讲座主题：The embedding problems of topological structures by expander methods
专家姓名：杨帆
工作单位：Institute for Basic Science（韩国）
讲座时间：2026年06月05日 14:30-16:30
讲座地点：#腾讯会议： 894-486-939
主办单位：烟台凯旋官网数学与信息科学学院
内容摘要：
In this talk, I will introduce our recent results on the embedding problem of topological structures. Given a graph H, a balanced subdivision of H is obtained by replacing all edges of H with internally disjoint paths of the same length. We prove that for any graph H, a linear-in-e(H) bound on average degree guarantees a balanced H-subdivision. This strengthens an old result of Bollobás and Thomason, and resolves a question of Gil-Fernández, Hyde, Liu, Pikhurko and Wu. We also give an improvement for Liu and Montgomery’s result by showing that for integers t≥s≥2, every Ks,t-free graph with average degree d contains a balanced subdivision of a clique with at least Ω(d^(s/2(s?1))) vertices. Furthermore, we show that if G is an n-vertex graph with average degree d(G)≥d, then G contains a balanced KΩ(d)-immersion. This result develops further the work of DeVos, Dvo?ák, Fox, McDonald, Mohar, Scheide on 1-immersions of cliques in dense graphs.
主讲人介绍：
杨帆，2022年博士毕业于山东凯旋官网数学学院。2022-2025年在山东凯旋官网数据科学研究院从事博士后，2024年9月由国家留学基金委(CSC)资助赴韩国基础科学研究院(Institute for Basic Science)ECOPRO组从事博士后。主持国家自然科学基金青年项目，山东省自然科学基金青年项目，第73批中国博士后科学基金面上项目，主要研究方向为拓扑子式的嵌入问题及染色问题，在JLMS，JCTB，EJC等国际期刊共发表学术论文9篇。
