The central object of my research is the hyperplane arrangement. A hyperplane arrangement is a collection of (n-1)-dimensional subspaces in a n-dimensional space. Such objects appear many area of mathematics. Recently, I am mainly working in the following topics.

(1) The freeness of the module of logarithmic vector fields and the construction of the basis.

(2) Topology of the Milnor fiber and covering spaces.

(3) Lattice points counting and the characteristic quasi-polynomials.

(1) has connections with algebraic geometry and representation theory, and recently, is influenced by the study of quantum integrable systems. In (2), the icosidodecahedral arrangement (Figure) plays crucial role in recent studies. (3) has very rich connections with many other topics such as the theory of polytopes, arrangements of tori, and generalizations of the notion of Tutte polynomial for graphs and matroids. I am also interested in the notion of the magnitude of metric spaces introduced by categorists, and more generally, categorification of combinatorial phenomena. My interests also include the notion of “periods” that are real numbers with integral expressions.