In our recent work with Andrei Okounkov, Rahul Pandharipande and Miguel Moreira we proved Virasoro relations for the integrals of the tautological classes over the moduli space of stable pairs on a compact topic three-fold. As an easy consequence of the relations we get previously unknown relations between the integrals of tautological classes on the Hilbert scheme of points on a compact surface. I will start with the case of Hilbert scheme of points on the surface while aiming to explain something about the case of the stable pairs by end of the talk.