The reaction-diffusion systems, which have been frequently used as the models for many problems in physics, chemistry and biology, can give rise to an important solutions – the wave solutions. In this talk we begin with a brief introduction to the history and development of research done on the traveling waves solutions for reaction-diffusion systems, such as the shooting method, monotone iteration for monotone systems, perturbation approach, and application of Schauder’s fixed point theorem. We then present a recently developed method to study the existence of traveling wave fronts for a general class of models of predator-prey interaction described by reaction-diffusion systems. Our approach consists of a geometrical shooting argument and an analytic method by the construction of a Liapunov function and the use of Lasalle's invariance principle. Our approach can be extended to larger class of reaction-diffusion systems,

本报告以具体的例子来介绍数学中重整化方法的应用。考虑有理多面体中的整点个数问题，经典的结果由这多面体对应的簇的Riemman-Roch定理给出。我们现在重新考虑这一问题，以重整化方法给出了相应的答案。这不单给出了一个简单的方法，同时也说明了代数簇特征类的几何含义。

第一届科学计算学术研讨会必赢76net线路，上海，中国会议组织委员会：许学军、徐承龙、殷俊锋、关晓飞会议地址：上海市杨浦区四平路1239号必赢76net线路数学系（致远楼107室）会议时间：2015年6月13日(周六)主持人：许学军(08:40-10:10), 程晋(10:25-11:55)08:30-08:40领导讲话08:40-09:10程晋复旦大学TBA09:10-09:40陈文斌复旦大学一类非线性对流方程控制问题的数值分析09:40-10:10高卫国复旦大学计算物质科学中的若干特征值问题10:10-10...

We consider a singular stochastic control problem arising from continuous-time investment and consumption with capital gains tax, where the associated Hamilton-Jacobi-Bellman (HJB) equation admits many solutions. We show that the value function corresponds to the minimal viscosity solution of the HJB equation. Moreover, we prove by an explicit construction that the optimal strategy can be approximated by a sequence of sub-optimal strategies with bounded control. As far as we know, this is the first paper to explicitly construct such approximations in the singular control literature.

This talk consists of three parts. First, we develop an optimal tax-timing model that takes into account asymmetric long-term and short-term tax rates for positive capital gains and limited tax deductibility of capital losses. In contrast to the existing literature, this model can help explain why many investors not only defer short-term capital losses to long term but also defer large long-term capital gains and losses. Because the benefit of tax deductibility of capital losses increases with the short-term tax rates, effective tax rates can decrease as short-term capital gains tax rates increase. Second, we show that the value function corresponds to the minimum viscosity solution to the associated HJB equation. Third, we provide some insights on optimal strategy using asymptotic analysis. This work is based on my recent works with Baojun Bian, Jiatu Cai, Xinfu Chen, Hong Liu, Chen Yang, and Yifei Zhong.

Lusztig proposed 15 conjectures for any weighted Coxeter groups. In the present talk, we consider the weighted Coxeter groups $(W,S,L)$ with complete graphs. We first propose some conjectures for left cells, two-sided cells,distinguished elements and the function $/bold{a}$ /, of $(W,S,L)$.Then we verify our conjectures in the special case where $(W,S,L)$ is the weighted universal Coxeter group, furthermore, we verify the 15 conjectures of Lusztig for this group.

In this talk, we shall discuss the linear determinacy for a class of partially cooperative reaction-diffusion systems and several diffusive SIR models in epidemiology. The SIR models are typical predator-prey models. We characterize the spreading speed as the slowest speed of a family of traveling wave solutions. Our results are applied to a non-cooperative system describing interactions between ungulates and grass. We shall identify conditions for a population of ungulates can invade an infinite grassland. For the diffusive SIR models, we show that the existence of traveling waves is determined by the basic reproduction number of the corresponding ordinary differential equations and wave speeds.

I will explain super Schur-Weyl duality between the category of finite dimensional rational representations of general linear Lie algebras and the categories of modules of level two walled walled Brauer algebras. This is a joint work with Y. Su.