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.