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

史塔克猜想起源于20世纪70年代中期的S，至今仍是数论中最深层次的悬而未决的问题之一。泰特1984年关于这一主题的著作为一代研究人员提供了对当时猜想状况的坚实阐述，并为进一步研究奠定了基础。最近，与猜想有关的工作吸引了越来越多的数字理论家，但从来没有关于这一主题的重大会议。NSF的这一奖项将为2002年8月4日至9日在巴尔的摩约翰·霍普金斯大学举行的关于斯塔克猜想及其变体的会议提供主要资金。计划包括上午关于背景和当前研究的全体演讲，然后是下午的贡献演讲。来自不同研究方向的研究人员的聚集应该会导致对各种猜测之间的联系的洞察，并为进一步研究斯塔克猜想的所有方面提供一个理想的平台。特别是，人们预计这次会议将导致一些新的和富有成效的合作，并使研究生在这项研究中有更大的进步。事实上，特别鼓励研究生、初级教员、妇女和传统上代表性不足的少数群体成员参加并申请资助。斯塔克在数论中的猜想表明，高等算术的基本概念背后有令人惊讶和有用的结构等待着人们去发现。在高等算术中，人们试图描述多项式方程的解及其性质。这是数论的代数论方面。这个猜想指出，某些多项式方程的解可以从特定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正是导致重大突破的原因。事实上，这一猜想已经导致了执行某些计算的新的、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.