The Yau-Tian-Donaldson conjecture states that the existence of canonical metrics on polarized manifolds is equivalent to certain algebro-geometric stability condition. In the Fano case, this conjecture has been verified due to many authors' work, which involves many deep and insightful ideas. In this series of talks we will present a relatively more modern approach to this problem using mainly pluripotential theory. This approach has the merit that it requires very little prerequisite and can be generalized to the non-Fano setting, which gives rise to new criterions for the existence of twisted Kahler-Einstein metrics and constant scalar curvature Kahler metrics.
The full details of the approach will be presented during this series of talks.