报告人：袁伟副研究员

        中山大学

报告题目：Deformations of scalar-type curvature

报告时间：2016年04月07日下午14:30

报告地点：海韵实验楼105

学院联系人:

报告摘要：Scalar-type curvature is referred to scalar functions defined on Riemannian manifolds which only depends on the Riemann curvature tensor and its derivatives. Typical examples of such quantities are scalar curvature and Q-curvature etc. In this talk, we will first focus on deformation problems of scalar curvature and give a relatively complete investigations on local stability and rigidity phenomena with respect to it, which would involve interesting and fundamental results in the study of scalar curvature such as Positive Mass Theorem, solution to Min-Oo conjecture etc. Then we turn to the Q-curvature, a fundamental curvature quantity in conformal geometry. Using similar ideas, we will discuss the local geometric structure with respect to Q-curvature in the space of Riemannian metrics. In particular, we show interesting results hold for Q-curvature, such as Schoen-Yau-Gromov-Lawson type rigidity results and Kazdan-Warner type existence results etc.

报告人简介：袁伟，2015年于加州大学圣克鲁斯分校（UCSC）取得理学博士学位，目前任中山大学数学与计算科学学院副研究员。主要从事微分几何及数学相对论方面的研究工作，并在真空静态空间的分类、数量曲率与Q-曲率形变问题以及共形拟局部质量等问题上做了深入的研究工作。曾两次访问法国庞加莱数学研究（IHP）所以及奥地利埃尔文薛定谔研究所（ESI）。目前主要关心广义相对论中黑洞唯一性、一般黎曼不变量的形变等几何问题。

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