1. 报告题目：Moser twist theorem and applications
报告人：柳彬教授（北京大学）
报告地点：数学楼二楼会议室
报告时间：2019年11月17日（星期日）上午9：00 -- 9：50。
摘要：in this talk, we report recent developemnts for the existence of invariant curves and its applications to differential eqautions, in particular, to the boundedness of solutions。
2. 报告题目: Dynamical Behaviors of A West Nile Virus Model with Age Structure
报告人： 毕平教授（华东师范大学）
报告地点：数学楼二楼会议室
报告时间：2019年11月17日（星期日）上午9：50 -- 10：40。
摘要：West Nile Virus (WNV) is the most commonly transmitted to humans by mosquitoes. There are no medications to treat or vaccines to prevent WNV infection. Recent research demonstrates that age plays an important factor in the infection of WNV among human population. In this talk, I introduce age structure to the humans into the WNV model of Chen et al., which include mosquito, bird and human populations. The results show the age-structure will not change the properties of the disease-free equilibrium. The stability of the positive steady state for the human subsystem is also studied.
This report shows the number of infected mosquitoes need to be controlled in order to reduce the risk of being infected with WNV.
3. 报告题目: Heteroclinic bifurcation in a class of piecewise smooth systems
报告人： 刘兴波教授（华东师范大学）
报告地点：数学楼二楼会议室
报告时间：2019年11月17日（星期日）上午10：50 -- 11：40。
摘要：In this talk, we consider a high–dimensional piecewise smooth system with heteroclinic orbits connecting two hyperbolic equilibria. We assume that the equilibria lie in different region separated by the discontinuity boundary, and the heteroclinic orbits cross transversally the discontinuity manifolds. We study the persistence of such a heteroclinic connection and the existence of limit cycle under small perturbation.
4.报告题目：Approximate controllability for a semilinear evolution system with infinite delay
报告人：傅显隆教授（华东师范大学）
报告地点：数学楼二楼会议室
报告时间：2019年11月17日（星期日）下午2：00 -- 2：50。
摘要：In this work, we study the approximate controllability for a class of control systems governed by semi-linear equations with infinite delay in Hilbert spaces. Sufficient conditions for approximate controllability are established by constructing fundamental solutions and using resolvent condition and techniques on fractional power operators. As an illustration of the application of the obtained results, an example is also provided.
5. 报告题目：一类脉冲微分方程组的多尺度研究
报告人：倪明康教授（华东师范大学）
报告地点：数学楼二楼会议室
报告时间：2019年11月17日（星期日）下午2：50 -- 3：40。
摘要：本文讨论了一类具有固定时间的平面脉冲微分方程组解的动力学性质。首先利用 Tikhonov 正则化原理, 引入一类具有无穷大初值的奇摄动方程组。利用 奇摄动问题的空间对照结构理论对原脉冲问题的定义域进行了划分，得到了正则区域和转换区域，在不同的区域通过引入不同的尺度，成功进行了流的转换，并求得了解的一致有效渐近表达式。
作者通过分析渐近表达式的动力学行为刻画了原脉冲微分方程组解的动力学性质,由极限定理可知当小参数趋向于零时,所构造的渐近解趋向于原脉冲问题的脉冲解，由此建立了研究这类脉冲微分方程的正则化理论框架。
6. 报告题目：Univoque Bases for Real Numbers
报告人：李文侠教授（华东师范大学）
报告地点：数学楼二楼会议室
报告时间：2019年11月17日（星期日）下午3：50 -- 4：40。
摘要：For real numbers $x>0$ and $\beta >1$, a sequence $(x_k)\in \{0, \cdots , \lfloor\beta\rfloor\}^{\mathbb N}$ is called an expansion of $x$ in base $\beta $ if$$x=\sum _{k=1}^\infty \frac{x_k}{\beta ^k},$$where $\lfloor\beta\rfloor$ denotes the biggest integer less than $\beta$.Fix an $x\in (0, +\infty )$. Let $$U(x)=\{\beta >1: x \;\textrm{has a unique expansion in base}\; \beta \}.$$
In this talk, I will introduce some results on $U(x)$ obtained by my students Jiayi Xu and Zhiqiang Wang. This work is motivated by the result Univoque sets for real numbers by F. Lv, B. Tan and J.Wu.
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