The Genesis of the Langlands Program

A step-by-step guide to Langlands' early work leading up the Langlands Program for mathematicians and advanced students.

Julia Mueller (Edited by), Freydoon Shahidi (Edited by)

9781108710947, Cambridge University Press

Paperback / softback, published 5 August 2021

450 pages
22.8 x 15.2 x 2.6 cm, 0.67 kg

'It is exciting to read this important book. It is a marvelous panorama of the life, work, and inspiration of Robert Langlands, as he discovered and developed his grand ideas, and as he guided his students. These ideas now largely shape the broad architecture of representation theory and automorphic forms, creating a grand bridge between analysis and arithmetic - with connections to mathematical physics. The contributors to this volume offer us - and will surely offer future historians of our mathematical age - a splendid introduction to, and overview of, the early days of Langlands' program.' Barry Mazur, Harvard University

Robert Langlands formulated his celebrated conjectures, initiating the Langlands Program, at the age of 31, profoundly changing the landscape of mathematics. Langlands, recipient of the Abel Prize, is famous for his insight in discovering links among seemingly dissimilar objects, leading to astounding results. This book is uniquely designed to serve a wide range of mathematicians and advanced students, showcasing Langlands' unique creativity and guiding readers through the areas of Langlands' work that are generally regarded as technical and difficult to penetrate. Part 1 features non-technical personal reflections, including Langlands' own words describing how and why he was led to formulate his conjectures. Part 2 includes survey articles of Langlands' early work that led to his conjectures, and centers on his principle of functoriality and foundational work on the Eisenstein series, and is accessible to mathematicians from other fields. Part 3 describes some of Langlands' contributions to mathematical physics.

Part I. Remembrance of Things Past: 1. A glimpse at the genesis of the Langlands program Julia Mueller
2. The early Langlands program – personal reflections Steve Gelbart
Part II. Langlands as Mentor: 3. Langlands and Turkey Cihan Saclioglu
4. Reminiscences by a student of Langlands Thomas Hales
5. Graduate school with Langlands Ali Altug
6. An unforgettable year at the Institute (Enstitü'de unutulmaz bir y?l) Dinakar Ramakrishnan
Part III. Langlands as Friend: 7. My reminiscences of Bob Langlands at the University of British Columbia Alan Goodacre
8. Robert P. Langlands: l'homme derrière le Mathématicien Claude Levesque
9. un homme de culture et de nature Claude Pichet
Part IV. Surveys of the Langlands Program – Early Years: 10. An introduction to Langlands functoriality James Arthur
11. In the beginning – Langlands' doctoral thesis Derek W. Robinson
12. The Langlands spectral decomposition Jean-Pierre Labesse
13. Automorphic representations and L-functions for the group GL(n) Dorian Goldfeld and Herveì Jacquet
14. Automorphic L-functions Freydoon Shahidi
15. Langlands reciprocity: L-functions, automorphic forms, and Diophantine equations Matthew Emerton
16. On some early sources for the notion of transfer in Langlands functoriality Diana Shelstad
Part V. Langlands' Contributions to Mathematical Physics: 17. Robert Langlands' work in mathematical physics Thomas Spencer
18. L'invariance conforme et l'universalité au point critique des modèles bidimensionnels Yvan Saint-Aubin.

Subject Areas: Topology [PBP], Geometry [PBM], Number theory [PBH], Algebra [PBF], Mathematics [PB]