Prof. Dr. Claude LeBrun, Stony Brook University, Vortrag: Four-Manifolds, Einstein Metrics, and Differential Topology

Thursday, 05.06.2014 16:30 im Raum M5

Mathematik und Informatik

Abstract: A Riemannian metric is said to be Einstein if it has constant Ricci curvature. A central problem in differential geometry is to determine which smooth compact manifolds admit an Einstein metric, and to completely understand the moduli space of all such metrics when they exist . The 4-dimensional case of this problem appears to be highly atypical. This lecture will explore the features of 4-dimensional geometry which lead to this remarkable situation, and survey our current knowledge concerning the existence of Einstein metrics on 4-manifolds. Particular emphasis will be placed on 4-manifolds which admit either a complex structure or a symplectic structure, as our current results are particularly sharp in this setting.

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Geändert am Tuesday, 06.05.2014 09:47 von shupp_01
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Kolloquium Wilhelm Killing