Special Year in Number Theory and Combinatorics

数论和组合学的特别年

• 批准号: 0412622
• 负责人: F. Garvan
• 金额: $ 1.5万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-09-01 至 2005-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0412622&HistoricalAwards=false
• 关键词: Special; Year; Number; Theory; Combinatorics

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.

提案编号：0412622提案标题：数论和组合学特别年收到日期：2003年12月17日主要研究者：F。GarvanCO-PI（s）：Miklos BonaNeil WhiteRichard Crew机构：佛罗里达大学摘要 佛罗里达数学系2004-2005年的特殊学年是数论和组合学，有两个并行项目。 2004-05特别年度的数论部分将通过两个会议突出：（i）2004年11月的加法数论国际会议，和（ii）2005年2月的算术几何国际会议。特别年计划的组合数学部分的亮点将是（iii）2004年9月的几何自动演绎讲习班，以及（iv）2005年3月的第三届模式避免排列国际会议。计划出版这些会议的参考记录。这些会议的主题是从我们的研究优势领域中选择的，但涉及更广泛的主题。会议将增加讲座全年研究的最新趋势，由著名的访问数学家，以及历史讲座，这应该吸引学生。 加法数论会议将涉及三个主要主题： 分区和q系列;哥德巴赫，华林型问题，筛;和基础和密度问题。算术几何会议将致力于算术和代数几何中的p-adic方法。 几何自动演绎工作坊将是一个交流思想和观点的论坛，展示研究成果和进展，并展示几何和自动演绎之间交叉的软件工具。 模式避免排列会议是关于具有子序列条件的排列的精确和渐近枚举和结构分析。这一领域与Young tableaux理论、标记树、偏序集、平面映射以及排序和搜索有关。 数论和组合学的特别年计划甚至对数学以外的研究人员也会感兴趣，因此将加强与其他学科的联系。数论是研究整数的性质，是数学最古老的分支。 主题，如分区，椭圆曲线和密码学，涵盖了我们的会议在数论将感兴趣的物理学家和计算机科学。 组合数学是研究对象的离散集合，以及如何有效地对它们进行分类和计数。 在组合学会议所涵盖的领域将呼吁计算机和工程科学。数论和组合数学非常适合吸引非专家和学生对数学重大发展的注意。因此，在这些领域的历史讲座将告知研究生和本科生如何发展的基本思想和概念，这反过来将有助于吸引有才华的学生采取更先进的数学学习。