Hyperplane arrangements, local system homology and iterated integrals

Abstract

We review some aspects of the homology of a local system on the complement of a hyperplane arrangement. We describe a relationship between linear representations of the braid groups due to R. Lawrence, D. Krammer and S. Bigelow and the holonomy representations of the KZ connection. We explain a method to describe such representations by the iterated integrals of logarithmic 1-forms.