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.

摘要主题研究者：Billey，Sara提案编号：DMS -0800978施工：华盛顿大学：拓扑，Coxeter组和代表理论的计算/组合考虑因素概述了三个领域的雄心勃勃的研究计划攻击问题：亲属性的Grassmannian，基本上，对置换理论和代表性理论启发性启发性启发。 中心主题是通过研究非常具体的poset，weyl群，生成功能和控制微水平结构的分区来促进和理解的中心主题，我们经常忽略了我们对主题的第一个瞥见，而代数组合主义者的核心是通过更精确的构建构建和更加依据的构建构成的哲学，并且可以更加精确地进行计算。 从分析中借用一个术语，该提案是关于``微观局部数学''的。 拟议的所有工作都将在纯数学和理论计算机科学领域产生广泛的影响。 所有提议的工作都将具有计算重点，该焦点将进一步开发计算机证明技术。 所有拟议的工作都将具有人为影响的成分。 PI在各个级别和初级教师的指导学生方面有很强的记录。 该赠款将大大增强华​​盛顿大学组合组合集团的垂直综合研究环境，并为集团提供攻击这些严重问题所需的资源。