Title: Unexpected Curves and Hyperplane Arrangements

Abstract: A recent paper by Cook, Harbourne, Migliore and Nagel, showed deep connections between objects known as unexpected curves in algebraic geometry and an open conjecture on Line Arrangements known as Terao's conjecture. After giving an exposition of this connection, I discuss some ongoing work in this area.  We put restrictions on when unexpected curves may occur and discuss why we might expect these curves to have certain types of symmetry.