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 .

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品种和痕量公式以及（ii）的一致性和Galois表示。 这些主题，尤其是它们的互动，肯定会成为21世纪开放几十年中自动形式和数字理论的许多研究活动的中心。 IHP的活动将使这些领域的世界领导人聚集在一起。 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. 该计划的范围鼓励在两个主要领域的界面上进行研究的新指导，并参与将为年轻的研究人员提供独特的机会，以在其职业生涯的早期阶段在这一重要领域发展专业知识。 在20世纪后期，数学方面的两个主要发展是兰兰兹（Langlands）自动形式/代表理论的计划，以及菲尔玛（Fermat）的最后定理和taniyama-shimura猜想的威尔斯和泰勒·韦尔斯（Wiles and Taylor-Wiles）证明。这些进步（与数字理论和几何形状相关，实际上都非常紧密地联系在一起，目前正在进行这两个领域的技术结合。最终的领域将是21世纪前几十年中数学研究活动的主要领域之一。该研究计划于2000年春季学期在巴黎的亨利·庞卡里（Henri Poincare）进行，并以全球领导人的讲座课程为中心，提供了无与伦比的愿景和洞察力。 NSF赠款奖将为来自美国数学商业的年轻研究人员提供资金，以参加IHP计划，因此将有助于确保在这些新发展中的这些新发展方面的强大专业知识。 该奖项得到了数学科学系（代数和数理论计划），国际计划的分区（西欧计划）和数学和物理科学局的多学科活动办公室的支持。