Department of Mathematics-SEMINAR ON PDE - Classical arguments and their limitations in conformal
geometry

We consider the classical conformally prescribed scalar curvature problem on a closed
Riemannian manifold. In the most generic and simple situations we review the relevant
formulations, strategies and arguments to show solvability, in particular exhibiting some
recent existence results. Complementarily we will see, that the theory as of today is far
from being complete, as in most situations and for generic curvature candidate functions
the underlying equation has trivial degree, but is solvable, while only a few obstructions
are explicitly known.