Sungmin Yoo, Bergman Metrics and Kähler-Einstein Metrics on Projective Manifolds

After Yau suggested the problem of approximations of Kähler-Einstein metrics by Bergman type metrics, various types of Bergman metrics have been developed and studied by Tian, Donaldson, Tsuji, etc. They showed that if a polarized manifold admits a Kähler-Einstein metric, there exist a sequence of Bergman type metrics which converges to the Kähler-Einstein metric. In this talk, we will survey their results and discuss some remaining problems in this subject.