Computational/Combinatorial Considerations In Topology, Coxeter Groups, and Representation Theory

拓扑、Coxeter 群和表示论中的计算/组合考虑

• 批准号: 0800978
• 负责人: Sara Billey
• 金额: $ 18.9万
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-06-15 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0800978&HistoricalAwards=false
• 关键词: Computational; Combinatorial; Considerations; Topology; Coxeter

ABSTRACTPrincipal Investigator: Billey, Sara Proposal Number: DMS - 0800978Institution: University of WashingtonTitle: Computational/Combinatorial Considerations In Topology, Coxeter Groups, and Representation TheoryThis proposal outlines an ambitious research program attacking problems in three areas: the affine Grassmannian, fundamentals of permutations, and representation theory inspired by complexity theory. The central theme is to facilitate computation and understanding in these areas through study of very specific posets, Weyl groups, generating functions, and partitions controlling the micro level structures which we often overlook on the first glimpse of the subjects.At the heart of algebraic combinatorics is the philosophy that every aspect of mathematics can be made more precise, more concrete and more computationally feasible by identifying key combinatorial structures. Borrowing a term from analysis, this proposal is about ``micro local mathematics''. All of the work proposed will have a broad impact in several areas of pure math and theoretical computer science. All of the proposed work will have a computational focus which will further develop computer proof techniques. All of the proposed work will have a human impact component. The PI has a strong track record of mentoring students at all levels and junior faculty. This grant will greatly enhance the vertically integrated research environment in the Combinatorics Group at the University of Washington and give the group the resources needed to attack these hard problems.

主要研究者：Billey，Sara 提案编号：DMS -0800978机构：华盛顿大学标题：计算/组合考虑拓扑，考克斯特群，和表示理论这一建议概述了一个雄心勃勃的研究计划，在三个领域的攻击问题：仿射格拉斯曼，置换的基本原理，和表示理论的复杂性理论的启发。 中心主题是通过研究非常具体的偏序集，外尔群，生成函数和控制微观层次结构的分区来促进这些领域的计算和理解，这些结构我们在第一眼看到这些学科时经常忽略。代数组合学的核心是数学的每个方面都可以变得更精确的哲学，通过识别关键的组合结构来更具体和更计算可行。 借用一个分析术语，这个建议是关于“微观地方自治”的。 所有提出的工作将在纯数学和理论计算机科学的几个领域产生广泛的影响。 所有提出的工作将有一个计算的重点，这将进一步发展计算机证明技术。 所有拟议的工作都将有一个人的影响部分。 PI在指导各级学生和初级教师方面有着良好的记录。 这笔赠款将大大提高华盛顿大学组合学小组的垂直整合研究环境，并为该小组提供解决这些难题所需的资源。