Conference on Stark's Conjectures and Related Topics, August 4 - 9, 2002, The Johns Hopkins University

起源于20世纪70年代中期，斯塔克猜想仍然是数论中最深的未解决的问题之一。泰特在1984年出版的关于这个主题的书为一代研究人员提供了当时猜想状态的坚实阐述，并为进一步的研究奠定了基础。与猜想相关的工作最近发展到涉及越来越多的数论，但从来没有一个主要的会议上的主题。这个NSF奖将提供主要资金的会议致力于斯塔克的猜想和它的变化将举行在约翰的霍普金斯大学在巴尔的摩2002年8月4日至9日。计划包括上午专门讨论背景和当前研究的全体会议，然后在下午进行贡献性的演讲。来自不同研究领域的研究人员的聚集应该会导致对不同学科之间联系的深入了解，并为进一步研究斯塔克的所有方面提供理想的平台。特别是，人们会期望这次会议将导致一些新的和富有成效的合作，并在这项研究的研究生更大的involvement。事实上，特别鼓励研究生、初级教师、妇女和传统上代表性不足的少数民族成员参加并申请资助。 斯塔克在数论中的猜想表明，在高等算术的基本概念背后，有着惊人而有用的结构等待被发现。在高等算术中，人们试图描述多项式方程的解及其性质。这是数论的代数方面。该猜想指出，某些多项式方程的解可以从值得到 具体的极限和无穷的总和，这自然涉及到微积分的方法。这是数论的分析方面。因此斯塔克猜想在数学的两个分支：代数和分析之间建立了惊人的联系。理解这种类型的联系正是导致重大突破的原因。事实上，这个猜想已经导致了新的和更有效的方法来执行某些计算。

Originating in the mid-1970's, Stark's Conjecture remains one of the deepest unsolved problems in number theory. Tate's 1984 book on the sub-ject provided a generation of researchers with a solid exposition of the state of the conjecture at that time, and a foundation for further in-vestigation. Work related to the conjecture has recently grown to in-volve more and more number theorists, but there has never been a major conference on the subject. This NSF award will provide major funding for a conference dedicated to Stark's conjecture and its variations tobe held at John's Hopkins University in Baltimore August 4-9, 2002. Plans include plenary talks devoted to background and current researchin the mornings, followed by contributed talks in the afternoons.The gathering of researchers from various strands of inquiry shouldlead to insight into the links between various conjectures and provide an ideal platform for further research on all aspects of Stark's Conj-ecture. In particular, one would expect that this conference would lead to a number of new and fruitful collaborations, and to the greater in-volvement of graduate students in this research. Indeed, graduate stu-dents, junior faculty members, women, and members of traditionally under-represented minorities are especially encouraged to attend and to apply for funding. Stark's conjecture in number theory suggests that there is astonishing and useful structure waiting to be discovered behind the fundamental concepts of higher arithmetic. In higher arithmetic, one seeks to de-scribe the solutions of polynomial equations and their properties. This is the algebraic side of number theory. The conjecture states that the solutions of certain polynomial equations can be obtained from the values of specific limits and infinite sums which naturally involve the methods of calculus. This is the analytic side of number theory. Thus Stark's conjecture makes a striking connection between two branches of mathematics:algebra and analysis. Understanding this type of connection is just whatleads to major breakthroughs. Indeed, the conjecture has already led to new and more efficient methods of performing certain computations.