In this talk, a semi-discrete DG method is first introduced to solve the Maxwell’s equations in three dispersive media in a uniform framework, which is described by an integral-differential equation. Accuracy of is obtained. Then it is also noted that the governing equations for three different meta-materials share a common feature. Based on this observation, a method combining the DG method in space with the CG method in time for Maxwell’s equation in meta-materials in an uniform framework is discussed. An energy identity is obtaiend and the unconditional stability is naturally reduced. Then the convergence rate of is verfied.

守恒律方程为20世纪50年代兴起的一个研究领域，此类型方程所涵盖的物理模型十分广泛，几乎所有的连续体力学的模型方程均属于这种形式，其中包含了气体、液体、弹性体、等离子体、星云等等。该领域作为数学与力学之间的一个重要枢纽十分重要，而双曲守恒律方程(组)的激波解和数值方法的研究更是科学界热门的研究课题。 本报告将回顾一下双曲守恒律数值方法的历史，并介绍与合作者一起在双曲守恒律方程（组）的数值方法的研究方面取得的一些工作，它们包括数值方法机理（局部振荡和声速点故障等）分析和高分辨自适应移动网格方法等及双曲守恒律的激波捕捉方法在计算流体力学中的应用等。

Networks come in different sizes and shapes, and it is of theoretical and practical interest to characterize aspects of networks. One important aspect is how strong the nodes in the network are associated to each other. In this paper, we propose a so-called normalized clustering coefficient (NCC) to measure the clustering strength of networks. The NCC has interesting theoretical properties and is potentially useful in many areas of network studies, e.g., network clustering, network sampling, and dynamic network analysis. Simulations and real examples will given to see how they work.

题目：Approximating Signals from Random Sampling in a Reproducing Kernel Subspace of Homogeneous Type报告人：冼军 教授 （中山大学）地点：宁静楼108室时间：2019年06月21日16:00-17:0

For the numerical simulation of Lagrangian multi-material radiation hydrodynamic problems, a challenging problem is to construct discrete schemes to solve energy diffusion equations with discontinuous coefficients on Lagrangian distorted meshes. This talk will describe briefly the physical background and some key numerical issues related to cell-centered finite volume schemes. Then some finite volume schemes satisfying maximum principle for diffusion equations on general meshes are constructed with a new way. Moreover, some numerical results will be presented to show the performance of our schemes.

This talk focuses on recent progress regarding the collapsing theory of Einstein spaces. Specifically, the talk consists of the following primary parts: (1) We will introduce some regularity and structure theorems for higher dimensional collapsing manifolds with Ricci curvature bounds which works in very general settings. (2) This talk is also concerned with the geometry of collapsed Ricci-flat Kähler manifolds. Besides exhibiting new collapsing Einstein families, we will establish the correspondence between complex structures (Type II) degeneration and the metric collapsing.

In 1950’s, Nash-Kuiper built up the C^1 isometric embedding for any surface into $/mathbb{R}^3$, this can be viewed as analysis side of isometric embedding. On the other hand, there is obstruction for the existence of $C^2$ isometric embedding of surface into $/mathbb{R}^3$ known since Hilbert, which reflects the geometry flavor of isometric embedding. What’s happening from $C^1$ to $C^2$ (from analysis to geometry)? We will present our partial progress along this direction. The talk will be accessible to audience with basic knowledge of analysis and differential geometry.

The subspace of symmetric tensors and the subspace of anti-symmetric tensors are two natural reducing subspaces of tensor product A⊗I+I⊗A and A⊗A for any bounded linear operator A on a complex separable Hilbert space H. We show the set of operators A such that these two subspaces are the only (nontrivial) reducing subspaces of A⊗I+I⊗A is a dense G_δ set in B(H). This generalizes Halmos’s theorem that the set of irreducible operators is a dense G_δ set in B(H). The same question for A⊗A is still open.