Universality of $\mathsf{C}\mathsf{o}\mathsf{h}\mathsf{F}\mathsf{T}$ of ${\mathsf{H}\mathsf{i}\mathsf{l}\mathsf{b}}_n(S)$

By virtue of their relation to Fulton–MacPherson compactifications, the cohomological field theory of Hilbert schemes of points on a surface, in extremal curve classes, is universally and effectively determined by the characteristic numbers of the surface and by the corresponding theory of Hilbert schemes of the affine plane. As a consequence, we compute the extremal genus 1 Gromov–Witten invariants of Hilbert schemes of all surfaces.