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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
Periods, $L$-functions, and the relative trace formula; Raphael Beuzart-Plessis
Introduction to the relative Langlands program; Wee Teck Gan
Explicit constructions of automorphic forms: Theta correspondence and automorphic descent; Dipendra Prasad
Homological aspects of branching laws; Pierre-Henri Chaudouard
Introduction to the (relative) trace formula; Ngo Bao Chau
On generalized Hitchin fibrations and orbital integrals; Yiannis Sakellaridis
Local and global questions ""beyond endoscopy""; Wei Zhang
High dimensional Gross-Zagier formula: A survey; Chao Li
Geometric and arithmetic theta correspondences
