Abstract: I will introduce the Ricci flow and its basic properties. As an application, I will sketch a proof of Hamilton’s differentiable sphere theorem in 3D, which says that every compact, simply-connected 3-manifold admitting a metric with positive Ricci curvature is diffeomorphic to the 3-sphere. Time permitted, I might briefly discuss Perelman’s work and/or some recent results related to exotic 4-manifolds.
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