This talk will be about refined curve counting on local $P^2$, the noncompact Calabi-Yau 3-fold total space of the canonical line bundle of the projective plane. I will explain how to construct quasimodular forms starting from Betti numbers of moduli spaces of one-dimensional coherent sheaves on $P^2$. This gives a proof of some stringy predictions about the refined topological string theory of local $P^2$ in the Nekrasov-Shatashvili limit. This work is in part joint with Honglu Fan, Shuai Guo, and Longting Wu.