The work of Robert Langlands

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is cooperating with us in providing on our site a large selection from his professional correspondence and previously unpublished work, as well as an almost complete collection of all of his published work.

This material is being put into TeX at the Institute in Princeton and will appear here as it becomes ready. We would like to thank Dorothea Phares, Marietta Chiorello, Elly Gustafsson, Michelle Huguenin, and Carol Warfield of the staff at the Institute, as well as Mark Goresky, for helping with this project.

The material

Ph.D. thesis

Semi-groups and representations of Lie groups Some holomorphic semi-groups On Lie semi-groups

Early work on the trace formula

Dimension of spaces of automorphic forms (American Journal of Mathematics)

Representation theory of real groups

Dimension of spaces of automorphic forms (from the Boulder conference) The classification of representations of real reductive groups Notes on Knapp-Zuckerman theory On unitary representations of the Virasoro algebra The factorization of a polynomial defined by partitions

Eisenstein series and automorphic forms

The volume of the fundamental domain for some arithmetical subgroups of Chevalley groups Eisenstein series Euler products Letter to Godement On the functional equations satisfied by Eisenstein series (Springer Lecture Notes #544) On the notion of an automorphic representation Rank-one residues of Eisenstein series

Functoriality

1967 Letter to Weil Letter to Serre Two letters to Roger Howe Problems in the theory of automorphic forms Representation theory of abelian algebraic groups A bit of number theory Representation theory---its rise and its role in number theory Where stands functoriality today?

First tests and first consequences of functoriality

Correspondence leading to the book by Jacquet and Langlands Automorphic Forms on GL(2) (the book Jacquet-Langlands) Artin L-functions On Artin's L-Functions (the Rice University lecture) Automorphic forms on GL(2) (delivered at the Nice ICM)

Base change

Base change (in the series published by the Annals of Mathematics and Princeton University) L functions and automorphic representations (a talk at the ICM in Helsinki, 1978)

Endoscopy

L-indistinguishability for SL(2) (with J.-P. Labesse) Stable conjugacy-definitions and lemmas Les débuts d'une formule des traces stable Orbital integrals on forms of SL(3) I On principal values on p-adic manifolds (with Diana Shelstad) Orbital integrals on forms of SL(3) II (with D. Shelstad) On the definition of transfer factors (with D. Shelstad) Descent for transfer factors (with D. Shelstad) Remarks on Igusa theory and real orbital integrals Eisenstein series, the trace formula, and the modern theory of automorphic forms Beyond endoscopy Un nouveau point de repère dans la theorie des forme automorphes

Shimura varieties

From the Antwerp conference Some contemporary problems with origins in the Jugendtraum Shimura varieties and the Selberg trace formula Comments on Shimura varieties and the Selberg trace formula On the zeta functions of some simple Shimura varieties Automorphic representations, motives, and Shimura varieties. Ein Märchen Sur la mauvaise réduction d'une variété de Shimura Algebraische Zyklen auf Hilbert-Blumenthal Flächen (with G. Harder and M. Rapoport) Shimuravarietäten und Gerben (with Michael Rapoport) Representation theory and arithmetic

Percolation

On the universality of crossing probabilities in two dimensions (with C. Pichet, P. Pouliot, and Y. Saint-Aubin) Finite models for percolation (with M.-A. Lafortune) Conformal invariance in two-dimensional percolation (with Philippe Pouliot and Yvan Saint-Aubin) Dualität bei endlichen Modellen der Perkolation

Mathematical physics

The Dirac monopole and induced representations An essay on the dynamics and statistics of critical field theories Algebro-geometric aspects of the Bethe equations (with Yvan Saint-Aubin) Aspects combinatoires des équations de Bethe (with Yvan Saint-Aubin) Universality and conformal invariance for the Ising model in domains with boundary (with Marc André Lewis and Yvan Saint-Aubin) The renormalization fixed-point as a mathematical object

Miscellaneous

Harish-Chandra (a memorial) Harish-Chandra 1923-1983 (biographical memoir for the Royal Society) André Weil 1906-1998 An interview with Stéphane Durand for Québec Science, May, 2000 Commencement address at the University of Toronto, June, 1993 Talk upon receiving the Grande Médaille d'Or in November, 2000 Report on the work of James Arthur On the occasion of an award to Günter Harder Review of SL2(R) by Serge Lang Review of The theory of Eisenstein systems by M. Scott Osborne and Garth Warner Review of Harish-Chandra's Collected Works Review of Elliptic curves by Anthony Knapp Review of Euclid's Window by Leonard Mlodinow Benim tanidigim Cahit Arf (Recollections of a year in Turkey with Cahit Arf) Descartes ile Fermat A review of Haruzo Hida's p-adic automorphic forms on Shimura varieties

Informal material

Endoscopy and beyond Istanbul konferans dizisi (in Turkish)

A list of Langlands' papers, notes, and books

Bibliography