Space of Ricci flows (II)

Based on the compactness of the moduli of non-collapsed Calabi-Yau spaces with mild singularities, we set up a structure theory for polarized K"ahler Ricci flows with proper geometric bounds. Our theory is a generalization of the structure theory of non-collapsed K"ahler Einstein manifolds. As applications, we prove the Hamilton-Tian conjecture and the partial-$C^0$-conjecture of Tian.