Research Activity
I am interested in discrete structures behind geometry.
I have been studying the following topics.

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.

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].

Lattice points countings
In [31, 35], I applied Ehrhart theory to a conjecture by
PostnikovStanley 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].

Matroids, Tutte polynomials, and their generalizations
In [38], we introduced GTutte polynomial, which provides a unified
framework of Tutte, arithmetic Tutte, characteristic quasipolynomials.

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 Postdocs and Students:
Ye Liu (PD),
Elisa Palezzato (JSPS),
Kenichiro Arima (PD),
Guo Weili (DC),
Tan Nhat Tran (DC), Ryo Murai (MC), Kentaro Akasaka (MC).
Former Postdocs:
I welcome students who are interested in (at least one of)
research areas: combinatorics, algebraic geometry and topology.
(01 Apr. 2018)