Operator Spaces and Locally Compact Quantum Groups

算子空间和局部紧量子群

• 批准号: 0901395
• 负责人: Zhong-Jin Ruan
• 金额: $ 22.27万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-01 至 2013-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0901395&HistoricalAwards=false
• 关键词: Operator; Spaces; Locally; Compact; Quantum

RuanDuring the last few years, the PI has focused his research on the local theory of operator spaces and the applications of operator spaces to abstract harmonic analysis and locally compact quantum groups. In this proposal, he plans to continue his research in these directions and he proposes the following research projects. (1) Investigate some local properties of operator spaces. (2) Investigate some problems on locally compact quantum groups.(3) Investigate some problems related to Kadison-Singer problem and the q-deformation factors introduced by Bozejko and Speicher.The theory of operator space theory is a recently developed new research area in modern analysis. The PI, together with some other mathematicians, has made significant contributions to this area. The projects proposed in this proposal contain some important questions in operator spaces, and their applications to operator algebras, abstract harmonic analysis, and locally compact quantum groups. The progress on these problems will have significant impact to these areas. It will also have important impact to some other related areas such as quantum information theory, noncommutative geometry, and geometric group theory. Projects in this proposal also provide excellent resources and research problems for PI's Ph.D students. The PI will continue to organize learning seminars on recent research progress at the University of Illinois. This will encourage and attract his students to get involved in these research projects.The PI will also continue to organize Wabash Seminar and Miniconference, which has provided a very unique opportunity for his students, postdocs, and visitors to regularly meet and exchange ideas with some leading experts in the fields.

阮在过去的几年里，PI专注于他的研究算子空间的局部理论和算子空间的应用，以抽象调和分析和局部紧量子群。在这份提案中，他计划继续在这些方向上进行研究，并提出了以下研究项目。 (1)研究算子空间的一些局部性质。 (2)研究了局部紧量子群的一些问题。(3)研究了与Kadison-Singer问题有关的一些问题以及Bozejko和Speicher引入的q-形变因子。算子空间理论是现代分析中一个新的研究领域。 PI，连同其他一些数学家，作出了重大贡献，这一领域。在这个建议中提出的项目包含了一些重要的问题，在算子空间，及其应用到算子代数，抽象调和分析，局部紧量子群。这些问题的进展将对这些领域产生重大影响。 它对量子信息论、非对易几何、几何群论等相关领域也将产生重要影响。本计划书中的项目也为PI的博士生提供了优秀的资源和研究问题。研究所将继续在伊利诺伊大学举办关于最新研究进展的学习研讨会。这将鼓励和吸引他的学生参与这些研究项目。PI还将继续组织瓦巴什研讨会和小型会议，这为他的学生，博士后和访客提供了一个非常独特的机会，定期与该领域的一些领先专家会面和交流思想。