  The main focus of these notes is recent work on linear systems in which line
arrangements play a role, including problems such as semi-effectivity,
containment problems of symbolic powers of homogeneous ideals in their powers,
bounded negativity, and a new perspective on the SHGH Conjecture. Along the way
we will be concerned with asymptotic invariants such as Waldschmidt constants,
resurgences and H-constants.
