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日在法国马赛国际数学会议中心举行的研讨会“朗兰兹计划，L函数和超越内窥镜的相关方面”。现代数学中的朗兰兹纲领自诞生以来一直在发展更深层次的思想。本次研讨会将提供一个相对朗兰兹计划最近的快速进展的概述，并通过鼓励高级和初级研究人员之间的互动促进进一步发展。鉴于最近令人兴奋的事态发展，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。朗兰兹的函性原理和自守L-函数是朗兰兹纲领和自守形式理论的两个中心主题。尽管四十多年的进步和无数的突破，在这个程序中的许多问题仍然是开放的，甚至更深层次的问题已经出现。内窥镜理论是函性的一个特殊但非常重要的例子，在过去的30年里吸引了巨大的努力，导致了突破，如基本引理的证明和经典群的自守表示的内窥镜分类。超越这些卓越的成就需要新的技术和想法。近年来，出现了令人兴奋的新想法，这些想法有可能更新我们对整个主题的看法。会议将集中在三个主要议题：（1）相对朗兰兹计划，（2）L-函数的（高）导数的特殊值之间的关系，（3）超越内窥镜和可能的新情况下函。研讨会的细节公布在https://conferences.cirm-math.fr/2154.html.This奖项反映了NSF的法定使命，并已被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估的支持。

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.