Combinatorial constructions in geometry and topology

几何和拓扑中的组合构造

• 批准号: 249737-2012
• 负责人: Denham, Graham
• 金额: $ 0.87万
• 依托单位: University of Western Ontario
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=570707
• 关键词: Combinatorial; constructions; geometry; topology

The proposed research is in an area of mathematics known as algebraic or topological combinatorics. The main theme there is an interchange of ideas and techniques: some well-developed, core subjects (algebraic geometry and algebraic topology) have deep and surprising applications to discrete (combinatorial) mathematics, the branch of mathematics that is ubiquitous in areas of computer science and operations research. Going in the other direction, combinatorial methods can often be used to construct particularly interesting families of "test" objects for use as concrete tools in exploring otherwise abstract conceptual landscapes.

这项拟议的研究是在一个被称为代数或拓扑组合学的数学领域进行的。主旋律是思想和技术的交流：一些发展良好的核心学科(代数几何和代数拓扑学)对离散(组合)数学有着深刻而令人惊讶的应用，离散(组合)数学是计算机科学和运筹学领域中普遍存在的数学分支。相反，组合方法通常可以用来构建特别有趣的“测试”对象家族，作为探索其他抽象的概念景观的具体工具。