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

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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.