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Day & Time: Tuesday and Thursday 10:10am — 11:25am Location: 230 Malott Hall Instructor: Xiaodong Cao
Office : 507 Malott hall Textbook: We recommend the following two books for references:
Prerequisites: Some knowledge about Riemannian Geometry, Partial Differential Equations and Topology. |
| Class | Topic | |||
| Aug 24 | Overview (I). | |||
| Aug 29 | Overview (II). | |||
| Aug 31 | Review of Riemannian geometry. | |||
| Sep 5 | Variation formulas and Ricci flow equation. | |||
| Sep 7 | Maximum principles. | |||
| Sep 12 | Riwview of parabolic PDE. | |||
| Sep 14 | Short time existence. | |||
| Sep 19 | Ricci flow on surfaces (I). | |||
| Sep 21 | Uniqueness of Ricci soliton. | |||
| Sep 26 | Ricci flow on surface (II): r < 0. | |||
| Sep 28 | Ricci flow on surface (III) : r = 0. | |||
| Oct 3 | Ricci flow on surface (IV) : R > 0. | |||
| Oct 5 | Ricci flow on surface (V) : R changes sign. | |||
| Oct 10 | Fall Break. | |||
| Oct 12 | Ricci flow on surface: convergence. | |||
| Oct 17 | Ricci flow on 3-manifolds. | |||
| Oct 19 | Pinching estimate. | |||
| Oct 24 | No Class. | |||
| Oct 26 | No Class. | |||
| Oct 31 | Ricci flow on homogeous 3-manifolds (Allen Back) | |||
| Nov 2 | Gradient estimate. | |||
| Nov 7 | Maximal time existence. | |||
| Nov 9 | Normalized Ricci flow. | |||
| Nov 14 | ||||
| Nov 16 | ||||
| Nov 21 | ||||
| Nov 23 | Thanksgiving. | |||
| Nov 28 | ||||
| Nov 30 | ||||
| Dec 5 | ||||
| Dec 7 | ||||
| Dec 12 |