Celebrated work of Bridgeland and Smith shows a correspondence between quadratic differentials and stability conditions. Part of this correspondence is that finite-length trajectories of the quadratic differential correspond to stable objects of the stability condition. Speaking roughly, these stable objects are then counted by an associated Donaldson–Thomas invariant. In this talk, I will explain this correspondence in simplified terms and outline recent joint work with Omar Kidwai in which we compute these Donaldson–Thomas invariants and show that they match predictions coming from physics.