# Seminar 9.7.17 Lemanczyk

Title: Moebius disjointness for models of an ergodic system and beyond

SpeakerMariusz Lemanczyk (Nicolaus Copernicus University, Toruń, Poland)

Abstract: In 2010, P. Sarnak formulated the following conjecture:

For each zero entropy topological system (X,T), we have

$$\lim_{N\to\infty}\frac1N\sum_{n\leq N}f(T^nx)\mu(n)\to 0$$

for each $f\in C(X)$ and $x\in X$.  Here $\mu$ stands for the arithmetic

Moebius function. The talk will concentrate on motivations for Sarnak’s conjecture

(relations with celebrated Chowla conjecture in number theory), role of ergodic theory in it and some recent progress.