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.

阮先生在过去的几年里，主要研究算子空间的局部理论以及算子空间在抽象调和分析和局部紧量子群中的应用。在这份提案中，他计划继续在这些方向上进行研究，并提出以下研究项目。 (1)研究算子空间的一些局部性质。 (2)研究局部紧量子群的一些问题。(3)研究与Kadison-Singer问题以及Bozejko和Speicher引入的q变形因子有关的一些问题。算子空间理论是近年来发展起来的一个新的研究领域。现代分析。 PI 与其他一些数学家一起为这一领域做出了重大贡献。该提案中提出的项目包含算子空间中的一些重要问题及其在算子代数、抽象调和分析和局部紧量子群中的应用。这些问题的进展将对这些领域产生重大影响。 它还将对量子信息论、非交换几何、几何群论等其他相关领域产生重要影响。该提案中的项目还为 PI 的博士生提供了优秀的资源和研究问题。 PI将继续组织伊利诺伊大学近期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 Wabash 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，可以定期与一些研究人员会面并交流想法。领域的顶尖专家。