Algebraic combinatorics and its application to algebraic geometry and low dimensional topology

代数组合及其在代数几何和低维拓扑中的应用

• 批准号: 8235-2011
• 负责人: Jackson, David
• 金额: $ 1.31万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2011
• 资助国家: 加拿大
• 起止时间: 2011-01-01 至 2012-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=474351
• 关键词: Algebraic; combinatorics; its; application; algebraic

Since about the 1980's there has been a long period of remarkable and intense activity in modern geometry, spurred on by the deep connexions with mathematical physics. For the same reason, there were advances in Modern Knot Theory, prompted partly by the occurrence of a particular fundamental equation, the Yang-Baxter Equation, in both mathematical physics and knot theory. As research progressed in these areas, it became increasingly apparent that deeply within questions about individual knot invariants lay new questions of great complexity about Vassiliev invariants, and aggregates of new objects, or diagrams, constrained by complex relations. These new questions are essentially combinatorial in nature, and may be expressed abstractly, without reference to their original context. An instance of such a diagram is the Feynman diagram from quantum field theory.

大约自20世纪80年代以来，在与数学物理的深刻联系的推动下，现代几何在很长一段时间里出现了显著而激烈的活动。出于同样的原因，现代结理论也取得了进步，部分原因是在数学物理和结理论中出现了一个特殊的基本方程，即杨-巴克斯特方程。随着这些领域的研究进展，越来越明显的是，在关于单个结不变量的问题的深处，存在着关于瓦西里耶夫不变量的新问题，以及受复杂关系约束的新对象或图的集合。这些新问题本质上是组合的，可以抽象地表达，而不参考它们的原始背景。这种图的一个例子是量子场论中的费曼图。