报告题目：Singularly perturbed stochastic functional differential equations with infinite delay

报 告 人：吴付科教授（华中科技大学）

报告时间：2023年12月17日上午8:30-9:00

摘要：This talk examines singularly perturbed stochastic functional differential equations (SFDEs) with infinite delay. The fast component system under consideration is also described by the SFDE, which introduces essential difficulties. This talk aims to establish the averaging principle to simplify the original system. To overcome the difficulty due to delay and the coupling of the segment process, some properties as continuity and tightness on a space of continuous functions have to be investigated for the segment process. This work coauthors with Professors George Yin and Chao Zhu

个人简历：吴付科，华中科技大学数学与统计学院教授、博士生导师，主要从事随机微分方程及其相关领域研究，2011年入选教育部新世纪优秀人才支持计划，2014年获得国家自然科学基金委员会优秀青年基金资助，主要成果发表于SIAM系列，JDE和SPA等期刊。

报告题目：tiling structure of amenable groups and its applications

报 告 人：张国华教授（复旦大学）

报告时间：2023年12月17日上午9:00-9:30

摘要：The concept of amenable groups was introduced by von Neumann in 1929 while studying the Banach-Tarski paradox. However, the structure of amenable groups has been a bit mysterious since then. In their seminal work published in 1987 Donald Ornstein and Benjamin Weiss developed the machinery of quasitilings for it. Along with my colleagues we solved a question about tileability of countable amenable groups using finitely many tiles with good invariance properties. The problem was open for a long time, but it was overshadowed by another, more difficult, problem about tileability using only one tile. In this talk, I will report our finitileability theorem for amenable groups and some of its applications, including the study of symbolic extensions of amenable group actions and new dynamical characterizations of amenable groups.

个人简历：张国华，2007年7月博士毕业于中国科学技术大学数学系（现为数学科学学院），2013年起任职复旦大学数学科学学院教授。研究方向是拓扑动力系统，主要研究动力系统的复杂性理论和可数离散群作用动力系统的熵理论。在Memoirs Amer. Math. Soc., J. Reine Angew. Math., Adv. Math., Ergod. Th. Dynam. Systems, J. Mod. Dyn., J. Funct. Anal., J. Differential Equations等国际知名刊物上发表论文30余篇。

报告题目：Long time behavior of first order Hamilton-Jacobi equations

报 告 人：王楷植教授（上海交通大学）

报告时间：2023年12月17日9:30-10:00

摘要：The long time behavior problem for Hamilton-Jacobi equations is a very important problem which has received much attention over the past 20 years. We will first recall some known results on this problem for classical Hamilton-Jacobi equations (where Hamiltonians are defined on the cotangent bundle T*M of a manifold M). And then we introduce several new long time behavior results for contact Hamilton-Jacobi equations (where Hamiltonians are defined on the extended cotangent bundle T*M × R equipped with the canonical contact form).

个人简历：王楷植，上海交通大学数学科学学院，教授、博导、院长助理，上海高校特聘教授(东方学者)。主要从事哈密顿系统弱KAM理论的研究，相关成果发表在《Communications in Mathematical Physics》，《Journal de Mathématiques Pures et Appliquées 》，《SIAM Journal on Mathematical Analysis》，《Journal of Differential Equations》， 《Communications in Partial Differential Equations》等学术杂志。

报告题目：Periodic orbits on Hamiltonian energy surfaces

报 告 人：刘会教授（武汉大学）

报告时间：2023年12月17日10:30-11:00

摘要：It is a classical problem in conservative dynamics to investigate the existence of periodic motions of Hamiltonian systems restricted to energy levels. Since the global existence result of Rabinowitz and Weinstein in 1978, the problems about multiplicity and stability of closed characteristics on compact convex or star-shaped hypersurfaces in $\R^{2n}$ have been widely studied by many mathematicians. In this talk, I will review the history of the studies and main problems in this field ,and also report our recent results on the related topics.

个人简历：刘会，武汉大学数学与统计学院教授、博导。研究领域为哈密顿动力系统、非线性分析与辛几何，长期从事哈密顿能量面上的闭特征、芬斯勒流形上的闭测地线、切触流形上Reeb轨道等相关课题的研究，已在Geom. Topol., Adv. Math, J. Funct. Anal.等数学期刊上发表论文30余篇，获得优青、面上项目等多个国家级项目资助。

报告题目：multi-bump traveling waves in two kind of FitzHugh Nagumo type excitable systems

报 告 人：李骥教授（华中科技大学）

报告时间：2023年12月17日11:00-11:30

摘要：We study two excitable system including: FitzHugh Nagumo with several turning points, and a simplified cardiac cell model. Both of the two systems support traveling waves of various types.

Applying the framework of geometric singular perturbation theory, we show existence of multi-bumped waves based on heteroclinic bifurcation or exchange lemma. Then we analyze the spectrum of simple traveling pulse as well as multiple front/backs and prove spectral stability. The main tool is exponential dichotomies, Evans function, and Melnikov method.

个人简历：李骥，华中科技大学数学与统计学院教授，博士生导师，2008年本科毕业于南开大学数学试点班，2012年在美国杨伯翰大学取得博士学位，后在明尼苏达大学和密西根州立大学做博士后及访问助理教授，2016年加入华中科技大学。主要研究两类问题：1.几何奇异摄动理论及其在尤其是反应扩散方程组中的应用，尤其是行波的存在性，稳定性，以及其分支和相关动力学行为；2.浅水波孤立子稳定性问题，尤其是一类拟线性的浅水波孤立子问题。在包括TAMS , JMPA，JFA，AnnPDE，JDE，PhyD等杂志发表论文三十多篇。