Convergence of the Kahler-Ricci Flow on a Kahler-Einstein Fano Manifold

The goal of these notes is to sketch the proof of the following result, due to Perelman and Tian-Zhu: on a Kahler-Einstein Fano manifold with discrete automorphism group, the normalized Kahler-Ricci flow converges smoothly to the unique Kahler-Einstein metric. We also explain an alternative approach due to Berman-Boucksom-Eyssidieux-Guedj-Zeriahi, which only yields weak convergence but also applies to Fano varieties with log terminal singularities.