Mathematical Sciences: Combinatorial Methods in Algebra and Geometry; Macdonald Polynomials, Diagonal Harmonics, and the Hilbert Scheme

数学科学：代数和几何的组合方法；

• 批准号: 9400934
• 负责人: Mark Haiman
• 金额: $ 6.68万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400934&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Combinatorial; Methods; Algebra

9400934 Haiman This project involves research into modules associated with the Macdonald polynomials and the module of diagonal harmonics. The work promises to establish new relationships between these objects and other parts of algebraic combinatorics and algebraic geometry. Preliminary work has already established the framework for the connections and has produced important new algebraic identities. This research falls in the broad category of combinatorics, which is one of the most active fields in today's mathematics. At its roots, combinatorics is the study of systematic counting. Counting can be incredibly difficult when the objects are difficult to list, and combinatorists look for general methods for overcoming these difficulties. Today's combinatorics makes use of a wide variety of the most advanced and modern mathematical techniques. Although its roots go back several centuries, the field has had an explosive development in the past few decades. This growth comes from its importance in communications and information technology and from the success of modern techniques to problems of counting.

9400934海曼该项目涉及研究与MacDonald多项式相关的模块和对角谐波模块。 这项工作有望在这些对象与代数组合学和代数几何形状之间建立新的关系。 初步工作已经建立了连接的框架，并产生了重要的新代数身份。 这项研究属于广泛的组合学类别，这是当今数学中最活跃的领域之一。在其根基上，组合学是对系统计数的研究。 当对象难以列出，并且组合主义者寻找克服这些困难的一般方法时，计数可能非常困难。 当今的组合技术利用了各种最先进和现代的数学技术。 尽管它的根源可以追溯到几个世纪，但在过去的几十年中，该领域的发展发展了。 这种增长源于其在通信和信息技术中的重要性，以及现代技术的成功到计数问题。