Mathematical Sciences: Quantized Analysis

数学科学：量化分析

• 批准号: 9500882
• 负责人: Masamichi Takesaki
• 金额: $ 43.29万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1999-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500882&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Quantized; Analysis; Mathematical; Sciences; Quantized; Analysis

9500882 Effros Effros will continue to investigate the mysterious mathematical world of quantum group analysis, in collaboration with his former Ph. D student Z.-J. Ruan. This work is based on his new approach to quantizing functional analysis - the theory of operator spaces. Popa plans to broaden his wide-ranging studies in the rapidly evolving field of subfactors, using both analytic and algebraic points of view. Popa is one of very few researchers who has been working on theanalytical aspects of subfactor theory. It may be argued that this technically difficult area has thus far constituted the deepest aspect of the subject. Takesaki, together with several coworkers, has very recently completed one of the central classification programs for discrete amenable group actions on operator algebras. He would like to build on this success by returning to the largely unexplored area of continuous group actions. He also plans to work once again on his earlier theory of duality, which is currently playing a major role in quantum group theory. Quantized analysis was introduced in the 1930's by John von Neumann in order to provide a mathematical framework for quantum mechanics. This development has had a profound effect on the field of mathematics itself, since it has enabled researchers to formulate non-commutative or "quantized" versions of many quite distinct mathematical disciplines. We now have quantized versions of ergodic theory, the non-commutative geometry of Alain Connes, the non-commutative probability theory of Dan Voiculescu, and the remarkable interactions of operator algebras, knot theory, low dimensional topology, and conformal quantum field theory in large part pioneered by Vaughan Jones. Effros, Popa and Takesaki have been actively involved in working on the frontier of some of these exciting new areas of mathematics. ***

9500882 EFFROS EFFROS将继续与他的前博士Z.-J.合作调查量子组分析的神秘数学世界。鲁恩。这项工作是基于他量化功能分析的新方法 - 操作员空间的理论。 POPA计划使用分析和代数观点，扩大他在快速发展的子因子领域的广泛研究。 Popa是少数从事亚基理论的研究方面的研究人员之一。可以说，迄今为止，这个技术困难的领域构成了该主题的最深处。 Takeaki与几个同事一起，最近完成了一项中央分类计划，用于离散的操作员代数行动。 他想通过返回持续的小组行动的很大程度上未开发的领域来建立成功。 他还计划再次研究他较早的二元理论，该理论目前在量子群体理论中发挥了重要作用。 约翰·冯·诺伊曼（John von Neumann）在1930年代引入了量化分析，以便为量子力学提供数学框架。这种发展对数学本身的领域产生了深远的影响，因为它使研究人员能够制定许​​多完全不同的数学学科的非交互或“量化”版本。现在，我们已经量化了千古理论的版本，Alain Connes的非交通性几何形状，Dan Voiculescu的非交互性概率理论以及操作员代数的显着相互作用，结理论，低维拓扑结构，低维拓扑结构，以及在Vaughan Jones的大型部分中的整形量子理论。 Effros，Popa和Takeaki一直积极参与这些令人兴奋的新数学领域的边界。 ***