Noncommutative Analytic Approach for Discrete Group Theory

算子代数理论是分析中研究非交换现象的一个分支。在这个项目中，Ozawa运用了算子代数理论，并研究了离散群理论的泛函分析方面。作为应用，他构造了第一个可服从但非核算子代数的例子。cones嵌入猜想是目前算子代数理论中最重要的猜想。Ozawa证明了这个猜想与量子信息论中一直在研究的Tsirelson猜想是等价的。他还研究了这些猜想的非交换实代数几何方面。

Theory of operator algebras is a branch in Analysis which deals with noncommutative phenomena. In this project, Ozawa applied theory of operator algebras and studied the functional analytic aspects of theory of discrete groups. As an application, he constructed the first example of an amenable but not nuclear operator algebra. Connes's Embedding Conjecture is currently the most important conjecture in theory of operator algebras. Ozawa has proved that this conjecture is equivalent to Tsirelson's Conjecture, which has been being studied in Quantum Information Theory. He also studied the noncommutative real algebraic geometric aspects of these conjectures.