Research Activity

I am interested in discrete structures behind geometry. I have been studying the following topics.
  1. Logarithmic vector fields and freeness
    I have studied several characterizations of freeness of hyperplanes [2, 3, 4, 13, 14, 21], the Coxeter arrangements in connection with K. Saito's theory of primitive forms [1, 17], and vector bundles associated to log vector fields [6, 8,12]. [22] is a survey paper.
  2. Topology of hyperplane arrangements
    I am mainly interested in the minimality of complex hyperplane arrangements discovered by Dimca, Papadima, and Randell, and its applications. I am studying the description of the minimal CW complex in terms of real structure and applications [5, 7, 10, 16, 20, 23, 24, 28, 29].
  3. Lattice points countings
    In [31, 35], I applied Ehrhart theory to a conjecture by Postnikov-Stanley concerning the distribution of zeros of the characteristic polynomials of Linial arrangements. As a byproduct, a new characterization of the Eulerian polynomial is obtained [36].
  4. Matroids, Tutte polynomials, and their generalizations
    In [38], we introduced G-Tutte polynomial, which provides a unified framework of Tutte, arithmetic Tutte, characteristic quasi-polynomials.
  5. Euler characteristics, categorification of enumerative problems
    I am interested in "Categorification" of enumerative problems [32, 34, 39].
I am also interested in computational complexity of real numbers, especially for the so called "periods" (introduced by Kontsevich and Zagier), the real numbers which have integral expressions.

See also List of papers and Comments (JAPANESE).

Current (June 2022) Students: Yu Tajima (Hokkaido/Osaka), Zixuan Wang (Hokkaido/Osaka) (also ongoing project with S. Sugawara (Hokkaido) and M. Oyama (Hokkaido)).

Former Postdocs: I welcome students who are interested in (at least one of) research areas: combinatorics, algebraic geometry and topology. (01 Apr. 2018)