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，波士顿大学将举办为期一周的国际会议，题为“伊瓦沙理论上的开放问题和最新发展”。 在五天的时间里，该会议将涵盖硫磺理论中的广泛主题，并重点介绍其许多阵营和非交流性iwasawa理论的主要猜想。 伊瓦川理论在过去几年中取得了重大进展（例如，Skinner-Urban证明了模块化形式的环球组主要猜想，而Coates，Fukaya，Kato，Sujatha，Sujatha和Venjakob提出的非阿伯里亚主要猜想的提议）使专家们变得更加重要，使这些成果变得更加广泛，并使这些成果变得更加广泛，并使其更加有用，以使其成为数学上的社区。 会议的一个关键方面将强调伊瓦沙理论的未来方向。 的确，将要求每个说话者提出他们认为对领域发展重要的开放问题和猜想。Iwasawa理论是数字理论的子字段，其基本问题将代数信息（例如，与多项式方程的解决方案）与分析信息（例如，函数产生的值）相关联。 这两个不同的想法的合并是使伊瓦泽理论如此神秘而有力的领域的原因。 人们可以使用Iwasawa理论来研究各种几何对象（例如椭圆曲线）的算术。 由于椭圆曲线的理论在编码理论和密码学上都有应用，因此硫磺理论的进步可能会导致这两个主题的进步