Abstract: In this talk, we first review the definitions and relevant properties of geometric and topological quantities of graphs. Subsequently, we delved into the external and probabilistic constructions of expanders of regular graphs. Furthermore, we introduce a random probability model incorporating the topological genus g and n boundary vertices. Within this framework, we explore the asymptotical behaviors of Cheeger constants and eigenvalues of random graphs, considering various relationships between g and n. Notably, when g and n exhibited a comparable growth rate, we construct expanders explicitly.
报告人简介: 郭琪，中科院数学与系统科学研究院数学所博士，中国人民大学数学学院博士后，现任中国人民大学数学学院讲师。研究兴趣为变分法，临界点理论，随机图等，部分研究成果发表在Calc. Var. Partial Differential Equations, J. Differential Equations, SIAM J. Math. Anal., J. Math. Phys., Discrete Contin. Dyn. Syst. 等杂志上，已出版2本学术专著。主持或完成国家自然基金项目3项。
