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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...

Talk Title and AbstractOn the study of the first order Melnikov functionnear homoclinic and heteroclinic loops韩茂安Shanghai Normal University, ChinaIn this talk, we introduce some advances on the expansion of the first order Melnikov function appearing by perturbing a Hamiltonian or integrable system with a homoclinic or heteroclinic loop. We obtain formulas for computing the first coefficient...

拓扑学青年学者论坛程序册(Program)5月15日星期五 上午8:50-9:00欢迎词梁汉营9:00-9:50Witten Rigidity on Odd Dimensional Manifolds韩飞梁汉营9:50-10:15拍照10:15-11:05TBA王诗宬赵学志11:10-12:00Matrix group actions on CAT(0) spaces and Spheres叶圣奎12:00-2:30午餐5月15日星期五 下午时间报告(致远楼107)报告人主持人2:30-3:00实moment-angle流形的上同调环蔡力潘生亮3:20-3:50self-dual codes and simple polytopes...