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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.

Asymptotics of linear systems, with connections to line arrangements