Mariusz Lemanczyk: Furstenberg Disjointness, Ratner Properties and Sarnak’s Conjecture
International Mathematical Union via YouTube
Overview
Syllabus
Intro
Mobius orthogonality and Sarnak's conjecture
Multiplicative functions
General motivations: mean of p, Prime Number Theorem (PNT). Riemann Hypothesis (RH) Thecrem Landau The following conditions are equivalent
What makes it a difficult problem?
Chawla conjecture on autocorrelations Chowla conjecture
Multiplicative weights (MW-) strategy
Ergodic weights (EW-) strategy
MW-strategy: discussion on "controversies"
MW-strategy, basics 2
Sarnak's conjecture - selected examples
Topological dynamics. Visible measures and (quasi-)generic points
Chowla conjecture and Furstenberg systems
log S holds for deterministic uniquely ergodic systems
Reductions in the logarithmic Sarnak conjecture case
Further reductions for the logarithmic Sarnak conjecture
Veech's conjecture.III
Taught by
International Mathematical Union