Title: Rational cuspidal curves, symplectic isotopy, and symplectic fillings

Abstract: A rational cuspidal curve is a complex curve whose singularities are
irreducible (i.e. they have connected link), and that is homeomorphic to a
2-sphere. These are more elusive objects than one could expect, and, for
instance, their classification in the projective plane is not yet complete. I
will discuss a symplectic perspective on the subject and some results obtained
with Laura Starkston (in progress).