Geometry of Arrangements

Resonance varieties are cohomological invariants that are studied in a variety of topological, combinatorial and geometric contexts. I will discuss their structure in an algebraic setting and will present a sharp formula for the Hilbert series of the Koszul module associated to the resonance variety in question. I will then explain how this can be applied to prove Suciu's Conjecture on the Chen invariants of hyperplane arrangements. Based on joint work with Aprodu, Raicu and Suciu.