Mathematical Sciences: Logarithmic Sobolev Inequalities and Knot Theory

数学科学：对数索博列夫不等式和结理论

• 批准号: 8922941
• 负责人: Leonard Gross
• 金额: --
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-01 至 1992-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8922941&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Logarithmic; Sobolev; Inequalities

Professors Gross and King will conduct research in the areas of harmonic analysis and geometrical quantum field theory. Professor Gross' research will be in the flourishing field of logarithmic Sobolev inequalities which he will attempt to prove in various untried circumstances including some infinite dimensional situations. Professor King's research will involve quantum field theory and its relation to geometry and topology. In particular he will use ideas of quantum field theory to investigate the theory of knots, links, and braids in Euclidean three space. Logarithmic Sobolev inequalities have been useful in many areas of mathematics ranging from the theory of smooth surfaces and how they vibrate to how fast systems of various kinds reach equilibrium. The theory of knots, an area within the branch of mathematics called topology, was recently shown to be connected to other formalisms in physics and mathematics, in particular the theory of quantum fields.

格罗斯和金教授将在以下领域进行研究 调和分析和几何量子场论的基础 格罗斯教授的研究将在蓬勃发展的领域， 对数Sobolev不等式，他将试图证明 在各种未经试验的情况下，包括一些无限 维度情境 金教授的研究将涉及 量子场论及其与几何和拓扑的关系。 特别是，他将利用量子场论的思想， 研究欧几里德中的结、连接和辫子的理论 三空间 对数索博列夫不等式在许多方面都很有用 数学领域从光滑表面理论 以及它们如何振动到各种系统到达 均衡 结理论，结的分支内的一个领域 数学中的拓扑学最近被证明是 物理学和数学中的其他形式主义，特别是 量子场论