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Full Description
These three volumes comprise the proceedings of a summer school on the Langlands Program held at the Institut des Hautes Etudes Scientifiques during the three weeks of July 11-29, 2022. The twenty-five articles in these proceedings capture the content of lectures given by thirty-one leading experts at the summer school. They showcase the state of the art in some (but not all) aspects of the Langlands program, such as the theory of endoscopy, the trace formula, the local Langlands correspondence, Shimura varieties, and shtukas. In addition, the volumes highlight several emerging unifying themes and new connections that are expected to be influential in the future development of the subject, such as the ideas of geometrization and categorification and the evolving Relative Langlands Program. The broad spectrum of topics reflects the continued growth of the Langlands Program, and the articles are written to help overcome the language barrier that sometimes exists between different subfields, while highlighting the connecting threads that run through different parts of it. These volumes should serve as a useful resource for beginning PhD students as well as more seasoned researchers who are interested in learning about the new directions and developments of this fascinating subject.
Contents
Geometrization of the Langlands correspondence; Jean-Francois Dat
Moduli spaces of local Langlands parameters; Xinwen Zhu
Coherent sheaves on the stack of Langlands parameters; Laurent Fargues and Peter Scholze
The Langlands program and the moduli of bundles on the curve; Matthew Emerton
Toby Gee and Eugen Hellmann
An introduction to the categorical $p$-adic Langlands program; David Ben-Zvi
Harrison Chen
David Helm and David Nadler
Between coherent and constructible local Langlands correspondences; Tony Feng and Michael Harris
Derived structures in the Langlands correspondence
