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To understand the spreading and interaction of prey and predator, in this talk we study the dynamics of the diffusive Lotka-Volterra type prey-predator model with different free boundaries. These two free boundaries, which may intersect each other as time evolves, are used to describe the spreading of prey and predator. We investigate the existence and uniqueness, regularity and uniform estimates, and long time behaviors of global solution. Some sufficient conditions for spreading and vanishing are established. When spreading occurs, we provide the more accurate limits of (u, v), and give some estimates of asymptotic spreading speeds of u, v and asymptotic speeds of g, h. Some realistic and significant spreading phenomena are found.

R. A. Brualdi is a professor emeritus of combinatorial mathematics at the University of Wisconsin–Madison. Brualdi received his Ph.D. from Syracuse University in 1964; his advisor was H. J. Ryser. Brualdi is an Editor-in-Chief of the Linear Algebra and its Applications and the Electronic Journal of Combinatorics. He has over 200 publications in several mathematical journals. According to current on-line database of Mathematics Genealogy Project, Richard Brualdi has 37 Ph.D. students and 48 academic descendants. The concept of incidence coloring was introduced in 1993 by Brualdi and Massey.

For every finite collection of closed curves on a surface, we introduce an associated norm on the homology of this surface. These norms are reminiscent of Thurston's norm on the homology of a 3-manifold and share many of its properties, but they are more elementary. In particular, the unit ball of the dual norm on the cohomology is the convex hull of finitely many explicit points. We give an interpretation of these points in terms of certain coorientations of the original curves. All of this is then used in order to classify up to isotopy surfaces with prescribed boundary in the unit tangent bundle that are transverse to the geodesic flow.

Brauer代数起源于正交群和辛群的Schur-Weyl对偶。Brauer代数能被看成一种付随于置换群的数学对象。本次报告中我们考虑如何对一般的Coxeter群以及拟反射群引进类似的代数，即广义Brauer代数。我们介绍给出这些代数的表现，并且在某些特殊情形给出它们的结构与表示的描述。这些广义Brauer代数的变形有望能给出许多新的拟反射群对应的复辫子群的表示，有助于回答这些复辫子群是否为线性群之类的问题

In this talk, we firstly present bifurcation analyses in predator-prey systems of Leslie type with generalized Holling type III functional response, and then introduce our recent works about bifurcation applications in predator-prey systems with harvesting.

酗酒是危害人类健康的危险行为之一，本报告考虑公共健康教育、Twitter和时滞的影响，建立三类酗酒动力学模型，给出了模型的基本再生数。同时研究了平衡点的局部和全局稳定性。进一步研究了前向，后向和Hopf分支以及最优控制问题。同时给出了数值模拟

本文主要研究污染环境下具有年龄结构的种群复杂系统的最优控制问题。即建立了小环境容量下具有年龄结构和毒素作用的种群模型， 利用不动点定理讨论了该模型解的存在唯一性；采用法锥技巧得到了控制的最优性条件；同时利用Ekeland's 变分原理得到了最优控制的存在性。

Online social network as a new platform for information diffusion and establishing social relations has gradually become a hot topic of researches. However, due to the less constraint for virtual crowds in online social networks, it has greatly weakened the certainty and the reliability of all kinds of network information. In view of this, through establishing an appropriate mathematical model to analyze, forecast and control rumor propagation is particularly important. This report comprehensively considers the effects of time delay, spatial diffusion, the government, media and network topology on rumor propagation and established several delayed reaction-diffusion network rumor propagation models.