Relative Aspects of the Langlands Program, L-Functions, and Beyond Endoscopy

该奖项支持美国研究人员参加2020年5月25日至29日在法国马赛国际伦孔特雷斯数学中心举行的题为《朗兰兹计划的相关方面，L-功能和超越内窥镜》的研讨会。现代数学中的朗兰兹计划自成立以来一直在演变着更深层次的思想。本次研讨会将概述相对朗兰兹计划的最新快速进展，并通过鼓励高级和初级研究人员之间的互动来促进进一步的发展。鉴于最近令人振奋的事态发展，举办一次关于这一主题的讲习班是及时的，将鼓励年轻人进入这一非常活跃的领域。朗兰兹的函数性原理和自同构L函数是朗兰兹计划和自同构形式理论的两个中心主题。尽管已经取得了四十多年的进步和无数的突破，但这个项目中的许多问题仍然悬而未决，甚至出现了更深层次的问题。内窥镜理论是函数论的一个特殊而重要的例子，在过去的三十年里，它吸引了人们的巨大努力，导致了一些突破，如基本引理的证明和经典群自同构表示的内窥镜分类。要超越这些非凡的成就，需要新的技术和想法。近年来，令人振奋的新想法不断涌现，有可能更新我们对整个学科的看法。会议将集中讨论三个主要主题：(1)相对朗兰兹程序，(2)L函数的(高)导数的特殊值之间的关系，以及(3)超越内窥镜和可能的新的函数性案例。研讨会的细节张贴在https://conferences.cirm-math.fr/2154.html.This上，该奖项反映了国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award supports participation of US-based researchers in the workshop "Relative Aspects of the Langlands Program, L-Functions, and Beyond Endoscopy" taking place May 25-29, 2020 at the Centre International de Rencontres Mathematiques in Marseille, France. The Langlands program in modern mathematics has been evolving with deeper ideas since its inception. This workshop will provide an overview of recent rapid progress in the relative Langlands program and foster further development by encouraging interactions between senior and junior researchers. Given the recent exciting developments, a workshop on the subject is timely and will encourage young people to enter this very active field. Langlands's principle of functoriality and the automorphic L-functions are two central themes of the Langlands program and the theory of automorphic forms. Despite more than forty years of progress and numerous breakthroughs, many questions in this program are still open and even deeper questions have arisen. The theory of endoscopy, a special but very important case of functoriality, attracted immense efforts in the past thirty years, leading to breakthroughs such as the proof of the Fundamental Lemma and the endoscopic classification of automorphic representations of classical groups. Going beyond these remarkable achievements requires new techniques and ideas. In recent years, exciting new ideas have emerged, which have the potential to renew our vision of the whole subject. The conference will focus on three main topics: (1) the relative Langlands program, (2) relations between special values of (higher) derivatives of L-functions, and (3) beyond endoscopy and possible new cases of functoriality. Details of the workshop are posted at https://conferences.cirm-math.fr/2154.html.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.