报告名称：Complex structures on Einstein four-manifolds

报告专家：吴鹏

专家所在单位： 复旦大学

报告时间：2021年4月17日16:40-17:30

报告地点： 腾讯会议956 965 967

专家简介：吴鹏，现任复旦大学上海数学中心研究员，博士生导师。主要研究领域是微分几何，具体研究兴趣是四维流形上爱因斯坦度量和梯度Ricci孤立子,部分研究成果发表在Math. Ann.,Calc. Var. PDEs, J. Geom. Anal.等国际高水平数学期刊上。

报告摘要：The question that when a 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 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.

邀请人： 毛井