Abstract: Gromov–Witten invariants enumerate curves in a variety X via stable maps. In practise, degenerate contributions lead to substantial overcounting which makes these invariants far from being optimal. When X is a Calabi–Yau threefold, a set of more fundamental curve counting invariants is provided by Gopakumar–Vafa invariants. In this talk, I will propose a refined correspondence conjecture between Gromov–Witten and Gopakumar–Vafa invariants when X carries a non-trivial torus action. This refinement mathematically realises and generalises features which were expected from the so called refined topological string in physics literature. I will present evidence for the conjecture in case X is the local projective plane. This is based on joint work with Andrea Brini.