Tasho Kaletha - Böcker

Bruhat-Tits theory is an important topic in number theory, representation theory, harmonic analysis, and algebraic geometry. This book gives the first comprehensive treatment of this theory over discretely valued Henselian fields. It can serve both as a reference for researchers in the field and as a thorough introduction for graduate students and early career mathematicians. Part I of the book gives a review of the relevant background material, touching upon Lie theory, metric geometry, algebraic groups, and integral models. Part II gives a complete, detailed, and motivated treatment of the core theory as well as an axiomatic summary of Bruhat-Tits theory that suffices for the main applications. Part III treats modern topics that have become important in current research. Part IV provides a few sample applications of the theory. The appendices contain further details on the topic of integral models, including a detailed study of integral models.

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.

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.

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.