题目：非紧Kahler流形的典则度量报告人：傅吉祥 教授 （复旦大学 太平洋在线会员登录）时间：2017年6月2日（周五）下午15：30-16:30地点：致远楼105室欢迎广大师生参加

We study optimal bandwidth selection in nonparametric cointegrating regression where the regressor is a stochastic trend process driven by short or long memory innovations. Unlike stationary regression, the optimal bandwidth is found to be a random sequence which depends on the sojourn time of the process. All random sequences that lie within a wide band of rates as the sample size goes to infinite have the property that local level and local linear kernel estimates are asymptotically normal

We consider a priori estimates of the Weyl's embedding problem of $(/mathbb{S}^2, g)$ in general $3$-dimensional Riemannian manifold $(N^3, /bar g)$. We establish mean curvature estimate under natural geometric assumption. Together with a recent work by Li-Wang, we obtain an isometric embedding of $(/mathbb{S}^2,g)$ in Riemannian manifold. In addition, we reprove Weyl's isometric embedding theorem in space form under the condition that $g/in C^2$ with $D^2g$ Dini continuous.

In this talk, we study a reaction-diffusion population model with time delay. We establish a comparison principle for coupled upper/lower solutions and prove the existence/uniqueness result for the model. We then show the global asymptotic behavior of the model.

In this talk, I will present some results on chemostat models. In particular, I will report some progress on competitive exclusion principle. In addition, I will also present some results on factors leading to transient oscillations in chemostat.

Mathematical biologists apply mathematical, computational and experimental techniques to investigate biological processes at all levels, from the molecular to the population. To setup an approach spanning multiple levels of biophysical reality, I will describe a new 3D hybrid framework which includes three major submodels: the discrete stochastic Subcellular Element Model for individual cellular activity; continuum reaction-diffusion-advection partial differential equations of extracellular biomolecules; a stochastic decision-making model for cell lineage transition.

We study the existence and nonexistence of traveling waves of diffusive epidemic models. The model systems are non-monotone because the disease models exhibit a predator-prey mechanism. We will construct a suitable convex set in a weighted function space, and then apply Schauder fixed point theorem. It turns out that the basic reproduction number of the corresponding ordinary differential equations plays an important role in the existence theory of traveling waves.

I first talk about the importance of phage therapy in fighting bacteria infections and review the advances of mathematical modeling in the study of phage dynamics. Then, I introduce our researches on how immune responses affect the outcomes of phage therapy. It is shown that the host immune response induces the backward bifurcation.