We survey the results about exact multiplicity of positive solutions of a semilinear elliptic equation with zero Dirichlet boundary condition, and the domain is the unit ball or the whole space of n-dimensional space. It is well known that if the nonlinearity is smooth, then any positive solution to the equation is radially symmetric, and the solution set consists of curves. There are numerous work on the positive radially symmetric solutions of the equation in the last two decades. I will describe a unified approach by Tiancheng Ouyang and myself (and also Philip Korman and Yi Li) which determines the exact multiplicity of solutions and classifies the global bifurcation diagrams of the equation according to the convexity conditions on the nonlinearities. Related recent results will also be discussed.

The International Workshop on Nonlinear Elliptic and Parabolic Partial Differential Equations is scheduled to be held on 24-25 July, 2010, at Tongji University, Shanghai, China. The workshop aims to discuss research results and trends in elliptic and parabolic partial differential equations and related topics. All teachers and students are welcome.Scientific Committee:Zihua Chen, Tongji Univers...

Predator-prey interaction is a basic interspecies relation for ecological and social models. We review some recent results on global bifurcation of limit cycles, steady states in general predator-prey models, some with spatial structure. These results help to explain the rich spatial- temporal patterns which the system possesses.

This presentation includes two parts. The first part considers the problem of stability of linear time-delay systems. Firstly, a delay decomposition approach is proposed to deal with the problem. The idea of the approach is that the delay interval is uniformly divided into N segments with N a positive integer, and a proper Lyapunov-Krasovskii functional is chosen with different weighted matrices corresponding to different segments in the Lyapunov-Krasovskii functional. Secondly, based on the delay decomposition approach, some new delay-dependent stability criteria for linear time-delay systems are derived. These criteria are much less conservative and include some existing results as their special cases.

题目： An Effective Shafarevich Theorem for Elliptic Curves报告人：威廉希尔中文网站注册顾问教授、瑞士苏黎世高工(ETH)数学系资深教授Gisbert Wüestholz博士时 间：2010年7月1日星期四下午15:30-16:30地 点：威廉希尔中文网站注册数学系致远楼学术报告厅107室热烈欢迎有兴趣的老师和同学参加

LOGISTIC方程是自然科学中许多自然现象的基本数学模型。我们将回顾LOGISTIC方程的历史演变，推广和抽象过程，以及它在生态学，化学，基因学中的广泛应用。我们也介绍扩散过程，时滞，空间非均匀性对 LOGISTIC 模型的影响。

题目：A New Collocation Method For Ordinary DifferentialEquations of First Order报告人：郭本瑜 教授上海师范大学数学系时间：2010年6月23日（星期三）下午3：00地点：数学系107欢迎有关教师、研究生及有兴趣者参加

报告人：麻希南教授（中国科技大学）报告题目：Curvature estimates for the convex level sets of harmonic function时间：2010年6月22日，星期二上午10：30—11：30地点：数学系致远楼107欢迎各位参加