Langlands programme

Etymology
Named after Canadian mathematician, who proposed it in 1967 (privately) and publicly in 1970.

Proper noun

 * 1)  A set of interconnected, far-reaching and consequential conjectures connecting number theory with geometry.
 * 2) * 2009, Clifton Cunningham, Monica Nevins (editors), Ottawa Lectures on Admissible Representations of Reductive p-adic Groups,, , page xii,
 * The Langlands Programme gives the study of representations of p-adic groups context and relevance, without which it almost certainly would not have enjoyed such a rich half-century of research. As we are reminded in Chapter 4, one should never forget that the study of representations of p-adic groups is inextricably linked with harmonic analysis. The Langlands Programme gives us a beautiful illustration of this fact.
 * 1) * 2014,, Collected Works, Volume 7: 2002—2013, (Oxford Science Publications), page 233,
 * The Langlands programme is a large programme which, if completed, will give a very satisfactory answer to the question of how to extend abelian class field theory to the general case of non-abelian extensions. It is a very big programme, that in many ways has only just started, and in it a fundamental role is played by complex linear representations of the Galois groups of algebraic extensions.
 * 1) * 2019,, The Universe Speaks in Numbers, Faber & Faber, unnumbered page,
 * Quickly recognised as an imaginative vision, the so-called Langlands programme has been a bountiful source of ideas and might conceivably lead one day to a unified approach to mathematics.

Translations

 * French:
 * German: Langlands-Programm
 * Italian:

Noun

 * 1)  Any of several similar sets of conjectures applicable to restricted domains of number theory and/or geometry.