Georg Oberdieck:Holomorphic anomaly equations for the Hilbert schemes of points of a K3 surface

Abstract: Holomorphic anomaly equations are structural properties predicted by physics for the Gromov-Witten theory of Calabi-Yau manifolds. In this talk I will explain the conjectural form of these equations for the Hilbert scheme of points of a K3 surface, and explain how to prove them for genus 0 and up to three markings. As a corollary, for fixed n, the (reduced) quantum cohomology of Hilb^n K3 is determined up to finitely many coefficients.