Lecturer:Harald Helfgott

Abstract:

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: forthe Liouville function (that is, the completely multiplicative function withfor every prime),

which is stronger than well-known results by Tao and Tao-Teravainen. We also manage to prove, for example, thataverages to 0 at almost all scales whenrestricted to have a specific number of prime divisors, for any "popular" value of(that is,for).

Introduction to the Lecturer:

Harald Helfgott, Humboldt-Professur of Georg-August-University of Göttingen, Germany, Researcher of CNRS (Centre National de la Recherche Scientifique), France; Winner of a series of awards, including Leverhulme Award, Whitehead Award and Adams Award, etc., giving a complete proof of Weak Goldbach Conjecture in 2013; Invited Reporter of ICM (International Congress of Mathematicians) in 2014, and Elected Fellow of American Mathematical Society in 2019.

Invitee:

LIU Jianya MENG Xianchang

Time:

20:00-22:00, March 30 (Wednesday)

Venue:

Tencent Rooms ID: 965-071-968

Sponsor: Mathematics School of Shandong University