Hyper-Kaehler varieties and Jacobi forms

The Yau-Zaslow formula relates the number of rational curves on a K3 surface to Fourier coefficients of the modular discriminant. Hyper-Kaehler varieties are analogs of K3 surfaces in higher dimension, and an analog of rational curves are the uniruled divisors. I will discuss how one can use Gromov-Witten theory to enumerate these divisors in terms of Jacobi forms. More generally, the full Gromov-Witten theory of hyper-Kaehler varieties is conjecturally governed by Jacobi forms. I will explain how holomorphic anomaly equations fit into this picture.