This course has been postponed. The new date will be announce later.

 

This series of lectures focus on the compactness of the Ricci flow. In the first lecture, I will present a chronological review on this topic, from the era of Hamilton-Chow to post-Perelman time. Along this line, I will show you how to derive a compactness theorem when the full curvature is unknown. So some technical issues will be given in the second lecture. In the last lecture, I will talk about some related recent developments and future directions.

 

Lecture 1. Compactness of the Ricci flow

-Abstract: Perelman's no-local-collapsing theorems and pseudolocality theorem lay down the fundamental mechanism of the Ricci flow. I will explain how to use these theorems to blow up singularities.

 

Lecture 2. Curvature, volume and the injectivity radius

-Abstract: Hamilton's compactness theorem assumes bounds on the curvature operator and the volume ratio. These assumptions can be replaced by bounds on the Ricci curvature and the injectivity radius on (0,T], and a C^3 bound of metric at t=0. The proof mainly combines Anderson's trick on harmonic coordinates and Perelman's point-picking lemma.

 

Lecture 3. Further discussions 

-Abstract: I will talk about some recent developments in this direction, including theorems on the extension problem, on the localized W-functional, and on the eigenfunction coordinates.