Abstract: A complexified hyperplane arrangement is a (locally finite) collection of hyperplanes with real equations in a finite-dimensional complex affine space. In this talk, I will describe a combinatorial method to study the homotopy type of the complement of a complexified hyperplane arrangement, by applying discrete Morse theory to the “Salvetti complex” of the arrangement. I will mention the following two consequences: (1) The complement is a minimal space (a property already well known for finite arrangements); (2) The Betti numbers can be computed through a simple geometric procedure which involves projecting a generic point onto all the chambers of the arrangement. This is joint work with Davide Lofano.