HIV infection is still a serious health problem in the world. Effective combination therapy can control viral replication but cannot eradicate the virus. Mathematical models, combined with experimental data, have provided important insights into HIV dynamics and immune responses. In this talk, I will present some recent work on modeling HIV infection and treatment, such as HIV latency and persistence, viral blips, virus dynamics under different drugs, treatment intensification with additional drugs, and the slow time scale of target cell depletion. Model formulation, mathematical analysis, numerical simulation (deterministic or stochastic) and comparison with data will be presented. Implications of modeling results for viral control strategies will also be discussed.

In this talk I will introduce our recent work on a generalization of the Fenchel theorem to the 3-dimensional Lorentz space. The total curvature of a spacelike closed curve is the same as the length of its tangent indicatrix. The estimation of this length is non-trivial. Here we will explain our discovery of an alternative phenomenon about closed spacelike curves on the de-sitter space, which helps to establish the desired inequality. Moreover, this also helps to obtain a necessary and sufficient condition for a curve to be realizable as the tangent indicatrix.

It will be shown that many of the deep and beautiful results for minimal graphs in codimension 1 fail utterly in higher codimensions. More precisely, (1) For the case of dimension 2, the Dirichlet problem is solvable, but these solutions are not unique in general. (2) When the dimension is no less than 4, the Dirichlet problem is not even solvable. (3) The minimal graphs need not even be stable. (4) There exist Lipschitz solutions to minimal surface equations which is not smooth.

In this talk, I report progress my team has made on modeling of Ebola Virus Diseases (EVD), Middle-East Respiratory Syndrome (MERS) and global spatio-temporal pattern of human influenza. Firstly, I introduce a new approach to disentangle common and distinct components in the transmission rate of EVD across countries. Secondly, I compare the seasonality of MERS versus influenza in the Middle East. Finally, I report a skip-and-resurgence phenomenon of human influenza H1N1 in Europe/East Asia and the spatial pattern of proportions of Influenza B in the post-pandemic era.

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.