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.

9626698释放了这笔赠款支持德克萨斯大学奥斯汀分校的全球分析和差异几何组。提出的研究集中于数学物理学的分析和代数方面。要追求的研究主题包括：Chern-Simons理论和拓扑量子场理论的结构；无限尺寸可集成系统和非线性schrodinger方程；符号动力学和分支歧管；非层次量子力学中的几何结构。该项目还包括涉及本科生和高中生的教育活动。 量子场理论是理论和数学物理学中的一个活跃领域：最终，该领域的研究人员希望提出一个严格而统一的框架，以解释自然的各种基本力量。可集成的系统构成了动态系统理论中的一个重要子区域 - 动态系统由普通微分方程的系统给出。在这样的系统中，系统随时间发展的速率独立于时间。动态系统用于建模各种自然现象，例如人口增长和天气系统。