题目：Cone Spherical Metrics
报告人：许斌 副教授 （中国科学技术大学）
摘要: Cone spherical, flat and hyperbolic metrics are conformal metrics with constant curvature +1; 0 and -1, respectively, and with finitely many conical singularities on compact Riemann surfaces. The Gauss-Bonnet formula gives a natural necessary condition for the existence of such three kinds of metrics with prescribed conical singularities on compact Riemann surfaces. The condition is also sufficient for both flat and hyperbolic metrics. However, it is not the case for cone spherical metrics, whose existence has been an open problem over twenty years. In this talk, we shall report the respectable audience the recent progresses on cone spherical metrics via Complex Analysis and Algebraic Geometry, which consist of several joint research works with Qing Chen, Lingguang Li, Jijian Song, Yingyi Wu and some of my (former) students.