I will talk about joint work with Amin Gholampour and Richard Thomas on proving the S-duality conjecture regarding modularity of DT invariants of sheaves with 2 diemnsional support in an ambient CY threefold. One of the crucial ingredients needed for our analysis is the relative Hilbert scheme of points on a surface. More precisely, together with Gholampour we have proven that the generating series, associated to the Hibert scheme of points, relative to an effective divisor, on a smooth quasi-projective surface is a modular form. This is a generalization of the result of Okounkov-Carlsson for absolute Hilbert schemes. We extend their constructions to the relative setting, and using localization and degeneration techniques, express the intersection numbers of the relative Hilbert scheme in terms of tangent bundle of the surface with logarithmic zeros and derive a nice formula as a modular form. I will then show how this leads to the proof of a well known conjecture in string theory, called the S-duality modularity conjecture.