“On Four-Dimensional Einstein Manifolds”
Claude LeBrun, SUNY, Stony Brook

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 survey some recent results regarding the special case of 4-manifolds which admit either a complex structure or symplectic structure.