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

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. ***

小行星9500882 Effros将继续调查神秘的数学世界， 量子群分析，与他以前的博士生合作， Z.- J.阮。这项工作是基于他的新方法来量化功能 分析-算子空间理论。波帕计划扩大他广泛的 使用分析和分析方法研究快速发展的子因素领域 代数的观点。波帕是为数不多的 致力于子因素理论的分析方面。可以说，这 迄今为止，技术上困难的领域构成了 个话题吧竹崎和几个同事最近 完成了一个中央分类程序，用于离散的 算子代数上的群作用 他想在此基础上再接再厉 通过回到基本上未被探索的持续群体行动领域。 他还计划再次研究他早期的二元性理论， 目前在量子群论中扮演着重要角色。 量子化分析是在1930年由约翰·冯·诺依曼提出的。 为量子力学提供数学框架。这 数学的发展对数学本身产生了深远的影响， 因为它使研究人员能够制定非交换或 许多截然不同的数学学科的“量化”版本。我们 现在有了量子化版本的遍历理论，非交换几何， 阿兰·康纳斯的非对易概率论，丹·沃伊库列斯库的非对易概率论， 和显着的相互作用的算子代数，纽结理论，低 维拓扑学和共形量子场论 由沃恩·琼斯开创 埃弗罗斯、波帕和竹崎一直积极地 参与了一些令人兴奋的新领域的前沿工作， 数学 ***