Mathematical Sciences: Topics in Modern Analysis

数学科学：现代分析主题

• 批准号: 9303386
• 负责人: Marc Rieffel
• 金额: $ 7.73万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-05-15 至 1996-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9303386&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Modern; Analysis

Rieffel will continue his investigation of C*-algebraic quantization. Topics to be studied include quantization and quantum groups, aspects of quantum topology and differential geometry, and harmonic analysis on Lie groups. Attention will also be given to relationships with applications in such areas as quantum mechanics and field theory, and signal processing and pattern recognition. The general area of mathematics of this project has its basis in the theory of algebras of Hilbert space operators. Operators can be thought of as finite or infinite matrices of complex numbers. Special types of operators are often put together in an algebra, naturally called an operator algebra. These abstract objects have a surprising variety of applications. For example, they play a key role in knot theory, which in turn is currently being used to study the structure of DNA, and they are of fundamental importance in noncommutative geometry, which is becoming increasingly important in physics.

Rieffel将继续他对C*-代数的研究 量子化 要研究的主题包括量化和 量子群，量子拓扑学和微分学的各个方面 李群的调和分析。 注意力也将 与应用程序的关系， 量子力学和场论，信号处理， 模式识别 这个项目的一般数学领域有其基础 在Hilbert空间算子代数理论中。 运营商 可以被认为是复数的有限或无限矩阵 号码 特殊类型的运算符通常放在 代数，自然称为算子代数。 这些抽象 物体的应用范围之广令人惊讶。 比如说， 它们在纽结理论中起着关键作用，而纽结理论目前 被用来研究DNA的结构， 在非对易几何中的重要性， 在物理学中变得越来越重要。