Title: The dichotomy between structure and randomness in multiplicative number theory
Speaker: Florian Richter (Ohio State University)
Abstract: We will begin the talk by discussing a dichotomy theorem in multiplicative number theory which asserts that any multiplicative function (that satisfies certain minor regularity conditions) is either a (special kind of) almost periodic function or a pseudo-random function. Then we will explore how this phenomenon extends to other classical objects coming from multiplicative number theory. In particular, we will study the combinatorial and dynamical properties of level sets of multiplicative functions and I will present a structure theorem which says that for any level set E of an arbitrary multiplicative function there exists a highly structured superset R such that E is a pseudo-random subset of R.