第一届科学计算学术研讨会同济大学，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号同济大学数学系（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.

Biological control is an environmentally sound and effective means of reducing or mitigating pests and pest effects through the use of natural enemies. In this talk, we propose and analyze a model on biological control, which is based on the abundance of pest and a simple predator-prey model. We first study the existence and stability of equilibria. It turns out that backward bifurcation occurs with the migration rate as the bifurcation parameter. The stability of the trivial equilibrium and the boundary equilibrium is delay-independent. However, the stability of the positive equilibrium may be delay-dependent. Moreover, delay can switch the stability of the positive equilibrium. When the positive equilibrium loses stability, Hopf bifurcation can occur.

报告人：张同华 教授Swinburne University of Technology, Australia题目：Delay-induced Turing instability时间：5月29日 下午3:00-4:00地点：数学系致远楼102欢迎各位老师和同学参加！张同华教授，澳大利亚斯威本科技大学（Swinburne University of Technology）数学系博士生导师。2005年－2010年就职于澳大利亚科廷大学（助理研究员，研究员）。2004年以来发表SCI论文40余篇；出版专著《Computation of Mathematical Models...