Laurent Fargues | |
|---|---|
 Fargues at Oberwolfach, 2016 | |
| Born | 19 June 1975 Cagnes-sur-Mer |
| Nationality | French |
| Scientific career | |
| Fields | Mathematics |
| Thesis | Correspondances de Langlands locale dans la cohomologie des espaces de Rapoport-Zink. |
| Doctoral advisor | Michael Harris |
Laurent Fargues (born 19 July 1975 in Cagnes-sur-Mer) is a French mathematician working in number theory and arithmetic geometry.
Fargues was an invited speaker at the International Congress of Mathematicians in 2018 in Rio de Janeiro.
From 2002 to 2011, Fargues was a chargé de recherches at the CNRS in Orsay, from 2011 to 2013 he was CNRS research director at the IRMA in Strasbourg and, from 2013, CNRS research director at the l'Institut de mathématiques de Jussieu in Paris (a campus of the Sorbonne University). [1]
Fargues work mainly centers around the study of Shimura varieties, p-divisible groups and their moduli spaces, and p-adic Hodge theory. One of his most significant contributions has been to link the local Langlands correspondence with the Fargues–Fontaine curve, an object introduced by Fargues together with Jean-Marc Fontaine. In particular, Fargues has formulated a general geometric conjecture [2] which refines the classical local Langlands conjecture, and at the same time introduces extra structure which mirrors the more categorical formulation of the geometric Langlands conjecture. These works were (in part) the subject of a Séminaire Bourbaki exposé in 2018 by Matthew Morrow [3] and an Arbeitsgemeinschaft meeting at Oberwolfach in 2016. [4] His work with Peter Scholze on the stack of vector bundles on the Fargues–Fontaine curve is expected to have implications for the construction of a local Langlands correspondence for general groups. [5] [6]
Fargues gave the Peccot course at the Collège de France in the spring of 2004, was awarded the Petit d'Ormoy, Carriere, Thebault prize from the French academy of sciences in 2009, and was an invited speaker at the International Congress of Mathematicians 2018 in Rio de Janeiro [7] in both the number theory and algebraic geometry sessions.
Laurent Lafforgue is a French mathematician. He has made outstanding contributions to Langlands' program in the fields of number theory and analysis, and in particular proved the Langlands conjectures for the automorphism group of a function field. The crucial contribution by Lafforgue to solve this question is the construction of compactifications of certain moduli stacks of shtukas. The proof was the result of more than six years of concentrated efforts.
In representation theory and algebraic number 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."
Pierre René, Viscount Deligne is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord Prize, and 1978 Fields Medal.
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.
In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties.
Claire Voisin is a French mathematician known for her work in algebraic geometry. She is a member of the French Academy of Sciences and holds the chair of algebraic geometry at the Collège de France.
In mathematics, the geometric Langlands correspondence is a reformulation of the Langlands correspondence obtained by replacing the number fields appearing in the original number theoretic version by function fields and applying techniques from algebraic geometry. The geometric Langlands correspondence relates algebraic geometry and representation theory.
Christophe Breuil is a French mathematician, who works in arithmetic geometry and algebraic number theory.
Jean-Marc Fontaine was a French mathematician. He was one of the founders of p-adic Hodge theory. He was a professor at Paris-Sud 11 University from 1988 to his death.
Vincent Lafforgue is a French mathematician who is active in algebraic geometry, especially in the Langlands program, and a CNRS "Directeur de Recherches" at the Institute Fourier in Grenoble. He is the younger brother of Fields Medalist Laurent Lafforgue.
Pierre Colmez is a French mathematician, notable for his work on p-adic analysis.
Michael Howard Harris is an American mathematician known for his work in number theory. He is a professor of mathematics at Columbia University and professor emeritus of mathematics at Université Paris Cité.
Guy Henniart (born 1953, Santes) 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.
Georges Skandalis is a Greek and French mathematician, known for his work on noncommutative geometry and operator algebras.
Wiesława Krystyna Nizioł is a Polish mathematician, director of research at CNRS, based at Institut mathématique de Jussieu. Her research concerns arithmetic geometry, and in particular p-adic Hodge theory, Galois representations, and p-adic cohomology.
Colette Moeglin is a French mathematician, working in the field of automorphic forms, a topic at the intersection of number theory and representation theory.
Vincent Pilloni is a French mathematician, specializing in arithmetic geometry and the Langlands program.
Élisabeth Bouscaren is a French mathematician who works on algebraic geometry, algebra and mathematical logic.
Mikhail Vol'fovich Borovoi is a Soviet and Israeli mathematician. He has worked on Galois cohomology and on the arithmetic of linear algebraic groups, homogeneous spaces, Shimura varieties, and spherical varieties.
Nicolas Bergeron is a French mathematician born on 19 December 1975, who works in Pierre and Marie Curie University in Paris.
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