The analytic Minimal Model Program can be regarded as a complex geometric analogue of a refined geometrization of 3-manifolds. It provides an approach to classifying compact Kahler manifolds through Ricci flow. The key part of this program is study singularity formation of Kahler-Ricci flow at finite-time and infinite time. In this expository talk, I will start with some basic results on Kahler-Ricci flow, then I will discuss some recent progress on this flow, especially, its limiting behavior at time infinity.

Gang Tian graduated from Harvard University, and has been a professor at Princeton, MIT, NYU, and Stony Brook. Currently he is Vice President of Peking University. He is a member of the Chinese Academy of Sciences and the American Academy of Arts and Sciences, and a winner of the Waterman and Veblen Prizes.