Open Questions and Recent Developments in Iwasawa Theory

岩泽理论的悬而未决的问题和最新进展

• 批准号: 0509836
• 负责人: Robert Pollack
• 金额: $ 1.56万
• 依托单位: Trustees of Boston University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-03-01 至 2006-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0509836&HistoricalAwards=false
• 关键词: Open; Questions; Recent; Developments; Iwasawa

In June of 2005, Boston University will host a weeklong international conference entitled "Open questions and recent developments in Iwasawa theory". Over five days, the conference will cover a broad range of topics in Iwasawa theory with an emphasis towards the main conjecture in its many guises and non-commutative Iwasawa theory. Iwasawa theory has seen major advances in the last few years (e.g. the Skinner-Urban proof of the cyclotomic main conjecture for modular forms and the Coates, Fukaya, Kato, Sujatha and Venjakob proposal of a non-abelian main conjecture) making it important to have experts come together to discuss these results and make them more widely available to the mathematical community. A key aspect of the conference will be an emphasis on the future direction of Iwasawa theory. Indeed, each speaker will be asked to present open questions and conjectures that they feel are important to the development of the field.Iwasawa theory is a subfield of number theory whose fundamental questions relate algebraic information (e.g. solutions to polynomial equations) to analytic information (e.g. values of functions arising from calculus). The merging of these two disparate ideas is what makes Iwasawa theory such a mysterious and powerful field. One can use Iwasawa theory to study the arithmetic of a variety of geometric objects such as elliptic curves. Since the theory of elliptic curves has applications to coding theory and cryptography, advances in Iwasawa theory could lead to advances in these two subjects

2005年6月，波士顿大学将举办一个为期一周的国际会议，题为“岩泽理论的开放性问题和最新发展”。在为期五天的会议中，会议将涵盖岩泽理论的广泛主题，重点是各种形式的主要猜想和非交换的岩泽理论。Iwasawa理论在过去几年中取得了重大进展（例如，模形式的环切主猜想的Skinner-Urban证明以及Coates， Fukaya, Kato， Sujatha和Venjakob提出的非阿贝主猜想），这使得专家聚集在一起讨论这些结果并使其更广泛地应用于数学界变得非常重要。会议的一个关键方面将是强调岩泽理论的未来方向。事实上，每位演讲者都将被要求提出他们认为对该领域的发展很重要的开放性问题和猜想。Iwasawa理论是数论的一个子领域，其基本问题涉及代数信息（如多项式方程的解）和解析信息（如由微积分产生的函数值）。这两种截然不同的思想的融合使岩泽理论成为一个如此神秘而强大的领域。人们可以使用岩泽理论来研究各种几何对象的算法，如椭圆曲线。由于椭圆曲线理论在编码理论和密码学中都有应用，因此岩川理论的进步可能会导致这两个学科的进步