Langlands programme
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English
Alternative forms
Etymology
Named after Canadian mathematician Robert Langlands, who proposed it in 1967 (privately) and publicly in 1970.
Proper noun
- (mathematics) A set of interconnected, far-reaching and consequential conjectures connecting number theory with geometry.
- 2009, Clifton Cunningham, Monica Nevins (editors), Ottawa Lectures on Admissible Representations of Reductive p-adic Groups, American Mathematical Society, Fields Institute for Research in Mathematical Sciences, 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.
- 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.
- 2014, Michael Francis Atiyah, Collected Works, Volume 7: 2002—2013, Oxford University Press (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.
- 2019, Graham Farmelo, 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.
- 2009, Clifton Cunningham, Monica Nevins (editors), Ottawa Lectures on Admissible Representations of Reductive p-adic Groups, American Mathematical Society, Fields Institute for Research in Mathematical Sciences, page xii,
Translations
set of conjectures connecting number theory with geometry
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Noun
Langlands programme (plural Langlands programmes)
- (mathematics) Any of several similar sets of conjectures applicable to restricted domains of number theory and/or geometry.