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

斯塔克猜想起源于20世纪70年代中期，至今仍是数论中最深刻的未解决问题之一。泰特在1984年出版的关于这一主题的书，为当时的一代研究者提供了对这一猜想的坚实阐述，并为进一步的调查奠定了基础。最近，越来越多的数论学家参与到与这一猜想相关的工作中来，但从未召开过关于这一主题的大型会议。这项NSF奖将为一个致力于Stark猜想及其变体的会议提供主要资金，该会议将于2002年8月4日至9日在巴尔的摩的约翰霍普金斯大学举行。计划包括上午专门讨论背景和当前研究的全体会议，然后是下午的专题会议。来自不同领域的研究人员聚集在一起，应该能够深入了解各种猜想之间的联系，并为进一步研究斯塔克猜想的各个方面提供一个理想的平台。特别是，人们期望这次会议将导致一些新的和富有成效的合作，并使研究生更多地参与这项研究。事实上，研究生、初级教员、女性和传统上代表性不足的少数民族的成员被特别鼓励参加并申请资助。斯塔克的数论猜想表明，在高等算术的基本概念背后，有一种惊人而有用的结构等着我们去发现。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由特定的极限和无穷和的值得到，这自然涉及到微积分的方法。这是数论的分析方面。因此，斯塔克的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会带来重大突破。事实上，这个猜想已经导致了执行某些计算的新的和更有效的方法。

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.