="Secondary">Algebraic Geometry</BookSubject><BookSubject Code="SCP19005" Priority="3" Type="Secondary">Theoretical, Mathematical and Computational Physics</BookSubject><SubjectCollection Code="SUCO11649">Mathematics and Statistics</SubjectCollection></BookSubjectGroup></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff1"><EditorName DisplayOrder="Western"><GivenName>Pierre</GivenName><FamilyName>Cartier</FamilyName></EditorName><Contact><Email>cartier@ihes.fr</Email></Contact></Editor><Editor AffiliationIDS="Aff2"><EditorName DisplayOrder="Western"><GivenName>Pierre</GivenName><FamilyName>Moussa</FamilyName></EditorName><Contact><Email>moussa@spht.saclay.cea.fr</Email></Contact></Editor><Editor AffiliationIDS="Aff3"><EditorName DisplayOrder="Western"><GivenName>Bernard</GivenName><FamilyName>Julia</FamilyName></EditorName><Contact><Email>Bernard.Julia@lpt.ens.fr</Email></Contact></Editor><Editor AffiliationIDS="Aff4"><EditorName DisplayOrder="Western"><GivenName>Pierre</GivenName><FamilyName>Vanhove</FamilyName></EditorName><Contact><Email>pierre.vanhove@cern.ch</Email></Contact></Editor><Affiliation ID="Aff1"><OrgName>I.H.E.S.</OrgName><OrgAddress><Street>35 route de Chartres</Street><Postcode>F-91440</Postcode><City>Bures-sur-Yvette</City><Country>France</Country></OrgAddress></Affiliation><Affiliation ID="Aff2"><OrgDivision>Service de Physique Théorique</OrgDivision><OrgName>CEA/Saclay</OrgName><OrgAddress><Postcode>F-91191</Postcode><City>Gif-sur-Yvette</City><Country>France</Country></OrgAddress></Affiliation><Affiliation ID="Aff3"><OrgName>LPTENS</OrgName><OrgAddress><Street>24 rue Lhomond</Street><Postcode>F-75005</Postcode><City>Paris</City><Country>France</Country></OrgAddress></Affiliation><Affiliation ID="Aff4"><OrgDivision>Service de Physique Théorique</OrgDivision><OrgName>CEA/Saclay</OrgName><OrgAddress><Street>24 rue Lhomond</Street><Postcode>F-91191</Postcode><City>Gif-sur-Yvette</City><Country>France</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Part ID="Part2"><PartInfo TocLevels="0"><PartID>2</PartID><PartNumber>Part II</PartNumber><PartSequenceNumber>2</PartSequenceNumber><PartTitle>Discrete Groups and Automorphic Forms</PartTitle><PartChapterCount>6</PartChapterCount><PartContext><BookID>978-3-540-30308-4</BookID><BookTitle>Frontiers in Number Theory, Physics, and Geometry II</BookTitle></PartContext></PartInfo><Chapter ID="Chap11" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingStyle="Unnumbered" TocLevels="0"><ChapterID>11</ChapterID><ChapterDOI>10.1007/978-3-540-30308-4_11</ChapterDOI><ChapterSequenceNumber>11</ChapterSequenceNumber><ChapterTitle Language="En">Lectures on the Langlands Program and Conformal Field Theory</ChapterTitle><ChapterFirstPage>387</ChapterFirstPage><ChapterLastPage>533</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer</CopyrightHolderName><CopyrightYear>2007</CopyrightYear></ChapterCopyright><ChapterGrants Type="Regular"><MetadataGrant Grant="OpenAccess"></MetadataGrant><AbstractGrant Grant="OpenAccess"></AbstractGrant><BodyPDFGrant Grant="Restricted"></BodyPDFGrant><BodyHTMLGrant Grant="Restricted"></BodyHTMLGrant><BibliographyGrant Grant="Restricted"></BibliographyGrant><ESMGrant Grant="Restricted"></ESMGrant></ChapterGrants><ChapterContext><PartID>2</PartID><BookID>978-3-540-30308-4</BookID><BookTitle>Frontiers in Number Theory, Physics, and Geometry II</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff5"><AuthorName DisplayOrder="Western"><GivenName>Edward</GivenName><FamilyName>Frenkel</FamilyName></AuthorName></Author><Affiliation ID="Aff5"><OrgDivision>Department of Mathematics</OrgDivision><OrgName>University of California</OrgName><OrgAddress><Postcode>94720</Postcode><City>Berkeley</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading><Emphasis Type="Bold">Abstract</Emphasis></Heading><Para TextBreak="No">These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. It has long been suspected that the Langlands duality should somehow be related to various dualities observed in quantum field theory and string theory. Indeed, both the Langlands correspondence and the dualities in physics have emerged as some sort of non-abelian Fourier transforms. Moreover, the so-called Langlands dual group introduced by R. Langlands in [1] that is essential in the formulation of the Langlands correspondence also plays a prominent role in the study of S-dualities in physics and was in fact also introduced by the physicists P. Goddard, J. Nuyts and D. Olive in the framework of four-dimensional gauge theory [2].</Para></Abstract></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Lectures on the Langlands Program and Conformal Field Theory</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Lectures on the Langlands Program and Conformal Field Theory</title></titleInfo><name type="personal"><namePart type="given">Edward</namePart><namePart type="family">Frenkel</namePart><affiliation>Department of Mathematics, University of California, 94720, Berkeley, CA, USA</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Pierre</namePart><namePart type="family">Cartier</namePart><affiliation>I.H.E.S., 35 route de Chartres, F-91440, Bures-sur-Yvette, France</affiliation><affiliation>E-mail: cartier@ihes.fr</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Pierre</namePart><namePart type="family">Moussa</namePart><affiliation>Service de Physique Théorique, CEA/Saclay, F-91191, Gif-sur-Yvette, France</affiliation><affiliation>E-mail: moussa@spht.saclay.cea.fr</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Bernard</namePart><namePart type="family">Julia</namePart><affiliation>LPTENS, 24 rue Lhomond, F-75005, Paris, France</affiliation><affiliation>E-mail: Bernard.Julia@lpt.ens.fr</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Pierre</namePart><namePart type="family">Vanhove</namePart><affiliation>Service de Physique Théorique, CEA/Saclay, 24 rue Lhomond, F-91191, Gif-sur-Yvette, France</affiliation><affiliation>E-mail: pierre.vanhove@cern.ch</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="chapter" displayLabel="chapter" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-CGT4WMJM-6"></genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2007</dateIssued><dateIssued encoding="w3cdtf">2007</dateIssued><copyrightDate encoding="w3cdtf">2007</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract : These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. It has long been suspected that the Langlands duality should somehow be related to various dualities observed in quantum field theory and string theory. Indeed, both the Langlands correspondence and the dualities in physics have emerged as some sort of non-abelian Fourier transforms. Moreover, the so-called Langlands dual group introduced by R. Langlands in [1] that is essential in the formulation of the Langlands correspondence also plays a prominent role in the study of S-dualities in physics and was in fact also introduced by the physicists P. Goddard, J. Nuyts and D. Olive in the framework of four-dimensional gauge theory [2].</abstract><relatedItem type="host"><titleInfo><title>Frontiers in Number Theory, Physics, and Geometry II</title><subTitle>On Conformal Field Theories, Discrete Groups and Renormalization</subTitle></titleInfo><name type="personal"><namePart type="given">Pierre</namePart><namePart type="family">Cartier</namePart><affiliation>I.H.E.S., 35 route de Chartres, F-91440, Bures-sur-Yvette, France</affiliation><affiliation>E-mail: cartier@ihes.fr</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Pierre</namePart><namePart type="family">Moussa</namePart><affiliation>Service de Physique Théorique, CEA/Saclay, F-91191, Gif-sur-Yvette, France</affiliation><affiliation>E-mail: moussa@spht.saclay.cea.fr</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Bernard</namePart><namePart type="family">Julia</namePart><affiliation>LPTENS, 24 rue Lhomond, F-75005, Paris, France</affiliation><affiliation>E-mail: Bernard.Julia@lpt.ens.fr</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Pierre</namePart><namePart type="family">Vanhove</namePart><affiliation>Service de Physique Théorique, CEA/Saclay, 24 rue Lhomond, F-91191, Gif-sur-Yvette, France</affiliation><affiliation>E-mail: pierre.vanhove@cern.ch</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book" displayLabel="Collection of essays" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-5WTPMB5N-F">book</genre><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">2007</copyrightDate><issuance>monographic</issuance></originInfo><subject><genre>Book-Subject-Collection</genre><topic authority="SpringerSubjectCodes" authorityURI="SUCO11649">Mathematics and Statistics</topic></subject><subject><genre>Book-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="SCM">Mathematics</topic><topic authority="SpringerSubjectCodes" authorityURI="SCM25001">Number Theory</topic><topic authority="SpringerSubjectCodes" authorityURI="SCM11019">Algebraic Geometry</topic><topic authority="SpringerSubjectCodes" authorityURI="SCP19005">Theoretical, Mathematical and Computational Physics</topic></subject><identifier type="DOI">10.1007/978-3-540-30308-4</identifier><identifier type="ISBN">978-3-540-30307-7</identifier><identifier type="eISBN">978-3-540-30308-4</identifier><identifier type="BookTitleID">112476</identifier><identifier type="BookID">978-3-540-30308-4</identifier><identifier type="BookChapterCount">16</identifier><identifier type="PartChapterCount">6</identifier><part><date>2007</date><detail type="part"><title>Part II: Discrete Groups and Automorphic Forms</title></detail><detail type="part"><number>Part II</number></detail><extent unit="pages"><start>387</start><end>533</end></extent></part><recordInfo><recordOrigin>Springer, 2007</recordOrigin></recordInfo></relatedItem><identifier type="istex">043EEDC3726A102FC937D808A5B7E2CF24419D3A</identifier><identifier type="ark">ark:/67375/HCB-12X4CPXF-9</identifier><identifier type="DOI">10.1007/978-3-540-30308-4_11</identifier><identifier type="ChapterID">11</identifier><identifier type="ChapterID">Chap11</identifier><accessCondition type="use and reproduction" contentType="copyright">Springer, 2007</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-3XSW68JL-F">springer</recordContentSource><recordOrigin>Springer, 2007</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/document/043EEDC3726A102FC937D808A5B7E2CF24419D3A/metadata/json</uri></json:item></metadata><annexes><json:item><extension>txt</extension><original>true</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/document/043EEDC3726A102FC937D808A5B7E2CF24419D3A/annexes/txt</uri></json:item></annexes><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Mathematiques/explor/BourbakiV1/Data/Istex/Corpus
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000078 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Istex/Corpus/biblio.hfd -nk 000078 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Mathematiques
|area= BourbakiV1
|flux= Istex
|étape= Corpus
|type= RBID
|clé= ISTEX:043EEDC3726A102FC937D808A5B7E2CF24419D3A
|texte= Lectures on the Langlands Program and Conformal Field Theory
}}
| This area was generated with Dilib version V0.6.33. |  |