Abstract:  

We first prove a uniform integral  Laplace comparison result for the Kahler Ricci flow on Fano manifolds which depends only on the initial metric. As an application, we give a direct and independent proof of the Hamilton-Tian conjecture on convergence of Kahler-Ricci flows, modulo a codimension 4 singular set. This is a joint work of G. Tian, Z.L.Zhang, M. Zhu and X.H.Zhu