应兰州大学数学与统计学院邀请，大连理工大学数学科学学院魏润菊博士将于2025年4月3日上午举行线上学术报告。

报告题目: Measure-theoretic complexity, rigidity andlogarithmic Sarnak conjecture

报告摘要：In this talk,we will present theconnection of complexity functions and rigidity both in measure-theoretic and topological settings. We will give a sufficient condition for the logarithmic Sarnak conjectureto be valid.

In precise, we introduce max metric $d_{n,q}$ and mean metric \bar{d}_{n,q}. By these two metrics,we introduce periodic sequence complexity functions both in measure-theoretic and topological settings. It turns out that $(X,B_X,\pho, T)$ is rigid if and only if the invariant measure $\pho$ has bounded periodic sequencec omplexity with respect to if and only if the invariant measure $d_{n,q}$ has bounded periodic sequence complexity with respect to

$d_{n,q}$ . Then, we obtain formulas for the measure-theoretic entropy of an ergodic measure preserving system (resp. the topological entropy of a topological dynamical system) in these two metrics $d_{n,q}$ and $\bar{d}_{n,q}$ respectively.

Moreover. By replacing the periodic time sequence with general strictly increasing time sequence,we introduce sequence complexity functions both in measure-theoretic and topological settings, and give the equivalent characterization of uniform rigidity and measurerigidity.It turns out that if each invariant measure $\pho$ of a topological dynamical system $(X, T)$ has sub-linear measure-theoretic sequence mean complexity, then $(X, T)$ meets the logarithmic Sarnak conjecture.In particular, if each invariant measure $\pho$ of $(X, T)$ is measure rigidity, then logarithmic Sarnak conjecture holds.

时 间：4月3日（星期四）9：00-10:30

腾讯会议ID：845-851-444

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报告人简介

魏润菊博士，现在大连理工大学数学科学学院从事博士后研究工作，合作导师柳振鑫教授。2014年本科就读于西北师范大学数学与应用数学专业，2018年进入中国科学技术大学数学科学学院硕博连读，2023年获得理学博士学位，博士生导师黄文教授。目前主持博士后基金（国家资助博士后研究人员计划C档）1项和国家自然基金委员会青年项目1项，并在国内外知名数学期刊Ergodic Theory and Dynamical Systems、Discrete and Continuous Dynamical Systems、Acta Mathematica Sinica, English Series、Communications in Mathematics and Statistics发表数篇文章。

数学与统计学院

甘肃应用数学中心

甘肃省高校应用数学与复杂系统省级重点实验室 萃英学院

2025年4月1日