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Research Interests: Operator algebras

Research Topic: Type III von Neumann algebras and application to ergodic theory

Previous Affiliation: JSPS Superlative Postdoctoral Fellow

I am interested in the operator algebra theory in mathematics. Roughly speaking, it is a study of matrices of "infinite size." This theory was founded by von Neumann to provide a mathematical framework for quantum mechanics in physics, and it is now also studied by mathematicians from purely mathematical point of view because of its rich structures. In fact, this theory has deep connections with other areas in mathematics, such as K-theory, knot theory, ergodic theory, representation theory, etc. I am particularly interested in ''non-amenable algebras'' which do not appear from the physical viewpoints. As the term ''non-amenable'' indicates, structures of these algebras are quite difficult to understand. Although physical meanings of them are not known, they are very interesting objects for mathematicians and I would like to clarify these mysterious structures.