Mathematical Sciences: Topology, Geometry and Physics

数学科学：拓扑、几何和物理

• 批准号: 9626698
• 负责人: Daniel Freed
• 金额: $ 26.84万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-01 至 2001-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9626698&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topology; Geometry; Physics

9626698 Freed This grant supports the global analysis and differential geometry group at the University of Texas at Austin. The proposed research concentrates on the analytic and algebraic aspects of mathematical physics. Research topics to be pursued include: Chern-Simons theory and the structure of topological quantum field theory; infinite dimensional integrable systems and nonlinear Schrodinger equations; symbolic dynamics and branched manifolds; geometrical structures in nonrelativisitic quantum mechanics. The project also includes educational activities involving undergraduate students and high school students. Quantum field theory is an active area within theoretical and mathematical physics: ultimately, the researchers in this field hope to come up with a rigorous and unifying framework explaining various basic forces of nature. Integrable systems constitute an important subarea within the theory of dynamical systems - a dynamical system is given by a system of ordinary differential equations; in such a system the rate at which the system evolves over time is independent of time. Dynamical systems are used to model various natural phenomena such as population growth and weather systems.

小行星9626698 该补助金支持德克萨斯大学奥斯汀分校的全球分析和微分几何组。拟议的研究集中在数学物理的分析和代数方面。研究课题包括：陈-西蒙斯理论和拓扑量子场论的结构;无限维可积系统和非线性薛定谔方程;符号动力学和分支流形;非相对论量子力学的几何结构。该项目还包括涉及本科生和高中生的教育活动。 量子场论是理论物理和数学物理中的一个活跃领域：最终，该领域的研究人员希望提出一个严格和统一的框架来解释自然界的各种基本力。可积系统构成了动力系统理论中的一个重要子领域--动力系统由一个常微分方程系统给出;在这样的系统中，系统随时间演化的速率与时间无关。动力系统被用来模拟各种自然现象，如人口增长和天气系统。