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Robert Phelan Langlands, is a Canadian mathematician. He is best known as the founder of the Langlands program, a vast web of conjectures and results connecting representation theory and automorphic forms to the study of Galois groups in number theory, for which he received the 2018 Abel Prize. He was an emeritus professor and occupied Albert Einstein's office at the Institute for Advanced Study in Princeton, until 2020 when he retired.
In representation theory, the Langlands program is a web of far-reaching and influential conjectures about connections between number theory and geometry. Proposed by Robert Langlands, it seeks to relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and adeles. Widely seen as the single biggest project in modern mathematical research, the Langlands program has been described by Edward Frenkel as "a kind of grand unified theory of mathematics."
Richard Lawrence Taylor is a British mathematician working in the field of number theory. He is currently the Barbara Kimball Browning Professor in Humanities and Sciences at Stanford University.
Vladimir Gershonovich Drinfeld, surname also romanized as Drinfel'd, is a renowned mathematician from the former USSR, who emigrated to the United States and is currently working at the University of Chicago.
In mathematics, the local Langlands conjectures, introduced by Robert Langlands, are part of the Langlands program. They describe a correspondence between the complex representations of a reductive algebraic group G over a local field F, and representations of the Langlands group of F into the L-group of G. This correspondence is not a bijection in general. The conjectures can be thought of as a generalization of local class field theory from abelian Galois groups to non-abelian Galois groups.
In mathematics, admissible representations are a well-behaved class of representations used in the representation theory of reductive Lie groups and locally compact totally disconnected groups. They were introduced by Harish-Chandra.
Hervé Jacquet is a French American mathematician, working in automorphic forms. He is considered one of the founders of the theory of automorphic representations and their associated L-functions, and his results play a central role in modern number theory.
Edward Vladimirovich Frenkel is a Russian-American mathematician working in representation theory, algebraic geometry, and mathematical physics. He is a professor of mathematics at University of California, Berkeley, member of the American Academy of Arts and Sciences, and author of the bestselling book Love and Math.
Pierre Colmez is a French mathematician, notable for his work on p-adic analysis.
Freydoon Shahidi is an Iranian American mathematician who is a Distinguished Professor of Mathematics at Purdue University in the U.S. He is known for a method of automorphic L-functions which is now known as the Langlands–Shahidi method.
In mathematics, the Langlands–Shahidi method provides the means to define automorphic L-functions in many cases that arise with connected reductive groups over a number field. This includes Rankin–Selberg products for cuspidal automorphic representations of general linear groups. The method develops the theory of the local coefficient, which links to the global theory via Eisenstein series. The resulting L-functions satisfy a number of analytic properties, including an important functional equation.
Michael Howard Harris is an American mathematician and professor of mathematics at Columbia University who specializes in number theory and representation theory. He made notable contributions to the Langlands program, for which he won the 2007 Clay Research Award. In particular, he proved the local Langlands conjecture for GL(n) over a p-adic local field, and he was part of the team that proved the Sato–Tate conjecture. He was elected a member of the National Academy of Sciences in 2022.
Guy Henniart is a French mathematician at Paris-Sud 11 University. He is known for his contributions to the Langlands program, in particular his proof of the local Langlands conjecture for GL(n) over a p-adic local field—independently from Michael Harris and Richard Taylor—in 2000.
In mathematics, Lafforgue's theorem, due to Laurent Lafforgue, completes the Langlands program for general linear groups over algebraic function fields, by giving a correspondence between automorphic forms on these groups and representations of Galois groups.
Colin John Bushnell was a British mathematician specialising in number theory and representation theory. He spent most of his career at King's College London, including a stint as the head of the School of Physical Sciences and Engineering, and made several contributions to the representation theory of reductive p-adic groups and the local Langlands correspondence.
Zhiwei Yun is a Professor of Mathematics at MIT specializing in number theory, algebraic geometry and representation theory, with a particular focus on the Langlands program.
Toby Stephen Gee is a British mathematician working in number theory and arithmetic aspects of the Langlands Program. He specialises in algebraic number theory.
Gan Wee Teck is a Malaysian mathematician of Chinese descent, and Distinguished Professor of Mathematics at the National University of Singapore (NUS). He is known for his work on automorphic forms and representation theory in the context of the Langlands program, especially the theory of theta correspondence, the Gan–Gross–Prasad conjecture and the Langlands program for Brylinski–Deligne covering groups.
Jack A. Thorne is a British mathematician working in number theory and arithmetic aspects of the Langlands Program. He specialises in algebraic number theory. Thorne was awarded the Whitehead Prize in 2017, and he was an invited speaker at the International Congress of Mathematicians in 2018. He was awarded the 2018 SASTRA Ramanujan Prize for his contributions to the field of mathematics. He shared the prize with Yifeng Liu. In April 2020 he was elected a Fellow of the Royal Society. In 2020 he received the EMS Prize of the European Mathematical Society, in 2021 he was awarded a New Horizons in Mathematics Prize and in 2022 he was awarded the Adams Prize.
James Wesley Cogdell is an American mathematician.
References
- ↑ Date information sourced from Library of Congress Authorities data, via corresponding WorldCat Identities linked authority file (LAF).
- ↑ Kutzko, Philip (1980). "The Langlands Conjecture for Gl2 of a Local Field". Annals of Mathematics . 112 (2): 381–412. doi:10.2307/1971151. JSTOR 1971151.
- ↑ List of Fellows of the American Mathematical Society, retrieved 2014-12-17
