Sarnak’s conjecture implies Chowla’s conjecture along a subsequence - a dynamical proof
Dominik Kwietniak

The talk will have two parts: first, I will try to explain motivations and intuitions behind the conjectures of Chowla and Sarnak. Both problems remain open for some time (Chowla proposed his conjecture over 50 years ago), and both try to quantify randomness observed in the behavior of the Möbius function. I will rephrase these conjectures as problems about some specific dynamical system. In the second part of the lecture, I will discuss a recent result of Gomilko, Lemanczyk and me: the result says that the Sarnak conjecture implies that there is an increasing sequence of integers along which the Chowla conjecture holds. Our demonstration has two ingredients: the first is a result of Tao in the equivalence of logarithmic versions of the Sarnak and Chowla conjectures, and the second is a new tool: the set of limit points of the sequence of harmonic empirical measures.


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