We study small covers and the real moment-angle manifold over a simple polytope that admit Riemannian metrics of positive scalar curvature. We first explain some general facts on the existence of positive scalar curvature on a smooth manifold.Then we show a class of simple polytopes over which the small covers and the real moment-angle manifolds

In this talk, I will introduce a possible way to consider the cabling conjecture from the view of Heegaard splitting.

Let M be a unitary closed manifold that admits an action of a circle preserving the unitary structure and fixing some isolated points. Kosniowski conjectured in 1980 that if M is not a boundary, then the number of isolated points is at least [dim M/4]+1. This talk will discuss different statements of Kosniowski conjecture and state some recent progresses.

Positive mass theorem is one of the most fundamental results in both physics and mathematics. It has many applications in various fields of geometric analysis. As its compact manifold version, the positive mass theorem for Brown-York mass has been also proved to be a very powerful tool in the study of geometry. In this talk, we will briefly review the positive mass theorem due to Schoen-Yau-Witten and Brown-York mass theorem due to Shi-Tam. As applications of Shi-Tam's result, we show how to use it to derive some interesting geometric results such as estimates of first eigenvalue of Laplacian with scalar curvature positively lower bounded and an area estimate of critical set for Besse's conjecture etc.

题目：Integer Flows of Cayley Graphs报告人：张存铨 教授 （West Verginia University）时间：2018年6月9日上午10:00地点：致远楼101室欢迎大家前往听讲

在这个报告中，我们首先介绍分形几何中Hausdorff测度与Hausdorff维数的概念并介绍如何求解古典三分Cantor集的Hausdorff维数，然后简单介绍我们近期在Beta展式研究中所取得的部分结果。

In this talk, I will present our recent numerical methodology studies for unsteady moving interface problems and applications to dynamic fluid-structure interaction (FSI) problems. Our numerical methodologies include the arbitrary Lagrangian−Eulerian (ALE) method, the distributed Lagrange multiplier/fictitious domain (DLM/FD) method and their combinations with the mixed finite element method. A fully coupled (monolithic) mixed finite element approximation is developed for all numerical methodologies to unconditionally stabilize numerical computations for moving- interface and FSI problems. Numerical analyses on the well-posedness, stability and convergence are carried out for the proposed monolithic ALE and DLM/FD methods when they are applied to various moving−interface problems.

In this talk, we will introduce two classes of Hamiltonian systems: LV Hamiltonian system in R^4 and Kolmogorov Hamiltonian systems in R^2 . Global dynamics is given for the LV Hamiltonian system in R^4 and all kinds of centers are obtained for a Kolmogorov Hamiltonian system in R^2. Moreover, the topological structures of a class of real hypersurfaces in R_+^4 and real algebraic curves in R^2 are given.