On the Stability of Möbius Disjointness in Topological Models (Morlet Chair Mariusz Lemanczyk)

One of the main difficulties to deal with Sarnak’s conjecture on Möbius disjointness is to show that its validity is a measure-theoretic invariant, that is, if its holds for one topological model of an automorphism then it holds for all of them. The research will be focused on finding joining criteria sufficient for this stability of Sarnak’s conjecture. We conjecture that such criteria should work in the class of distal transformations.