Related papers: La correspondance de Langlands sur les corps de fo…
Cet expos\'e est consacr\'e \`a la preuve de la correspondance de Langlands pour les groupes $\GL_r$ sur les corps de fonctions. ----- This article is devoted to the proof of the Langlands correspondence for the groups $GL_r$ over function…
This is the text of the Bourbaki seminar that I gave on June 24, 2000.
Laurent Lafforgue has been awarded the Fields Medal for his proof of the Langlands correspondence for the full linear groups $\mathop{\rm GL}\nolimits_{r}$ ($r\geq 1$) over function fields. This article is a brief introduction to the…
The is the English version of the text of the talk at S\'eminaire Bourbaki on February 16, 2016
This is a survey lecture note on the applications of Langlands functoriality which were obtained recently by some people at the Langalnds school. This lecture was delivered at the Department of Mathematics, Kyoto University, Japan on June…
These are lecture notes (by the first author) from a course (by the second author) given over two extended semesters at the University of Sydney. The first part provides an introduction to the Langlands correspondence from an arithmetical…
This is a survey paper on the geometrization of the local Langlands correspondence by Fargues-Scholze.
We adapt to global fields of positive characteristic the contents of the book by Labesse and Waldspurger on the Twisted Trace Formula after the Friday Morning Seminar.
Bourbaki seminar 1062, October 2012.
This paper is a set of lecture notes of my course "Special functions, KZ type equations, and representation theory" given at MIT during the spring semester of 2002. The notes do not contain new results, and are an exposition (mostly without…
We extend the Langlands program in various subprograms with certain different generalizations: (1) Mixed-parity functorial perturbation of the usual Langlands program after Fargues-Scholze in all characteristics; (2) Robba-Frobenius…
These lecture notes give an overview of recent results in geometric Langlands correspondence which may yield applications to quantum field theory. We start with a motivated introduction to the Langlands Program, including its geometric…
These are expanded notes of some lectures given by the author for a workshop held at the Indian Statistical Institute, Bangalore in June, 2010, giving an exposition on the modular representations of finite groups of Lie type and $p$-adic…
This article is an overview of the geometrization conjecture for the local Langlands correspondence formulated by the author.
We argue that Lagrangian correspondences are the correct framework to study functoriality of virtual fundamental classes arising from a $-2$-symplectic derived structure.
This is an expanded version of one of the Lectures in memory of Lars Ahlfors in Haifa in 1996. Some mistakes are corrected and references added. It contains a survey of his work on meromorphic functions and related topics written in…
This is a pedagogical review on polarized structure functions .
The geometric Langlands correspondence for function fields over finite fields has been proved by Frenkel, Gaitsgory, Vilonen. The aim of this article is to write translation for curves over the complex field and prove the correspondence in…
In 1967, Langlands conjectured a natural correspondence between automorphic representations and Galois representations, over number fields as well as over function fields. In 1983, Drinfeld discovered a geometric analog of the Langlands…
This is a report on the work of Robert Langlands, following his award of the Abel Prize in 2018. It includes his contributions to the general areas of Representation Theory, Automorphic Forms, Number Theory and Arithmetic Geometry. We have…