One of my main research subjects is singularity theory in mathematics. Roughly speaking, a singularity is a special point that is different from others. Singularities are important objects not only in mathematics but also in various fields of science. In particular, I am studying the geometrical properties of singularities appearing in differentiable maps, and the local properties of curves and surfaces using the tools of singularity theory.

Researches on curves and surfaces using singularity theory can be directly applied to vision science. For example, the contour of a smooth object can be considered as the set of singularities of a projection mapping onto a plane, thus can be studied via singularity theory. Furthermore, in many cases, there is a surface structure behind various data, and the feature of the data is captured by the invariants of the surface. In particular, I believe that singularity theory is a useful tool for the discovery and analysis of feature points in data. I am also engaged in various interdisciplinary collaborative research aiming at practical research results on such applied themes of mathematics.