I am interested in discrete structures behind geometry.
I have been studying the following topics.
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.
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].
 is a survey paper.
Topology of hyperplane arrangements
I am mainly interested in the minimality of complex hyperplane arrangements
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
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 .
Matroids, Tutte polynomials, and their generalizations
In , we introduced G-Tutte polynomial, which provides a unified
framework of Tutte, arithmetic Tutte, characteristic quasi-polynomials.
Euler characteristics, categorification of enumerative problems
I am interested in "Categorification" of enumerative problems
[32, 34, 39].
List of papers and
Current Postdocs and Students:
Ye Liu (PD),
Elisa Palezzato (JSPS),
Ken-ichiro Arima (PD),
Guo Weili (DC),
Tan Nhat Tran (DC), Ryo Murai (MC), Kentaro Akasaka (MC).
I welcome students who are interested in (at least one of)
research areas: combinatorics, algebraic geometry and topology.
(01 Apr. 2018)