U.S.-Japan Cooperative Research: Primes and Knots

0124616 Morava该奖项支持美国科学家参与美国- 2003年3月15日至22日在马里兰州巴尔的摩的约翰霍普金斯大学举行的关于素数和纽结的日本研讨会。 共同组织者是约翰霍普金斯大学的Jack Morava教授和日本东京大学的Toshitake Kohno教授。 素数理论和纽结理论也许是代数和拓扑学中最受尊敬的分支，而且在许多方面，它们仍然是最容易理解的。 然而，直到最近，研究人员才开始通过数域的伽罗瓦群和环补的基本群之间的类比来认识它们之间的深层关系。 该主题的优点是可以从多个方向和多个层面进行讨论。 纽结理论和素数理论都是直观的，与会者希望这次研讨会能够促进这些领域研究人员之间的共同语言的发展。 一个素数就像一个纽结，而由代数整数生成的理想就像一个嵌入曲面的边界。 在这两个主题中，交换结构之间的关系，如亚历山大不变量，是相对较好的理解，和当前的研究中心更深层次的非交换问题;例如，现在已知的是，{5，41，61}是第一组博罗米安素数（其中没有两个是非平凡联系，但所有三个）。 研讨会的组织者作出了特别努力，让年轻的研究人员和研究生既作为与会者又作为观察员参加。 与日本专家在这一领域的想法和数据交流将使美国参与者能够推进自己的工作，并为未来的合作项目奠定基础。 将在万维网上传播关于讨论会的资料。

0124616MoravaThis award supports the participation of American scientists in a U.S.-Japan seminar on primes and knots to be held at the Johns Hopkins University in Baltimore, Maryland from March 15-22, 2003. The co-organizers are professors Jack Morava of the Johns Hopkins University and Professor Toshitake Kohno at the University of Tokyo in Japan. The theory of primes and the theory of knots are perhaps the most venerated branches of algebra and of topology, and in many ways, they are both still the most accessible. However, it is only relatively recently that researchers have begun to perceive deep relations between them, via analogies between the Galois groups of number fields and the fundamental groups of link complements. The topic has the advantage of being approachable from many directions and on many levels. The theory of knots and the theory of primes are both intuitively accessible, and the participants expect this seminar to foster the development of a common language between researchers in these areas. A prime resembles a knot, and the ideal generated by an algebraic integer is like the boundary of an embedded surface. In both subjects, relations between abelian constructions such as Alexander invariants are relatively well-understood, and much current research centers on deeper nonabelian questions; for example, it is now known that {5, 41, 61} is the first set of Borromean primes (in which no two are nontrivially linked, but all three are). Seminar organizers have made a special effort to involve younger researchers and graduate students as both participants and observers. The exchange of ideas and data with Japanese experts in this field will enable U.S. participants to advance their own work, and will set the stage for future collaborative projects. Dissemination of information on the seminar will be available on the World Wide Web.