In this talk, I will present a model of ordinary differential equations for populations which are structured by many stages. The model is general enough to apply to many biological systems. Our analysis identifies a basic reproduction number that acts as a threshold between population extinction and persistence. We establish conditions for the existence and uniqueness of nonzero equilibria and show that their local stability cannot be expected in general. Boundedness of solutions remains an open problem though we give some sufficient conditions. This talk is based on joint work with Guihong Fan, Horst R. Thieme and Jianhong Wu.

Reflection groups play an important role in various branches of mathematics. In the present talk, I mainly introduce real and complex reflection groups, which include the geometric and algebraic description, the classification, the characterization in terms ofinvariants, etc, of these groups.

我们研究非线性椭圆偏微分方程的Neumann边值问题，主要是梯度估计与二阶导数估计，然后得到存在性

I will give a survey on a long term program of constructing and studying two-dimensional conformal field theories using the representation theory of vertex operator algebras. I will discuss the major problems solved, some main open problems and, if there is enough time, the algebraic, analytic and geometric techniques developed in carrying out this program.

A diffusive plant-herbivore system with Neumann boundary conditions and Dirichlet boundary conditions is investigated. Local and global stability of spatially homogeneous steady states are established. We derive the conditions for the occurrence of Hopf bifurcation and steady state bifurcation and provide geometrical methods to locate the bifurcation values. A large variety of different types of short-term behavior, including oscillations both in space and in time, or oscillations with different amplitudes, are discussed.

We study the traveling wave solutions of a diffusive SIR model with standard incidence. The existence of traveling waves is determined by the basic reproduction number of the corresponding ordinary differential equations and the minimal wave speed. Our proof is based on Schauder fixed point theorem and Laplace transform.

The widely applied non-invasive imaging techniques such as Magnetic Resonance Imaging (MRI), Computed Tomography (CT), and ultrasound (US) have offered tremendously exciting opportunities and challenges for statistical analysis. The data we encounter these days are not only increasing in size, but also in complexity. In this talk, I will introduce several emerging complex data objects including tree-structured data, functional data, and imaging data. The structures of the data objects often arise from the scientific problems and lie in non-Euclidean space. Traditional statistical tasks such as regression, classification and hypothesis testing thus become rather difficult. I will talk about recent methods for modeling the data object and the regression and prediction methods. Simulation studies have shown impressive improvement in disease diagnosis, prognostication, treatment monitoring, etc.

In this talk, several classes of Errors-correction codes are constructed based on special algebraic structures.