My research field is probability theory. In particular I am interested in problems related to so-called "Hydrodynamic limit", which is a certain type of space-time scaling limits. Hydrodynamic limit means a method which determines a macroscopic quantity of a microscopic system such as particles systems. To tackle a difficult problem related to Hydrodynamic limit, it is necessary to invoke results on functional analysis or partial differential equations, and to use specific arguments for particle systems and wide knowledge of probability theory. Hydrodynamic limit is formulated as Law of large numbers for a macroscopic quantity such as the number of particle systems or the current for a microscopic system. I am working on related Central limit theorem and Large deviation principle.
In recent years, my another interest is Random topology, which has arisen from the development of Topological data analysis in applied mathematics. I am working on this new research area with my probabilistic technique although this theme is not related to above Hydrodynamic limit deeply.