Graphs and Patterns in Mathematics and Theoretical Physics

数学和理论物理中的图形和模式

• 批准号: 0107455
• 负责人: Mikhail Lyubich
• 金额: $ 7万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-09-01 至 2003-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0107455&HistoricalAwards=false
• 关键词: Graphs; Patterns; Mathematics; Theoretical; Physics

AbstractAward: DMS-0107455Principal Investigator: Mikhail LyubichThe International Conference on Graphs and Patterns inMathematics and Theoretical Physics at SUNY Stone Brook in 2001will bring together researchers in several branches ofmathematics and theoretical physics in which graphs play acentral role, hoping to encourage fruitful interactions betweenthese fields. This conference is a celebration of DennisSullivan's sixtieth birthday and addresses some of the topics ofrecent interest to Sullivan. Themes to be emphasized include (1)graphs and algebra, (2) graphs and discrete Riemannian geometryand discrete gauge theory, (3) graphs and bifurcation patterns indynamical systems, (4) graphs and quantum field theory andtopology. Minicourses on conference topics will be pointedtowards graduate students and junior researchers.A graph in the sense used in the title of this conference is adata structure consisting of some number of "vertices," usuallydrawn as dots, joined by "edges," usually drawn as curvesbeginning at one vertex and ending at another. This kind ofgraph is a common combinatorial structure, encountered every dayin problems of transportation and scheduling (consider a networkof roads or telephone lines, for example), but useful in manyless obvious ways. Some of the recent uses of graphs in geometryand physical theory grow out of Richard Feynman's celebrated ideaof describing parts of quantum theory with graphs that representpossible lifetimes for a particle in space-time. Feynman'snotion that a quantum theoretic quantity may represent a sum overall possible histories is reduced from a large, continuouscalculation to a summation indexed by the different possibleFeynman graphs. In a similar manner, modern geometers andphysicists are exploring ways to work with the very largecollections of all possible geometric structures on a particularspace by reducing to manipulations of a family of graphs.

摘要奖：DMS-0107455 首席研究员：Mikhail Lyubich 2001 年在纽约州立大学斯通布鲁克分校举行的国际数学和理论物理图形与模式会议将汇集数学和理论物理多个分支的研究人员，其中图形发挥着核心作用，希望鼓励这些领域之间富有成效的互动。 这次会议是为了庆祝丹尼斯·沙利文的六十岁生日，并讨论了沙利文最近感兴趣的一些话题。 需要强调的主题包括（1）图和代数，（2）图和离散黎曼几何和离散规范理论，（3）动态系统中的图和分岔模式，（4）图和量子场论和拓扑。 关于会议主题的迷你课程将针对研究生和初级研究人员。本次会议标题中使用的图形是一种数据结构，由一定数量的“顶点”组成，通常绘制为点，由“边”连接，通常绘制为曲线从一个顶点开始并在另一个顶点结束。 这种图是一种常见的组合结构，每天在运输和调度问题中都会遇到（例如，考虑道路或电话线网络），但在很多方面都很有用。 最近图形在几何和物理理论中的一些应用源于理查德·费曼的著名思想，即用代表时空粒子可能寿命的图形来描述量子理论的各个部分。 费曼的概念，即量子理论量可以代表所有可能历史的总和，从大型连续计算简化为由不同可能的费曼图索引的总和。 以类似的方式，现代几何学家和物理学家正在探索通过减少对一系列图的操作来处理特定空间上所有可能的几何结构的巨大集合的方法。