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.

In this talk, we present a method to analyze certain fast-slow motions in dynamical systems. For singular perturbed dynamical systems, the well-known Geometric Singular Perturbation Technique (GSPT) is usually applied to find the special limit cycles -- fast-slow periodic solutions. However, many practical problems may not be able to be put in the form of singular perturbed equations, but they still exhibit fast-slow motions. In that case, based on dynamical system theory

In this talk, I will give the Agmon-type estimates of Bergman kernels under the conditions of the curvature or the Ricci curvature bounds. This is joint work with Shoo Seto

Singular elliptic equations have been the target of investigation for decades. A very nice result for existence of solutions of such an equation is due to Lazer-McKenna [Proc.AMS 111(1991)]. In that paper the Lazer-McKenna obstruction was first presented: the equation has a solution if and only if –p>-3. In this talk we reveal the role of -3: why -3 is so crucial for elliptic equations with negative exponents. Then I shall talk about some about $L_{p}$ Minkowski problem with negative exponents $p$.

We develop a general equilibrium model of exhaustible resources with production adjustment costs based on singular control, and show that the classical Hotelling’s rule, which states that the prices of the exhaustible resources should grow at the risk-free rate, does not hold in the presence of adjustment costs; indeed, the adjustment costs can lead to a U-shaped price profile, while will significantly prolong the period of price staying at the bottom.

题目：Mathematical Analysis of Credit Default Swap报告人：陈新富 教授 (匹兹堡大学)时间：2017年5月5日(星期五) 下午2：00—3：00地点：致远楼107室欢迎各位参加