学术报告（刘爽 2025.7.16）

报告摘要：We shall discuss some qualitative properties of the principal eigenvalues for three classes of linear time-periodic problems: spatially discrete (patchy) operators, parabolic operators, and parabolic systems. Our primary focus lies in analyzing the effect of diffusion and frequency on the principal eigenvalue, particularly its monotonicity and asymptotic behaviors as diffusion rate and frequency approach zero or infinity. Additionally, if time allows, we will discuss some recent progress on the topological structures of level sets for the principal eigenvalue, as a function of diffusion rate and frequency.

主讲人简介：2021年毕业于中国人民大学，主要研究方向为偏微分方程和生物数学，关注椭圆和抛物算子的特征值理论和多物种的传播性质，在J. Math. Pures Appl., Trans. Amer. Math. Soc., J. Funct. Anal., SIAM J. Math. Anal.等期刊发表论文多篇。入选博士后创新人才支持计划，主持国家自然科学基金青年基金项目。