A Glimpse at the Genesis of the Langlands Program

Abstract

This chapter serves as an introduction to the volume as a whole, and it is aimed at a general mathematical audience. Our presentation of the early life and work of Robert Langlands, creator and founder of the Langlands program, is narrated, to a large extent, by Langlands himself. We focus on two of Langlands’ major discoveries: automorphic L-functions and the functoriality conjecture. Langlands’ desire to communicate his excitement about his newly discovered objects resulted in his famous letter to André Weil in January 1967, and the Langlands program was launched soon afterwards. Section 1.2 of this chapter focuses on Langlands’ early years, from 1936 to 1960, and the material is taken from an interview given by Langlands to a student, Farzin Barekat, at the University of British Columbia (UBC), Langlands’ alma mater, in the early 2000s. A copy of this interview is available on Langlands’ website at http://publications.ias.edu/rpl/. Section 1.3 is an overview of Langlands’ early work and professional life from 1960 to 1967. It contains a brief descriptive account of the essential events that led him to his discoveries of automorphic L-functions and the functoriality conjecture. Our source material in this part is taken largely from our correspondence and interviews with Langlands himself over the past few years. Those correspondence can also be found on Langlands’ website.