An arrangement of hyperplanes is a finite set of hyperplanes in a vector space. The origin of arrangements is the set of all reflecting hyperplanes of reflections in the Weyl group, and several researches to this object. As a generalization of Weyl group cases, arrangements of hyperplanes are now studied by using several mathematical methods including algebra, algebraic geometry, topology, combinatorics, repreentation theory, invariant theory, singularitiy theory, representation theory and so on.
I am studying arrangements of hyperplanes from the viewpoint of algebra and algebraic geometry, to investigate geometric and combinatorial structures of them. In particular, I am interested in the relation between freeness (algebro-geometric property) and intersection lattice (combinatorial structure) of arrangements, and several properties of arrangements consisting of root hyperplanes associated with root systems.