报告题目1： Pseudo-Einstein Structure, Eigenvalue Estimate for the CR Paneitz Operator and CR Rigidity Theorems　　

报告人：    林乾   博士（清华大学）　　

报告时间： 2018年11月27日（周二）10:00—12:00　　

报告地点： 数学与统计学院学术报告厅　　

报告摘要: In this talk, we will give some of sufficient conditions for the existence of pseudo-Einstein contact forms in a closed pseudohermitian 3-manifold. Beside, we obtain an upper bound eigenvalue estimate for the CR Paneitz operator. As applications, the rigidity theorems for Sasakian space forms are established.　　

报告题目2： Open Problems on CR Geometric Analysis　　

报告人：    张树城   教授（台湾大学）　　

报告时间： 2018年11月27日（周二）16:00—18:00　　

报告地点： 数学与统计学院学术报告厅　　

报告摘要: A central problem of modern geometry and geometric analysis is the geometrization problem on manifolds. It is to determine which smooth manifolds admit certain geometric structures. In particular, one of goals in geometric analysis is to understand and classify the singularity models of the nonlinear geometric equation, and to connect it to existence problem of geometric structures on manifolds.　　

Along these aspects, we will introduce some new and fundamental works on CR geometric analysis. More precisely, a CR manifold is modeled on a real hypersurface in a complex manifold and the subject has attracted the attentions of great geometers such as Poincare, Cartan, and Chern. The traditional approach is based on complex analysis. In recent years, new approaches based on Riemannian and Kaehlerian geometric analysis have been taken up to attack longstanding problems in CR geometry. Such geometric analysis, which involve deep understanding and delicate analysis of both CR and Kaehler gometries, have tremendous difficulties and are pioneering and of lasting impacts in the field, and opens up brand new avenue to research in CR geometric analysis. In this talk, we will focus on the following open problems : 　　

(I) The CR Li-Yau-Hamilton Gradient Estimate　　

(II) The Torsion Flow in a Three-Dimensional CR Manifold　　

(III) On Torsion Solitons　　

(Iv) On CR Frankel Conjecture　　

(V) On Yau Uniformization Conjecture on Sasakian Manifolds　　

报告人简介：

        林乾，北京清华大学丘成桐数学中心博士后，台湾清华大学数学系博士，师从著名几何分析学家张树城教授，主要从事微分几何、几何分析、CR几何的研究。目前已发表论文5篇，2013-2014年获得台湾清华大学校长奖学金。　　

张树城，博士，教授，博士生导师，杰出的几何分析学家。1985-1990在莱斯大学学习并获博士学位，2004-2007年间任台湾清华大学数学系系主任，2008年至今任教于台湾大学。主要研究领域为：微分几何、几何分析、伪Hermitian几何、Kaehler几何等。近年来专注于CR流形中的几何分析问题，包括CR Obata问题、CR heat equation 相应的Li-Yau gradient estimate，linear trace Li-Yau-Hamilton inequality问题的研究。在国际著名学术期刊，如J. Differential Geometry、Math Ann.、J. Geometric Analysis、Trans. AMS 等发表系列重要研究成果。