The Work of Robert Langlands

Robert P. Langlands was born in New Westminster, British Columbia, in 1936. He graduated from the University of British Columbia with an undergraduate degree in 1957 and an M.Sc. in 1958, and from Yale University with a Ph.D. in 1960. He has held faculty positions at Princeton University and Yale University, and is currently a Professor at the Institute for Advanced Study in Princeton New Jersey. He has won several awards recognizing his outstanding contributions to the theory of automorphic forms.

With the intention that the works be published eventually, perhaps posthumously if there is still an audience, Robert Langlands's papers and some of his correspondence and lectures are being collected on this site in a uniform format. This site has absorbed an earlier site created by Bill Casselman and most of the comments not directly attributed to Langlands himself are from Casselman's pen. The collection of papers is essentially complete; letters will be added as they turn up. The young Langlands made no systematic effort to retain copies of his correspondence.

This material is being put into TeX at the Institute for Advanced Study in Princeton New Jersey and will appear here as it becomes ready. We would like to thank Alice Garber, Dorothea Phares, Marietta Chiorello, Elly Gustafsson, Michelle Huguenin, and Carol Warfield of the present and former staff at the Institute, as well as Mark Goresky, for helping with this project. Above all we thank Bill Casselman for the initial suggestion, for a good deal of the original work, and for continuing advice.

Inevitably, the topics into which we have organized material overlap somewhat.

Semi-groups and representation theory
Mathematics Department, Yale University 1960
[pdf] [ps]

Some holomorphic semi-groups
Proceedings of the National Academy of Sciences 461960
[pdf] [ps]

On Lie semi-groups
Canadian Journal of Mathematics 121960
[pdf] [ps]

Dimension of spaces of automorphic forms
American Journal of Mathematics 851963
[pdf] [ps]

Dimension of spaces of automorphic forms
Proceedings of the AMS Symposium at Boulder, Colorado 1965
[pdf] [ps]

The classification of representations of real reductive groups
Math. Surveys and Monographs 311988
[pdf] [ps]

Notes on Knapp-Zuckerman theory
1977
[pdf] [ps]

On unitary representations of the Virasoro algebra
Infinite-dimensional Lie algebras and their applications, World Scientific 1988
[pdf] [ps]

The factorization of a polynomial defined by partitions
Commun. Math. Phys. 1241989
[pdf] [ps]

The volume of the fundamental domain for some arithmetical subgroups of Chevalley groups
Proceedings of the AMS Symposium at Boulder, Colorado 1965
[pdf] [ps]

Eisenstein series
Proceedings of the AMS Symposium at Boulder, Colorado 1965
[pdf] [ps]

Euler Products
Yale Mathematical Monographs 1967
[pdf] [ps]

On the Functional Equations Satisfied by Eisenstein Series
Springer Lecture Notes 5441965
[pdf] [ps]

On the notion of an automorphic representation
Proceedings of Symposia in Pure Mathematics XXXIII, AMS 1979
[pdf] [ps]

Rank-one residues of Eisenstein series
Israel Mathematical Conference Proceedings 3 1990
[pdf] [ps]

Letter to Godement
1967
[pdf]

Problems in the Theory of Automorphic Forms
Lectures in modern analysis and applications III, Lecture Notes in Mathematics 1701970
[pdf] [ps]

The representation theory of abelian algebraic groups
Pacific Journal of Mathematics 611998
[pdf] [ps]

A little bit of number theory

[pdf] [ps]

Representation theory - its rise and its role in number theory
Proceedings of the Gibbs symposium 1989
[pdf] [ps]

Where stands functoriality today?
Edinburgh conference on automorphic forms, AMS 1997
[pdf] [ps]

Letter to André Weil
1967
[pdf] [pdf] [ps] [ps]

Letter to Serre
1967
[pdf] [ps]

Letter to Deligne
1974
[pdf]

Letter to Roger Howe
1974
[pdf] [ps]

Letter to Roger Howe
1975
[pdf] [ps]

Correspondence leading to the book written with Jacquet
1967

A letter to Weil
1967
[pdf] [ps]

A long letter to Jacquet
1967
[pdf] [ps]

A collection of short letters to Jacquet
1967
[pdf] [ps]

A letter to Deligne
1967

A letter to Harish-Chandra
1967
[pdf] [ps]

A second letter to Harish-Chandra
1967
[pdf] [ps]

GL(2)
Springer 1970
[pdf] [ps]

Langlands' Notes on Artin L-functions
1970
[pdf] [ps]

On Artin's L-functions
Rice University Studies 561970
[pdf] [ps]

Automorphic forms on GL(2)
Actes du Congrès International des Mathématiciens 1971
[pdf] [ps]

Base change for GL(2)
Annals of Mathematics 961980
[pdf] [ps]

L-functions and Automorphic Representations
Proceedings of the International Congress of Mathematicians, Helsinki 1978
[pdf] [ps]

L-indistinguishability for SL(2)
Canadian Journal of Mathematics 311979
[pdf] [ps]

Stable conjugacy-definitions and lemmas
Canadian Journal of Mathematics 311979
[pdf] [ps]

Les débuts d'une formule des traces stable
Publications mathématiques de l'Université Paris VII 1979
[pdf] [ps]

Orbital integrals on forms of SL(3) I
American Journal of Mathematics 1051983
[pdf] [ps]

On principal values on p-adic manifolds
Lie group representations II, Lecture Notes in Mathematics 411984
[pdf] [ps]

Orbital integrals on forms of SL(3) II
Canadian Journal of Mathematics 411989
[pdf] [ps]

On the definition of transfer factors
Mathematischen Annalen 2781987
[pdf] [ps]

Descent for transfer factors
The Grothendieck Festschrift 21990
[pdf] [ps]

Remarks on Igusa theory and real orbital integrals
The zeta functions of Picard modular surfaces, Centre de Recherches Mathématiques, Montréal 1992
[pdf] [ps]

Eisenstein series, the trace formula, and the modern theory of automorphic forms
Number theory, trace formulas, and discrete groups 1987
[pdf] [ps]

Beyond endoscopy
Shalika volume, Johns Hopkins University Press 2004
[pdf] [ps]

Un nouveau point de repère dans la theorie des forme automorphes

[pdf] [ps]

Letter to Singer
1974
[pdf]

Modular forms and l-adic representations
Modular functions of one variable II, Lecture Notes in Mathematics 3491973
[pdf] [ps]

Some contemporary problems with origins in the Jugendtraum
Mathematical developments arising from Hilbert's problems, Proceedings of Symposia in Pure Mathematics 281974
[pdf] [ps]

Shimura varieties and the Selberg trace formula
Canadian Journal of Mathematics 291977
[pdf] [ps]

Comments on Shimura varieties and the Selberg trace formula
Canadian Mathematical Society Selecta 21995
[pdf] [ps]

On the zeta-functions of some simple Shimura varieties
Canadian Journal of Mathematics 311979
[pdf] [ps]

Automorphic representations, motives, and Shimura varieties. Ein Märchen
Proceedings of the 1977 A.M.S. conference on L functions and automorphic representations 1977
[pdf] [ps]

Sur la mauvaise réduction d'une variété de Shimura
Journées de Géométrie Algébrique de Rennes, Astérisques 651979
[pdf] [ps]

Algebraische Zyklen auf Hilbert-Blumenthal Flächen
Journal für die reine und angewandte Mathematik 3661986
[pdf] [ps]

Shimuravarietäten und Gerben
Journal für die reine und angewandte Mathematik 3781987
[pdf] [ps]

Representation theory and arithmetic
The mathematical heritage of Hermann Weyl, Proceedings of Symposia in Pure Mathematics, AMS 481987
[pdf] [ps]

Letter to Lang
December 5, 1970
[pdf]

Letter to Lang
December 17, 1970
[pdf]

Appendix to previous letter

[pdf]

Letter to Gee
2007
[pdf]

On the universality of crossing probabilities in two-dimensional percolation
Journal of Statistical Physics 671992
[pdf] [ps]

Finite Models for Percolation
Contemporary Mathematics 1771991
[pdf] [ps]

Conformal invariance for two-dimensional percolation
Bulletin of the AMS 301994
[pdf] [ps]

Dualität bei endlichen Modellen der Perkolation
Mathematische Nachrichten 1691993
[pdf] [ps]

The Dirac monopole and induced representations
Pacific Journal of Mathematics 1261987
[pdf] [ps]

An essay on the dynamics and statistics of critical field theories
Canadian Mathematical Society Selecta 31995
[pdf] [ps]

Algebro-geometric aspects of the Bethe equations
Strings and Symmetries, Proceedings of Gürsey Memorial Conference, Istanbul 1995
[pdf] [ps]

Aspects combinatoires des équations de Bethe
Advances in Mathematical Sciences: CRM's 25 years 1997
[pdf] [ps]

Universality and conformal invariance for the Ising model in domains with boundary
Journal of Statistical Physics 982000
[pdf] [ps]

The renormalization fixed point as a mathematical object

[pdf] [ps]

Review of SL₂(R) by Serge Lang
Bulletin of the American Mathematical Society 821976
[pdf] [ps]

Review of The theory of Eisenstein system by M. Scott Osborne and Garth Warner
Bulletin of the American Mathematical Society 91983
[pdf] [ps]

Review of Harish-Chandra's Collected Works
Bulletin of the London Mathematical Society 171985
[pdf] [ps]

Harish-Chandra 1923-1983
Biographical Memoirs of Fellows of the Royal Society 311985
[pdf] [ps]

Harish-Chandra
Memorial lecture, IAS 1984
[pdf] [ps]

Commencement address at the University of Toronto, June 1993
1993
[pdf] [ps]

Review of Elliptic Curves by Anthony Knapp
Bulletin of the American Mathematical Society 301994
[pdf] [ps]

André Weil (1906-98) - one of the century's most influential pure mathematicians
Nature 3961998
[pdf] [ps]

Interview with Stéphane Durand from Québec Science, May, 2000
Québec Science 2000
[pdf] [ps]

Response upon receiving the Grande Médaille d'Or of the Académie des sciences
2000
[pdf] [ps]

The trace formula and its applications (an introduction to the work of James Arthur)
Canadian Mathematics Bulletin 202001
[pdf] [ps]

Euclid's windows and our mirrors - review of Euclid's Window by Leonard Mlodinow
Notices of the American Mathematical Society 2002
[pdf] [ps]

Benim tanıdığım Cahit Arf (recollections of a year in Turkey with Cahit Arf)
Matematik Dünyası 2003
[pdf] [ps]

Robert Langlands in 1967
1967

Laudatio
on the occasion of an award to Günter Harder
[pdf] [ps]

Descartes ile Fermat
Matematik Dünyası 22005
[pdf]

A review of Haruzo Hida's p-adic automorphic forms on Shimura varieties,...
Bulletin of the American Mathematical Society 2006
[pdf] [ps]

A succinct biography

[pdf] [ps]

Mathematical retrospections

[pdf] [ps]

Reflexions on receiving the Shaw prize

[pdf] [ps]

Pour la science

[pdf] [ps]

Interview with Farzin Barekat for the University of British Columbia

[pdf]

Istanbul konferans dizisi

[pdf] [ps]

The practice of mathematics


The Work of Robert Langlands
¬ Main page ¬ Papers by group 1.PhD thesis 2.Trace formula 3.Representation theory... 4.Eisenstein series... 5.Functoriality 6.First tests... 7.Base change 8.Endoscopy 9.Shimura varieties 10.Percolation 11.Mathematical physics 12.Miscellaneous 13.Informal material 14.Visual material 15.Bibliography [pdf]	Introduction Robert P. Langlands was born in New Westminster, British Columbia, in 1936. He graduated from the University of British Columbia with an undergraduate degree in 1957 and an M.Sc. in 1958, and from Yale University with a Ph.D. in 1960. He has held faculty positions at Princeton University and Yale University, and is currently a Professor at the Institute for Advanced Study in Princeton New Jersey. He has won several awards recognizing his outstanding contributions to the theory of automorphic forms. With the intention that the works be published eventually, perhaps posthumously if there is still an audience, Robert Langlands's papers and some of his correspondence and lectures are being collected on this site in a uniform format. This site has absorbed an earlier site created by Bill Casselman and most of the comments not directly attributed to Langlands himself are from Casselman's pen. The collection of papers is essentially complete; letters will be added as they turn up. The young Langlands made no systematic effort to retain copies of his correspondence. This material is being put into TeX at the Institute for Advanced Study in Princeton New Jersey and will appear here as it becomes ready. We would like to thank Alice Garber, Dorothea Phares, Marietta Chiorello, Elly Gustafsson, Michelle Huguenin, and Carol Warfield of the present and former staff at the Institute, as well as Mark Goresky, for helping with this project. Above all we thank Bill Casselman for the initial suggestion, for a good deal of the original work, and for continuing advice. The material Inevitably, the topics into which we have organized material overlap somewhat. 1. Ph.D. thesis Semi-groups and representation theory Mathematics Department, Yale University 1960 [pdf] [ps] Some holomorphic semi-groups Proceedings of the National Academy of Sciences 461960 [pdf] [ps] On Lie semi-groups Canadian Journal of Mathematics 121960 [pdf] [ps] 2. Early work on the trace formula Dimension of spaces of automorphic forms American Journal of Mathematics 851963 [pdf] [ps] 3. Representation theory of real groups Dimension of spaces of automorphic forms Proceedings of the AMS Symposium at Boulder, Colorado 1965 [pdf] [ps] The classification of representations of real reductive groups Math. Surveys and Monographs 311988 [pdf] [ps] Notes on Knapp-Zuckerman theory 1977 [pdf] [ps] On unitary representations of the Virasoro algebra Infinite-dimensional Lie algebras and their applications, World Scientific 1988 [pdf] [ps] The factorization of a polynomial defined by partitions Commun. Math. Phys. 1241989 [pdf] [ps] 4. Eisenstein series and automorphic forms The volume of the fundamental domain for some arithmetical subgroups of Chevalley groups Proceedings of the AMS Symposium at Boulder, Colorado 1965 [pdf] [ps] Eisenstein series Proceedings of the AMS Symposium at Boulder, Colorado 1965 [pdf] [ps] Euler Products Yale Mathematical Monographs 1967 [pdf] [ps] On the Functional Equations Satisfied by Eisenstein Series Springer Lecture Notes 5441965 [pdf] [ps] On the notion of an automorphic representation Proceedings of Symposia in Pure Mathematics XXXIII, AMS 1979 [pdf] [ps] Rank-one residues of Eisenstein series Israel Mathematical Conference Proceedings 3 1990 [pdf] [ps] Letter to Godement 1967 [pdf] 5. Functoriality Problems in the Theory of Automorphic Forms Lectures in modern analysis and applications III, Lecture Notes in Mathematics 1701970 [pdf] [ps] The representation theory of abelian algebraic groups Pacific Journal of Mathematics 611998 [pdf] [ps] A little bit of number theory [pdf] [ps] Representation theory - its rise and its role in number theory Proceedings of the Gibbs symposium 1989 [pdf] [ps] Where stands functoriality today? Edinburgh conference on automorphic forms, AMS 1997 [pdf] [ps] Letter to André Weil 1967 [pdf] [pdf] [ps] [ps] Letter to Serre 1967 [pdf] [ps] Letter to Deligne 1974 [pdf] Letter to Roger Howe 1974 [pdf] [ps] Letter to Roger Howe 1975 [pdf] [ps] 6. First tests and first consequences of functoriality Correspondence leading to the book written with Jacquet 1967 A letter to Weil 1967 [pdf] [ps] A long letter to Jacquet 1967 [pdf] [ps] A collection of short letters to Jacquet 1967 [pdf] [ps] A letter to Deligne 1967 A letter to Harish-Chandra 1967 [pdf] [ps] A second letter to Harish-Chandra 1967 [pdf] [ps] GL(2) Springer 1970 [pdf] [ps] Langlands' Notes on Artin L-functions 1970 [pdf] [ps] On Artin's L-functions Rice University Studies 561970 [pdf] [ps] Automorphic forms on GL(2) Actes du Congrès International des Mathématiciens 1971 [pdf] [ps] 7. Base change Base change for GL(2) Annals of Mathematics 961980 [pdf] [ps] L-functions and Automorphic Representations Proceedings of the International Congress of Mathematicians, Helsinki 1978 [pdf] [ps] 8. Endoscopy L-indistinguishability for SL(2) Canadian Journal of Mathematics 311979 [pdf] [ps] Stable conjugacy-definitions and lemmas Canadian Journal of Mathematics 311979 [pdf] [ps] Les débuts d'une formule des traces stable Publications mathématiques de l'Université Paris VII 1979 [pdf] [ps] Orbital integrals on forms of SL(3) I American Journal of Mathematics 1051983 [pdf] [ps] On principal values on p-adic manifolds Lie group representations II, Lecture Notes in Mathematics 411984 [pdf] [ps] Orbital integrals on forms of SL(3) II Canadian Journal of Mathematics 411989 [pdf] [ps] On the definition of transfer factors Mathematischen Annalen 2781987 [pdf] [ps] Descent for transfer factors The Grothendieck Festschrift 21990 [pdf] [ps] Remarks on Igusa theory and real orbital integrals The zeta functions of Picard modular surfaces, Centre de Recherches Mathématiques, Montréal 1992 [pdf] [ps] Eisenstein series, the trace formula, and the modern theory of automorphic forms Number theory, trace formulas, and discrete groups 1987 [pdf] [ps] Beyond endoscopy Shalika volume, Johns Hopkins University Press 2004 [pdf] [ps] Un nouveau point de repère dans la theorie des forme automorphes [pdf] [ps] Letter to Singer 1974 [pdf] 9. Shimura varieties Modular forms and l-adic representations Modular functions of one variable II, Lecture Notes in Mathematics 3491973 [pdf] [ps] Some contemporary problems with origins in the Jugendtraum Mathematical developments arising from Hilbert's problems, Proceedings of Symposia in Pure Mathematics 281974 [pdf] [ps] Shimura varieties and the Selberg trace formula Canadian Journal of Mathematics 291977 [pdf] [ps] Comments on Shimura varieties and the Selberg trace formula Canadian Mathematical Society Selecta 21995 [pdf] [ps] On the zeta-functions of some simple Shimura varieties Canadian Journal of Mathematics 311979 [pdf] [ps] Automorphic representations, motives, and Shimura varieties. Ein Märchen Proceedings of the 1977 A.M.S. conference on L functions and automorphic representations 1977 [pdf] [ps] Sur la mauvaise réduction d'une variété de Shimura Journées de Géométrie Algébrique de Rennes, Astérisques 651979 [pdf] [ps] Algebraische Zyklen auf Hilbert-Blumenthal Flächen Journal für die reine und angewandte Mathematik 3661986 [pdf] [ps] Shimuravarietäten und Gerben Journal für die reine und angewandte Mathematik 3781987 [pdf] [ps] Representation theory and arithmetic The mathematical heritage of Hermann Weyl, Proceedings of Symposia in Pure Mathematics, AMS 481987 [pdf] [ps] Letter to Lang December 5, 1970 [pdf] Letter to Lang December 17, 1970 [pdf] Appendix to previous letter [pdf] Letter to Gee 2007 [pdf] 10. Percolation On the universality of crossing probabilities in two-dimensional percolation Journal of Statistical Physics 671992 [pdf] [ps] Finite Models for Percolation Contemporary Mathematics 1771991 [pdf] [ps] Conformal invariance for two-dimensional percolation Bulletin of the AMS 301994 [pdf] [ps] Dualität bei endlichen Modellen der Perkolation Mathematische Nachrichten 1691993 [pdf] [ps] 11. Mathematical physics The Dirac monopole and induced representations Pacific Journal of Mathematics 1261987 [pdf] [ps] An essay on the dynamics and statistics of critical field theories Canadian Mathematical Society Selecta 31995 [pdf] [ps] Algebro-geometric aspects of the Bethe equations Strings and Symmetries, Proceedings of Gürsey Memorial Conference, Istanbul 1995 [pdf] [ps] Aspects combinatoires des équations de Bethe Advances in Mathematical Sciences: CRM's 25 years 1997 [pdf] [ps] Universality and conformal invariance for the Ising model in domains with boundary Journal of Statistical Physics 982000 [pdf] [ps] The renormalization fixed point as a mathematical object [pdf] [ps] 12. Miscellaneous Review of SL₂(R) by Serge Lang Bulletin of the American Mathematical Society 821976 [pdf] [ps] Review of The theory of Eisenstein system by M. Scott Osborne and Garth Warner Bulletin of the American Mathematical Society 91983 [pdf] [ps] Review of Harish-Chandra's Collected Works Bulletin of the London Mathematical Society 171985 [pdf] [ps] Harish-Chandra 1923-1983 Biographical Memoirs of Fellows of the Royal Society 311985 [pdf] [ps] Harish-Chandra Memorial lecture, IAS 1984 [pdf] [ps] Commencement address at the University of Toronto, June 1993 1993 [pdf] [ps] Review of Elliptic Curves by Anthony Knapp Bulletin of the American Mathematical Society 301994 [pdf] [ps] André Weil (1906-98) - one of the century's most influential pure mathematicians Nature 3961998 [pdf] [ps] Interview with Stéphane Durand from Québec Science, May, 2000 Québec Science 2000 [pdf] [ps] Response upon receiving the Grande Médaille d'Or of the Académie des sciences 2000 [pdf] [ps] The trace formula and its applications (an introduction to the work of James Arthur) Canadian Mathematics Bulletin 202001 [pdf] [ps] Euclid's windows and our mirrors - review of Euclid's Window by Leonard Mlodinow Notices of the American Mathematical Society 2002 [pdf] [ps] Benim tanıdığım Cahit Arf (recollections of a year in Turkey with Cahit Arf) Matematik Dünyası 2003 [pdf] [ps] Robert Langlands in 1967 1967 Laudatio on the occasion of an award to Günter Harder [pdf] [ps] Descartes ile Fermat Matematik Dünyası 22005 [pdf] A review of Haruzo Hida's p-adic automorphic forms on Shimura varieties,... Bulletin of the American Mathematical Society 2006 [pdf] [ps] A succinct biography [pdf] [ps] Mathematical retrospections [pdf] [ps] Reflexions on receiving the Shaw prize [pdf] [ps] Pour la science [pdf] [ps] Interview with Farzin Barekat for the University of British Columbia [pdf] 13. Informal material Istanbul konferans dizisi [pdf] [ps] 14. Visual material The practice of mathematics
	Copyright ownership of the material in this project is complicated. Private use is unrestricted, but anyone who wishes to republish any of the material must first write for permission either to Bill Casselman, to Robert Langlands, or to Thomas Uphill, Computer Manager in the School of Mathematics.

The Work of Robert Langlands

Introduction

The material

1. Ph.D. thesis

2. Early work on the trace formula

3. Representation theory of real groups

4. Eisenstein series and automorphic forms

5. Functoriality

6. First tests and first consequences of functoriality

7. Base change

8. Endoscopy

9. Shimura varieties

10. Percolation

11. Mathematical physics

12. Miscellaneous

13. Informal material

14. Visual material