We show that any unique global solution (here we do not require any smallness condition beforehand) to 3-D axisymmetric Navier-Stokes equations in some scaling invariant spaces must eventually become a small solution. In particular, we show that the limits of $\|\omega^\theta(t)/r\|_{L^1}$ and $\|u^\theta(t)/\sqrt r\|_{L^2}$ are all $0$ as $t$ tends to infinity. And by using this, we can refine some decay estimates for the axisymmetric solutions.

tions The Poisson-Nernst-Planck (PNP) type of equations are one of the most extensively studied models for the transport of charged particles in many physical and biological problems. The solution to the PNP equahas many properties of physical importance, e.g., positivity, mass conservation, energy dissipation. It is desirable to design numerical methods that are able to preserve such properties at discrete level. In this talk, we will present two types of numerical schemes that can maintain physical properties. One is based on the so-called Slotboom variables; the other is based on the gradient flow structure of the PNP equations. Some numerical results are shown to demonstrate their performances. This is a joint work with Jie Ding, Chun Liu, Cheng Wang, Zhongming Wang, Xingye Yue, and many others.

近年来三维双曲流形的拓扑与几何方面取得了一些深刻的进展，加深了人们对三维流形的拓扑的理解。 我们将以三维双曲流形时的这些进展为基础，来对比的看高维双曲流形的拓扑与几何等问题。

In this talk, we discuss the generalization of Lappan's theorem to higher dimensional complex projective space.

I plan to review the connection between central extension of sln(A) coordinated by a unital associative algebra A and the cyclic homology of A due to Kassel and Loday. Then, I am going to present its generalization in unitary Lie algebras obtained by Y. Gao and its further generalizations in Lie superalgebra cases, including the H. Chen and J. Sun’s work on slm|n(A) and my joint work with Z. Chang on ortho-symplectic, periplectic and queer Lie superalgebras.

众所周知存在从ADE型Hecke代数到对应类型的Temperley-Lieb代数的自然满同态。我们发现从非ADE型Hecke代数也具有到某些类型的Temperley-Lieb代数的有趣的同态。利用这种同态能够恰好“实现”出二面体型Hecke代数的所有二维不可约表示。在这些同态的构造过程中意外遇见了切比雪夫多项式。

众所周知存在从ADE型Hecke代数到对应类型的Temperley-Lieb代数的自然满同态。我们发现从非ADE型Hecke代数也具有到某些类型的Temperley-Lieb代数的有趣的同态。利用这种同态能够恰好“实现”出二面体型Hecke代数的所有二维不可约表示。在这些同态的构造过程中意外遇见了切比雪夫多项式。

Let M be a compact smooth oriented manifold. The set of isotopy classes of orientation-preserving self-diffeomorphism of M is a group through composition of maps, which is called the mapping class group of M. In this talk, we mainly concern with the mapping class groups of high dimensional manifolds. This talk divides into three parts. In the first part, we will recall some basic definitions and propositions of mapping class groups of high dimensional manifolds. In the second part, we will discuss the calculations of the mapping class groups of standard spheres, exotic spheres and product of spheres. In the third part, we will say something about the mapping class groups of HP2-like manifolds. This work is joint with Yang Su.