一、题目：

Expansion, divisibility and parity

二、主讲人：

Harald Helfgott

三、摘要：

We will discuss a graph that encodes the divisibility properties of integers by primes. We show that this graph is shown to have a strong local expander property almost everywhere. We then obtain several consequences in number theory, beyond the traditional parity barrier, by combining our result with Matomaki-Radziwill. For instance: for the Liouville function (that is, the completely multiplicative function with for every prime),which is stronger than well-known results by Tao and Tao-Teravainen. We also manage to prove, for example, that averages to 0 at almost all scales when restricted to have a specific number of prime divisors , for any "popular" value of (that is, for ).

四、主讲人简介：

Harald Helfgott,德国哥廷根大学洪堡教授，法国CNRS研究员。Leverhulme奖、Whitehead奖、Adams奖等获得者。2013年给出弱哥德巴赫猜想的完整证明。2014年国际数学家大会ICM受邀报告人，2019年当选美国数学会会士。

五、邀请人：

刘建亚 孟宪昌

六、时间：

3月30日（周三）20:00-22:00

七、地点：

Zoom: 155 152 924, 密码: 093611

八：主办方：

山东大学数学学院