U.S.-Japan Cooperative Science: Shimura varieties and Automorphic Forms

该奖项支持马里兰州巴尔的摩市约翰霍普金斯大学的Steven Zucker教授和日本京都大学的Hiroyuki Yoshida教授为期三年的合作研究项目。研究人员将进行志村变种和自同构形式的研究。志村变分是对复杂几何的局部对称变分的数值理论阐述。后一种空间的重要性来自于它在数论和模问题中的应用。大多数局部对称变异都是非紧致的，因此有必要研究它们的紧致性。该项目的目标是研究各种紧化和自同构形式之间的相互作用。将有一系列的研讨会，其中一个将对研究生、博士后和教职员工开放。他们还将安排每周的会议和演讲。他们希望促进从事该学科不同方面工作的数学家之间的互动，并交流最新进展。该项目汇集了两个具有互补专业知识和研究能力的实验室的努力。这个领域从复杂几何、代数几何、谐波分析、拓扑和数论（代数和解析）中汲取。根据朗兰兹的猜想，自同构表征理论控制着一大类动机。因此，这个领域在整个数学中占有相当中心的地位。该项目通过博士后和研究生的参与来促进国际人力资源的发展。通过思想和技术的交流，该项目将扩大我们的基础知识基础，促进国际了解与合作。研究结果将发表在国际科学期刊上，并在美国和国外的科学会议上发表。

9909797ZuckerThis award supports a three-year collaborative research project between Professor Steven Zucker of Johns Hopkins University in Baltimore, Maryland and Professor Hiroyuki Yoshida of Kyoto University in Japan. The researchers will be undertaking a study of shimura varieties and automorphic forms. Shimura varieties comprise the number-theoretical elaboration on the locally-symmetric varieties of complex geometry. The importance of the later spaces comes from applications to number theory and moduli problems. Most locally-symmetric varieties are non-compact, so it becomes necessary to study their compactifications. The goal of the project will be research into the interplay between the various compactifications and automorphic forms. There will be a series of workshops, one of which will be accessible to graduate students, postdocs and faculty. They will also arrange for weekly meetings and presentations. They hope to foster interaction between mathematicians working on different aspects of the subject and the communication of recent progress. The project brings together the efforts of two laboratories that have complementary expertise and research capabilities. This field draws from complex geometry, algebraic geometry, harmonic analysis, topology, and number theory (both algebraic and analytic). According to conjecture of Langlands, the theory of automorphic representations controls a large class of motives. Therefore, the field holds a rather central place within mathematics as a whole. The project advances international human resources through the participation of postdocs and graduate students. Through the exchange of ideas and technology, this project will broaden our base of basic knowledge and promote international understanding and cooperation. Results of the research will be published in international scientific journals and also presented at scientific meetings in the U.S. and abroad.