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Claude LeBrun : Four-Dimensional Einstein Manifolds, and Beyond

An Einstein metric is a Riemannian metric of constant Ricci curvature. One of the central problems of modern Riemannian geometry is to determine which smooth compact manifolds admit Einstein metrics. This lecture will explain some recent results concerning the 4-dimensional case of the problem, and then compare and contrast these results with our current understanding of the problem in other dimensions.

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