Open Questions and Recent Developments in Iwasawa Theory

2005年6月，波士顿大学将主办一个为期一周的国际会议，题为“岩泽理论中的未决问题和最新发展”。 在五天的时间里，会议将涵盖岩泽理论的广泛主题，重点是以多种形式和非对易岩泽理论的主要猜想。 岩泽理论在过去的几年里取得了重大进展（例如，斯金纳-乌尔班证明了模形式的分圆主猜想，以及科茨、福谷、加藤、Sujatha和Venjakob提出了一个非阿贝尔主猜想），这使得专家们聚集在一起讨论这些结果并使它们更广泛地提供给数学界变得很重要。 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，每个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论点。岩泽理论是数论的一个子领域，其基本问题将代数信息（例如多项式方程的解）与分析信息（例如微积分产生的函数值）联系起来。 这两个完全不同的观点的融合使岩泽理论成为一个神秘而强大的领域。 人们可以使用岩泽理论来研究各种几何对象的算术，如椭圆曲线。 由于椭圆曲线理论在编码理论和密码学中有应用，岩泽理论的进步可能会导致这两个学科的进步

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