Langlands programme

English Alternative forms en Langlands program Etymology Named after Canadian mathematician Robert Langlands, who proposed it in 1967 (privately) and publicly in 1970. Proper noun en 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 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. 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. en 2019 Graham Farmelo The Universe Speaks in Numbers Faber & Faber https://books.google.com.au/books?id=1wGFDwAAQBAJ&pg=PT186&dq=%22Langlands+programme%22&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwjT5MK8ltWGAxVtTmwGHcowADkQ6AF6BAhXEAI#v=onepage&q=%22Langlands%20programme%22&f=false unnumbered 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 set of conjectures connecting number theory with geometry French: fr programme de Langlands m German: de Langlands-Programm n Italian: it Noun en mathematics Any of several similar sets of conjectures applicable to restricted domains of number theory and/or geometry. en p-adic Langlands programme en modulo p Langlands programme en eponyms