Noncommutative Analytic Approach for Discrete Group Theory

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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.