Two topics in conformal geometry: the singular Yamabe problem and some possible generalizations to fully non-linear equations

The talk will consist of two parts: the first one will deal with some topics about the singular Yamabe problem, more explicitly, of how to construct a metric of constant positive scalar curvature that is singular along a specified set of certain types, of dimension smaller than (n-2)/2. In second part I will consider some fully non-linear equations coming from conformal geometry that generalize scalar curvature, and in particular, obtain a dimension estimate for this singular set. If time permits, I will mention some relations between these two problems.