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

9909797 Zucker该奖项支持马里兰州巴尔的摩约翰霍普金斯大学的Steven Zucker教授和日本京都大学的Hiroyuki Yoshida教授之间为期三年的合作研究项目。 研究人员将进行志村品种和自守形式的研究。 志村变种包括复杂几何的局部对称变种的数论阐述。 后来的空间的重要性来自数论和模问题的应用。 大多数局部对称簇都是非紧的，因此研究它们的紧化就变得很有必要。 该项目的目标将是研究各种紧化和自守形式之间的相互作用。 将有一系列的研讨会，其中一个将是研究生，博士后和教师访问。 他们还将安排每周会议和演讲。他们希望促进数学家之间的互动工作的不同方面的问题和沟通的最新进展。 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。 这一领域借鉴了复几何、代数几何、调和分析、拓扑学和数论（代数和解析）。 根据朗兰兹的猜想，自守表象理论控制着一大类动机。 因此，该领域在整个数学中占有相当重要的地位。 该项目通过博士后和研究生的参与促进国际人力资源。通过交流思想和技术，该项目将扩大我们的基础知识，促进国际理解与合作。 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.