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The main theme of my research is the theory of operator algebras and their group actions. Although operator algebras are basically represented on infinite dimensional linear spaces, it is important to consider approximations by finite dimensional spaces in several topologies. Often times, an elementary technique of finite dimensional matrices plays a key role. The main goal of my research is to characterize classifiable C*-algebras abstractly. In particular, I am interested in the following problems.

1. Amenable C*-algebras, nuclear dimension, and Toms-Winter conjecture,
2. The classification theory of group actions on the Jiang-Su algebra,
3. Quasidiagonality, Rosenberg conjecture, and Blackadar-Kirchberg conjecture.