北航微分几何讨论班（2021年春第6讲）

题目：Complex structures on Einstein four-manifolds

报告人：吴 鹏 研究员（复旦大学）

报告时间：2021.4.30 9:00-10:00

腾讯会议号：570 714 666

摘要：The question that when a simply connected four-manifold with a complex structure admits a compatible Einstein metric of positive scalar curvature has been answered by Tian, LeBrun, respectively. Tian classified Kahler-Einstein four-manifolds with positive scalar curvature, LeBrun classified Hermitian, Einstein four-manifolds with positive scalar curvature. In this talk we consider the inverse problem, that is, when a simply connected four-manifold with an Einstein metric of positive scalar curvature admits a compatible complex structure. We will show that if the determinant of the self-dual Weyl curvature is positive then the manifold admits a compatible complex structure.

报告人简介：吴 鹏，现为复旦大学上海数学中心青年研究员。研究方向为微分几何，特别是关于4维爱因斯坦度量的研究。已经在Math. Ann., CVPDE, J. Geom. Anal. 等重要数学期刊上发表多篇论文。

邀请人：张世金