Seminar 03.25.21 Lemańczyk

Title: On Furstenberg systems of some aperiodic multiplicative functions

Speaker: Mariusz Lemańczyk – Nicolaus Copernicus University in Toruń

Abstract: Studying arithmetic properties of multiplicative functions through the so called Furstenberg systems became a powerful and fruitful ergodic tool when dealing with the Sarnak and Chowla conjectures, cf. Frantzikinakis-Host’s theorem on the validity of logarithmic Sarnak’s conjecture for systems having not too many ergodic measures.
The Chowla conjecture, originally formulated for the Liouville function, was expected to hold for a much larger class of multiplicative functions in the sense that it has precisely one Furstenberg system, and this system is “maximally random”.
In 2015‪ Matomäki‬ , Radziwiłł and Tao gave a counterexample to Elliot’s conjecture by constructing aperiodic multiplicative functions (bounded by 1) for which (already) the Chowla conjecture of order 2 fails.
During the talk I will try to describe recent results concerning a variety of Furstenberg systems for ‪Matomäki‬, Radziwiłł, Tao’s functions, in particular, showing that the Chowla conjecture holds for them along some subsequences. The talk is based on my joint work with Alex Gomilko and Thierry de la Rue.

Zoom link: https://osu.zoom.us/j/98033590349

Meeting ID: 980 3359 0349

Password: Mixing

Recorded Talk: https://osu.zoom.us/rec/play/PSnnADgz3z7coGFSBSjBqrbhouGsBc5pHy_Y4tNGRq09SGk1UlLhd-xFZkOPSvRQG0d6qqc7ZUqaJZn7.z4J5lZq-XrTXCnPN?continueMode=true&_x_zm_rtaid=jIq7z5RFQZ-o8LQDfPiUrA.1617500870127.d8f12381bc2a272d1c51682f2c0006f0&_x_zm_rhtaid=771