Related papers: La correspondance de Langlands sur les corps de fo…
We prove that V. Lafforgue's global Langlands correspondence is compatible with Fargues-Scholze's semisimplified local Langlands correspondence. As a consequence, we canonically lift Fargues-Scholze's construction to a non-semisimplified…
A summary of the experimental and theoretical presentations in the Structure Function Working Group on the proton and photon unpolarized structure functions is given.
This is my talk on the Bourbaki seminar, November 1996. It contains an elementary introduction to Borcherds' product formulas.
We survey several recent examples of derived structures emerging in connection with the Langlands correspondence. Cases studies include derived Galois deformation rings, derived Hecke algebras, derived Hitchin stacks, and derived special…
There are two versions of endoscopic transfer factors to accommodate the different versions, classical or renormalized, of the local Langlands correspondence. An examination of the structure of these complex-valued factors shows that the…
This paper formulates a conjectural description of of the space of weightless functions (see\cite{BK}) and raises a question about a possibility of extending such a description in a more general context.
These are slides for a talk given by the authors at the conference "Current developments and directions in the Langlands program" held in honor of Robert Langlands at the Northwestern University in May of 2008. The slides can be used as a…
This is an extended version of notes prepared for the talk at the conference "Rajchman-Zygmund-Marcinkiewicz 2000" based on recent works of the authors.
This paper serves as the announcement of my program---a joke version of the Langlands Program. In connection with this program, I discuss an old hat puzzle, introduce a new hat puzzle, and offer a puzzle for the reader.
We offer o reply for the comments of Rapisarda et al. cond-mat/0601409 on our letter "Entropy of Classical Systems with Long Range Interactios", published in Phys. Rev. Lett. Vol 95 (2005) 190601.
These are the notes of a lecture held by Michael Hopkins in march 2007, at the Talbot workshop.
V. Drinfeld proposed conjectures on geometric Langlands correspondence and its quantum deformation. We refine these conjectures and propose their relationship with algebraic conformal field theory.
This is the memoir of my habilitation thesis, defended on March 29 th, 2013 (Universit\'e Paris XI).
The Lagrangian formalism has attracted the attention of mathematicians and physicists for more than 250 years and has played significant roles in establishing modern theoretical physics. The history of the Lagrangian formalism in biology is…
In this note, we argue that there is a bug in [Tirole, J., "Hierarchies and bureaucracies: On the role of collusion in organizations," {\em Journal of Law, Economics and Organization}, vol.2, 181-214, 1986].
This is a credit mini-course in French prepared for a Summer School at the University of Sherbrooke. The course consists of three one-and-half hour lectures and three credit exercises for a class of advanced graduate students.
This is a survey of the proof of the global Jacquet-Langlands correspondence between GL_n and general inner forms, in characteristic zero. The proof is given after a long introduction recalling in some detail the objects and results…
This survey article on Hilbert's first and second problems is adapted from a one-hour colloquium lecture given at the University of Auckland in May, 2000, just three months before the 100th anniversary of Hilbert's lecture. It includes an…
This text was written to support a Bourbaki seminar given in January 2026 on the subject of the model theory of perfectoid fields, especially on the work of Jahnke and Kartas in their paper "Beyond the Fontaine-Wintenberger theorem", J.…
Notes of my 14 `lectures on everything' given at the 1995 Les Houches school. An introductory course in topological and conformal field theory, strings, gauge fields, supersymmetry and more. The presentation is more mathematical then usual…