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# Claude LeBrun : Einstein Metrics, Variational Problems, and Seiberg-Witten Theory

Abstract: One of the major themes of modern differential geometry is the relationship between the curvature and topology of Riemannian manifolds. In this lecture, I will describe some links between curvature and SMOOTH topological invariants --- i.e. invariants which can distinguish between different smooth structures on a given topological manifold. The specific invariants I will discuss are the Seiberg-Witten invariants of 4-manifolds, and I will describe the impact these have on the existence problem for Einstein metrics and some related Riemannian variational problems.

**Category**: Other Meetings and Events**Duration**: 01:17:32**Date**: March 21, 2001 at 4:00 PM**Views**: 37-
**Tags:**seminar, Geometry/Topology Seminar

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