Laurent Fargues Explained

Laurent Fargues
Birth Date:19 June 1975
Birth Place:Cagnes-sur-Mer
Nationality:French
Thesis Title:Correspondances de Langlands locale dans la cohomologie des espaces de Rapoport-Zink.
Thesis Url:https://arxiv.org/abs/math/0109209
Doctoral Advisor:Michael Harris
Field:Mathematics

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.

Career

Fargues received his doctorate in 2001 under Michael Harris at Paris Diderot University (Paris 7, Institut de Mathématiques de Jussieu) and his habilitation in 2009 at Paris-Sud University in Orsay. 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 in both the number theory and algebraic geometry sessions.

Selected publications

References

  1. Web site: Laurent Fargues, CV (English). Personal home page.
  2. Web site: Geometrization of the local Langlans correspondence: an overview.
  3. Web site: The Fargues-Fontaine curve and diamonds, d'après Fargues, Fontaine, and Scholze. bourbaki.ens.fr.
  4. Web site: Geometric Langlands, Perfectoid Spaces, and the Fargues-Fontaine Curve.
  5. Proc. Int. Cong. Of Math.. Rio de Janeiro. 1. 71–86. The Work of Peter Scholze. 28 December 2018. Michael Rapoport. 26 September 2019.
  6. New Shape Opens 'Wormhole' Between Numbers and Geometry . . July 19, 2021. Kevin. Hartnett.