Shimura Varieties, the Trace Formula, Congruences and Galois Representations

志村簇、迹公式、同余式和伽罗瓦表示法

• 批准号: 0071404
• 负责人: Freydoon Shahidi
• 金额: $ 4.2万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-05-15 至 2000-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0071404&HistoricalAwards=false
• 关键词: Shimura; Varieties; Trace; Formula; Congruences

Shimura varieties, the trace formula, congruences and Galois representationsStephen S. Kudla (University of Maryland)Freydoon Shahidi (Purdue University)This project will provide support allowing young researchers from the US mathematical community to benefit from participation in the special program at the Institute Henri Poincare (IHP) in Paris in the spring semester 2000. This program focuses on two topics: (i) Shimura varieties and the trace formula and (ii) congruences and Galois representations. These topics, and particularly their interaction, will certainly be at the center of much of the research activity in automorphic forms and number theory in the opening decades of the 21st century. The activity at IHP will bring together the world leaders in these areas. The program will center around a series of lecture `courses' covering the latest developments concering the trace formula, endoscopy, the fundamental lemma, L functions for Shimura varieties, global and local Langlands functoriality, Galois representations, p-adic Hecke algebras, p-adic modular forms, rigid analysis, the local Langlands correspondence and the geometric Langlands correspondence. The scope of the program encourages new directions for research at the interface of the two major fields and participation will provide young researchers a unique opportunity to develop expertise in this important area at an early stage in their careers. Two major developments in mathematics in the later part of the 20th century are the Langlands program in automorphic forms/representation theory and the Wiles and Taylor-Wiles proof of Fermat's Last Theorem and the Taniyama-Shimura conjecture. These advances, relating number theory and geometry, are in fact very closely linked, and a vigorous development of the union of the techniques from the two areas is currently taking place. The resulting field will be one of the main arenas of research activity in mathematics in the first decades of the 21st century. The research program taking place at the Institute Henri Poincare in Paris in the spring semester 2000 and centered around lecture courses by the world leaders provides an unparalleled level of vision and insight. This NSF Grant award will provide funding for young researchers from the US mathematical commmunity to participate in the IHP program, and hence will help to ensure a strong level of US expertise in these new developments in number theory. This award is being supported by the Division of Mathematical Sciences (Algebra and Number Theort program), the Divison of International Programs (Western Europe Program), and the Office of Multidisciplinary Activities of the Mathematical and Physical Sciences Directorate .

志村簇、迹公式、同余式和伽罗瓦表示Stephen S. Kudla（马里兰大学）Freydoon Shahidi（普渡大学）该项目将提供支持，让美国数学界的年轻研究人员从参与亨利研究所的特别项目中受益庞加莱 (IHP) 于 2000 年春季学期在巴黎举行。该课程重点关注两个主题：(i) Shimura 簇和迹公式以及 (ii) 同余和伽罗瓦表示。 这些主题，特别是它们的相互作用，无疑将成为 21 世纪初期自守形式和数论研究活动的中心。 国际水文计划的活动将汇集这些领域的世界领导人。该计划将以一系列讲座“课程”为中心，涵盖有关迹公式、内窥镜检查、基本引理、Shimura簇的L函数、全局和局部朗兰兹函数性、伽罗瓦表示、p进赫克代数、p- adic模形式、刚性分析、局部朗兰兹对应和几何朗兰兹对应。 该计划的范围鼓励在两个主要领域的交叉领域进行新的研究方向，参与将为年轻研究人员提供独特的机会，让他们在职业生涯的早期阶段发展这一重要领域的专业知识。 20 世纪后期数学的两个重大发展是自守形式/表示论中的朗兰兹纲领以及费马大定理和谷山-志村猜想的怀尔斯和泰勒-怀尔斯证明。这些与数论和几何相关的进步实际上是紧密相连的，并且这两个领域的技术的结合目前正在蓬勃发展。由此产生的领域将成为 21 世纪头几十年数学研究活动的主要领域之一。该研究项目于 2000 年春季学期在巴黎 Henri Poincare 研究所进行，以世界领导人的讲座课程为中心，提供了无与伦比的远见和洞察力。这项 NSF 拨款将为美国数学界的年轻研究人员参与 IHP 项目提供资金，从而有助于确保美国在数论新发展方面的专业知识达到高水平。 该奖项得到了数学科学部（代数和数论项目）、国际项目部（西欧项目）以及数学和物理科学理事会多学科活动办公室的支持。