In mathematics, the Langlands program is a set of conjectures about connections between number theory, the theory of automorphic forms, and geometry. It was proposed by the Canadian …

The Langlands program predicts a correspondence between two types of objects. On the one side we have automorphic representations and on the other side we have some arithmetic objects M which …

Jun 1, 2022 · What Is the Langlands Program? The Langlands program provides a beautifully intricate set of connections between various areas of mathematics, pointing the way toward novel solutions …

In his conjectures, now collectively known as the Langlands program, Robert Langlands drew on the work of Hermann Weyl (above), André Weil, and Harish-Chandra, among others with extensive ties …

Jan 20, 2004 · Introduction to the Langlands program, by J. Bernstein and S. Gelbart (Editors), with contributions by D. Bump, J. W. Cogdell, D. Gaitsgory, E. de Shalit, E. Kowalski, S. S. Kudla, …

Dec 3, 2025 · In a January 1967 letter to André Weil, Langlands proposed that the mathematics of algebra (Galois representations) and analysis (automorphic forms) are intimately related, and that …

Part I. The origins of the Langlands Program this article I review the origins of the Langlands Program. We start by recalling some basic notions of number theory

A geometric Langlands Program - analogue of the Langlands functoriality conjecture over global function eld - was formulated by Drinfeld and Laumon. Due to the e orts of Drinfeld, Laumon, La orgue and …

Introduction to the Langlands Program A. W. Knapp uctive group over a number field. The first half is a summary of aspects of local and global class field theory, with emphasis on the local Weil group, the …

Feb 21, 2025 · The Langlands Program seeks to take such translations to a new level, suggesting that for every important number-theoretic object or symmetry, there is a corresponding analytic or …