Combinatorial and Algebraic Aspects of Varieties

品种的组合和代数方面

• 批准号: 1101017
• 负责人: Sara Billey
• 金额: $ 45万
• 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: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1101017&HistoricalAwards=false
• 关键词: Combinatorial; Algebraic; Aspects; Varieties

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. This proposal addresses several specific problems that span a wide range of mathematics including topology, algebraic geometry, representation theory, statistics, computer science and combinatorics. The central theme is to facilitate computation and understanding in these areas. The four areas of research include varieties with combinatorial structures, k-Schur functions, branched polymers, and combinatorial/statistical algorithms for analyzing ordered data.The work proposed will have a broad impact in several areas of pure math, theoretical physics, computer science and statistics. All of the proposed work will have a computational focus which will further develop algorithms and proof techniques. All of the proposed work will have a human impact component through teaching and mentoring of undergraduates, graduate students and postdocs doing research. In terms of education, the PI has initiated a service learning course to address problems in non-profit organizations and small businesses in our community through mathematics.

代数组合主义者的核心是通过识别关键组合结构来使数学的每个方面都可以使数学的每个方面更加精确，更具体和计算。 该建议解决了跨越广泛数学的几个特定问题，包括拓扑，代数几何，表示理论，统计学，计算机科学和组合学。 中心主题是促进这些领域的计算和理解。 研究的四个领域包括具有组合结构，K-Schur功能，分支聚合物以及用于分析有序数据的组合/统计算法的品种。所提出的工作将对纯数学，理论物理学，计算机科学和统计的多个领域产生广泛的影响。 所有提议的工作都将具有计算重点，该计算将进一步开发算法和证明技术。 所有拟议的工作将通过教学和指导本科生，研究生和博士后进行研究来具有人为影响的成分。 在教育方面，PI启动了一项服务学习课程，以通过数学来解决我们社区中非营利组织和小型企业的问题。