|The Kähler-Ricci Flow|
|Time：||Tue/Thu 10:10-12:00, 2015-06-04 ~ 2015-08-13|
|Instructor：||Valentino Tosatti [Northwestern University]|
|Place：||Conference Room 3, Floor 2, Jin Chun Yuan West Building|
Classes on July 7/9/14/16 will be canceled and extra classes will be arranged on June 29/July 1/20/22, 13:00-14:50, Room 1, floor 1
The Ricci flow is an evolution equation which deforms a Riemannian metric in the direction of its Ricci tensor, with the goal of making it more "round". If the underlying manifold is complex and the initial metric is Kähler, then so are the evolved metrics, and the flow is called the Kähler-Ricci flow. When the manifold is also compact, the flow becomes intimately related to the complex structure of the manifold, and if the manifold is algebraic the convergence properties of the flow are directly related to the minimal model program in birational geometry.
In these lectures I will give an introduction to the Kähler-Ricci flow, and present some results which fit in this framework. Possible topics to be covered are: the characterization of the maximal existence time of the flow, the formation of singularities in finite time, the long time behavior on minimal Kahler manifolds, and the case of Kähler surfaces where the picture is essentially complete.
A basic knowledge of differential geometry is advisable. Previous study of the Ricci flow is a plus, but is not necessary.
1. J.Song, B.Weinkove, Lecture notes on the Kähler-Ricci flow, arXiv:1212.3653
2. B. Weinkove, The Kähler-Ricci flow on compact Kähler manifolds, arXiv:1502.06855