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Explore the intricate connections between Furstenberg disjointness, Ratner properties, and Sarnak's conjecture in this 46-minute lecture by Mariusz Lemanczyk. Delve into the world of multiplicative functions, examining key concepts such as Mobius orthogonality, the Prime Number Theorem, and the Riemann Hypothesis. Investigate the Chowla conjecture on autocorrelations and analyze various strategies, including multiplicative weights and ergodic weights approaches. Examine topological dynamics, visible measures, and quasi-generic points, while exploring the relationship between the Chowla conjecture and Furstenberg systems. Gain insights into reductions in the logarithmic Sarnak conjecture case and understand the implications of Veech's conjecture in this comprehensive mathematical exploration.
