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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.

Part I will give the brief introduction to portfolio management problem, including importance of finance, financial bubbles, key factors of investment, theory and problems. Part II will deal with a multi-period portfolio management problem over a finite horizon. The objective is to seek the optimal investment policy series which maximizes the weighted sum of a linear combination of the expected return and the variance of portfolio over all the investment periods.

A coupled degenerate reaction-diffudion SIR model for the overall dynamics of the interaction between fox rabies is considered. The model helps to explain the epidemiological patterns observed in Europe, including 3 to 5 year cycle in fox populations infected with rabies. We provided some global analysis of the model, including the asymptotical behaviors due to Hopf bifurcation in the homogeneous model bescribed by a set of ordinary differential equations.