一、题目：

Well-mixing vertices and almost expanders

二、主讲人：

刘鸿

三、摘要：

We study regular graphs in which the random walks starting from a positive fraction of vertices have small mixing time. We prove that any such graph is virtually an expander and has no small separator. This answers a question of Pak [SODA, 2002]. As a corollary, it shows that sparse (constant degree) regular graphs with many well-mixing vertices have a long cycle, improving a result of Pak. Furthermore, such cycle can be found in polynomial time. Secondly, we show that if the random walks from a positive fraction of vertices are well-mixing, then the random walks from almost all vertices are well-mixing (with a slightly worse mixing time).

四、主讲人简介：

刘鸿，2015在伊利诺伊大学厄本那—香槟分校(UIUC)取得博士学位，师从József Balogh。后于2019年在华威大学(Warwick)取得终身教职，并摘获英国科研创新未来领袖奖。于2022年加入韩国基础科学研究院(IBS)任首席科学家，现是其极值及概率组合研究组(ECOPRO)的领头人。研究领域包括极值、概率组合、图论、离散几何、组合数论等。

五、邀请人：

王光辉 数学学院教授

六、时间：

2月14日（周二）10:30-11:30

七、地点：

中心校区知新楼B座924报告厅

八、主办：

山东大学数学学院