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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
Representations, automorphic forms, and endoscopy; Olivier Taibi
The local Langlands conjecture; Jessica Fintzen
Supercuspidal representations: Construction, classification, and characters; Lucas Mason-Brown
Arthur's conjectures and the Orbit Method for real reductive groups; Tasho Kaletha
A brief introduction to the trace formula and its stabilization; Erez Lapid
Some perspectives on Eisenstein series; Shimura varieties and shtukas; Sophie Morel
Shimura varieties; Zhiwei Yun
Introduction to shtukas and their moduli; Jared Weinstein
Shtukas and the Langlands program: A bird's eye view; Ana Caraiani and Sug Woo Shin
Recent progress on Langlands reciprocity for general linear groups: Shimura varieties and beyond; Cong Xue
Cohomology sheaves of stacks of shtukas; Sam Raskin
An arithmetic application of geometric Langlands
