Special Year in Number Theory and Combinatorics

提案编号：0412622提案标题：数论和组合学的特殊年份2003年12月17日收到主要调查者：F.Garvanco-Pi(S)：Miklos Bona Neil White Richard Crew研究所：佛罗里达大学数学系2004-2005年的特殊年佛罗里达大学数论和组合学专业，有两个平行的课程。2004-05特别年度的数论部分将由两个会议重点介绍：(I)2004年11月举行的国际加数理论会议；以及(Ii)2005年2月举行的国际算术几何会议。特别年方案的组合学部分的亮点将是(Iii)2004年9月举行的几何自动推演研讨会，以及(Iv)2005年3月举行的第三届模式避免置换国际会议。有计划公布这些会议的参考会议记录。这些会议的主题是从我们的研究优势领域中挑选出来的，但涉及更广泛的主题。会议将在全年举行讲座，由杰出的访问数学家讲授最新的研究趋势，以及应能吸引学生的历史讲座。加法数论会议将涉及三个主题：划分和Q系列；哥德巴赫、瓦林型问题和筛子；以及基和密度问题。算术几何会议将专门讨论算术和代数几何中的p-adi方法。几何工作坊中的自动演绎将是一个交流想法和观点的论坛，展示研究成果和进展，并展示几何和自动演绎之间的交集的软件工具。模式避免排列会议讨论的是具有子序列条件的排列的精确和渐近列举和结构分析。这一领域与Young Tableaux、标号树、偏序集和平面映射理论以及排序和搜索有关。数论和组合学的特别年计划将会引起数学以外的研究人员的兴趣，因此将加强与其他学科的联系。数论是研究整数性质的学科，是数学中最古老的分支。我们的数论会议所涵盖的主题，如划分、椭圆曲线和密码学，将会引起物理学家和计算机科学人员的兴趣。组合学是研究离散的对象集合，以及如何有效地对它们进行排列和计数。组合学会议所涵盖的领域将对计算机和工程科学具有吸引力。数论和组合学非常适合吸引非专家和学生注意数学的重大发展。因此，这些领域的历史讲座将使研究生和本科生了解基本思想和概念是如何发展的，这反过来将有助于吸引有才华的学生进入更高级的数学学习。

Proposal Number: 0412622Proposal Title: Special Year in Number Theory and CombinatoricsReceived on 12/17/03Principal Investigator: F. GarvanCO-PI(s): Miklos BonaNeil WhiteRichard CrewInstitution: University of FloridaABSTRACT The 2004-2005 Special Year at the Department of Mathematics, Universityof Florida is in Number Theory and Combinatorics and features twoparallel programs. The Number Theory part of Special Year 2004-05 will be highlighted by two conferences: (i) An International Conference on Additive Number Theory in November 2004, and (ii) An International Conference on Arithmetic Geometry in February 2005. The highlight of the Combinatorics part of the Special Year Program will be (iii) A Workshop on Automated Deduction in Geometry in September 2004, and (iv) The Third International Conference on Pattern AvoidingPermutations in March 2005. There are plans to publish the refereedproceedings of these conferences. Topics for these conferences have been chosen from areas of our research strengths but involve broader themes. The conferences will be augmented by lectures throughout the year on the latest trends in research by eminent visiting mathematicians, as well as History Lectures which should appeal to students. The Additive Number Theory Conference will involvethree main themes: partitions and q-series; Goldbach, Waring type problems, and sieves; and basis and density questions. The Arithmetic Geometry Conference will be devoted to p-adic methods in arithmetic and algebraic geometry. Automated Deduction in Geometry Workshop will be a forum to exchange ideas and views, to present research results and progress, and to demonstrate software tools on the intersection between geometry and automated deduction. The Conference on Pattern Avoiding Permutations is on the exact and asymptotic enumeration and structural analysis, of permutations with subsequence conditions. This area is connected to the theory of Young tableaux, labeled trees, partially ordered sets, and planar maps, as well as sorting and searching. The Special Year Program in Number Theory and Combinatorics will be of interest even to researchers outside of mathematics and therefore will strengthen ties with other disciplines. Number Theory is the study of the properties of whole numbers and is the oldest branch of mathematics. Topics such as partitions, elliptic curves, and cryptography, covered by our conferences in number theory will be of interest to physicists and those in computer science. Combinatorics is the study of discrete collections of objects, and how they can be arrangedand counted efficiently. The areas covered by the conferences in combinatorics will be of appeal to computer and engineering sciences. Number Theory and Combinatorics are ideally suited to attract the attention of non-experts and students to significant developments in mathematics. Thus the History Lectures in these areas will inform graduate and undergraduate students as to how fundamental ideas and concepts developed, and this in turn will help in attracting talented students to take to more advanced study in mathematics.