Topology and combinatorics of hyperplane arrangements

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Hyperplane arrangements appear many branches of mathematics including combinatorics, representation theory, topology, etc. One of main problems is to decide to what extent the structures of arrangements are determined by the combinatorial structures. We have stdudied local system homology groups based on the recent developments of the irreducibility of the moduli space of line arrangements and minimal cell structures. We have obtained new algorithm computing local system homology, several qualitative results on the Milnor fibers and new characterization for the freeness.