The Kahler-Ricci Flow and the Minimal Model Program
Student No.:50
Time:Mon./Thu. 13:00-14:50 (Exception: First lecture May 15: 15:10-17:00; Last lecture June 20: 13:00-14:50)
Instructor:Valentino Tosatti  [Northwestern University]
Place:Conference Room 1, Floor 1, Jin Chun Yuan West Building (近春园西楼1层第一会议室)
Starting Date:2012-5-15
Ending Date:2012-6-20




Please be informed for the following course, time for the June 14 (Thursday) class has been changed to June 19 (Tuesday)13:00-14:50pm. 
Course Title: The Kahler-Ricci Flow and the Minimal Model Program
By Valentino Tosatti (Columbia University)
Course Schedule:
Time: June 19 Tuesday 13:00-14:50
Conference room 1, Floor 1, Jin Chun Yuan West Building (




Course description:

In this course we will give an introduction to the Kahler-Ricci flow and we will then study its properties on projective algebraic manifolds. The goal will be to explore the relations between the analytic behavior of the flow and the classification scheme for algebraic manifolds provided by the Minimal Model Program. First, we will characterize the maximal existence time for the flow on all compact Kahler manifolds. We will then examine the long time behavior of the flow on projective algebraic surfaces, where the relation with algebraic geometry is especially clear. After completing this course, the students should be able to read the most recent articles in this very active research area.

There will be weekly homework and a written final exam.



A basic knowledge of differential geometry is advisable. Previous study of the Ricci flow is a plus, but is not necessary.


Reference for the course:

We will use the “Lecture Notes on the Kahler-Ricci flow” by J.Song and B.Weinkove, available at