YOSHINAGA, Masahiko
 Position
 Professor
 Organization
 Department of Mathematics
 Research Interest
 Algebraic Geometry, Topology, Combinatorics
 Research Activities

Hyperplane arrangements relate several branches of mathematics, topology, representation theory, combinatorics, and so on. I am working in two aspects of hyperplane arrangements. The first is around logarithmic vector fields.
It is a reflexive sheaf on the projective space, which controls combinatorial structures of arrangements. The other is minimality of the homotopy types of the complements. Recently I am also interested in Ehrhart theory, Eulerian polynomials, and categorification of enumerative problems.Papers:
[1] Characterization of a free arrangement and conjecture of Edelman and Reiner. Invent. Math. 157(2004), no. 2, 449454.[2] Hyperplane arrangements and Lefschetz’s hyperplane section theorem. Kodai Math. J. 30, no. 2 (2007), 157–194.
[3] Milnor fibers of real line arrangements. Journal of Singularities, vol 7 (2013), 220237.
[4] Worpitzky partitions for root systems and characteristic quasipolynomials. To appear in Tohoku Math. J.
 Keywords
 enumerations, fundamental groups, homotopy types, hyperplane arrangements, logarithmic vector fields, periods
 WebPage
 http://www.math.sci.hokudai.ac.jp/~yoshinaga/index.html