2019年4月10日东南大学几何分析高级研讨班​

发布者：吕小俊发布时间：2019-04-02浏览次数：1278

2019年4月10日东南大学几何分析高级研讨班

东南大学九龙湖校区数学学院（李文正图书馆5楼）

  

时间安排

  

报告人

题目

主持人

9:00-9:45

徐国义 (清华大学)

The analysis and   geometry of isometric embedding

  

  

王小六

9:45-9:50 茶歇

9:50-10:35

王作勤 (中国科学技术学)

On Weyl Asymptotics

10:35-10:45 茶歇

  

10:45-11:30

华波波(复旦大学)

图上的分析和应用

  

  

李逸

11:30-11:35 茶歇

11:35-12:20

来米加 (上海交通大学)

The renormalized volume   on 4-dimensional CCE manifolds

  

报告摘要

  1. 徐国义：In 1950’s, Nash-Kuiper built up the C1 isometric embedding for any surface into R3, this can be viewed as analysis side of isometric embedding. On the other hand, there is obstruction for the existence of C2 isometric embedding of surface into R3 known since Hilbert, which reflects the geometry flavor of isometric embedding. What’s happening from C2 to C2 (from analysis to geometry)? The talk will be accessible to general audience with basic knowledge of analysis and geometry.

  2. 王作勤：Weyl law, first discovered by H. Weyl in 1911 for the Dirichlet-Laplace eigenvalues of bounded regions and then extended/strengthened by many mathematicians to various general settings, relates the asymptotic behavior of eigenvalues of certain operators with the background geometric/analytic/dynamic behavior. In this talk I will briefly describe these connections and discuss some recent work.

  3. 华波波：我们研究图和离散Laplace算子。用离散分析的技巧，研究图和Laplace算子的特征值问题、Schroendinger算子等。

  4. 来米加：The renormalized volume is a very important global invariant for conformally compact Einstein (CCE) manifolds. In dimension 4, it is the integral of sigma_2 of the Schouten tensor, which appears in the Gauss-Bonnet-Chern formula. Based on Gursky’s work on the Weyl functional and the de Rham cohomology on closed 4-manifolds and Chang-Gursky-Yang’s conformal 4-sphere theorem, one can deduce interesting topological consequences for 4-dim CCE manifolds under assumptions on the renormalized volume. I will survey results in this direction and discuss some recent thoughts.