Wu Peng, Shanghai Center for Mathematical Sciences
Middle Lecture Room, Math Building
Einstein metrics are most natural Riemannian metrics on differentiable manifolds. In dimensions 2 and 3, they must have constant sectional curvature, while in dimension 4, they are much more complicated. For the complex setting, in 1990 Tian classified Kahler-Einstein four-manifolds with positive scalar curvature, and in 2012 LeBrun classified Hermitian, Einstein four-manifolds with positive scalar curvature. For the real setting, however less is known, even assuming a (strong) condition of positive sectional curvature. In this talk I will first talk about some background on Einstein manifolds, then I will focus on Einstein four-manifolds with positive curvature. If time permitted, I will also talk about my recent attempts of attacking this problem via k-positive curvature operator.