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Ergodic Theory/Probability Seminar - Florian Richter

Florian Richter
September 28, 2017
3:00PM - 4:00PM
Math Tower 154

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Add to Calendar 2017-09-28 15:00:00 2017-09-28 16:00:00 Ergodic Theory/Probability Seminar - Florian Richter Title: The dichotomy between structure and randomness in multiplicative number theorySpeaker: 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. Math Tower 154 Department of Mathematics math@osu.edu America/New_York public

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.

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