Por Luca Scala (UFRJ, Brasil & Univ. Lusófona).

In this talk we will review recent results about tautological bundles on Hilbert schemes of points on a complex algebraic surface and their cohomology, giving motivations, explaining the techniques used to study them and pointing out the difficulties in the latest developments. During this survey we will pass through other interesting subjects, such as the singularities of the Isospectral Hilbert scheme, or the local geometry of diagonal ideals.