Corentin Correia, "Odomutants and flexibility results for quantitative orbit equivalence"

Thursday May 22, 2025, 10:30 AM → 12:00 PM Europe/Paris

Two measurable bijections of a standard probability space are orbit equivalent if they have the same orbits up to conjugacy. 

In recent years, odometers have been a central class of systems for explicit constructions of orbit equivalences, using their combinatorial structure. In this talk we introduce a construction of orbit equivalence between odometers and new systems that we call odomutants. This richer class, favourable to counter-examples, provides three flexibility results on quantitative versions of orbit equivalence. During this talk, we will emphasize on one of them, about the optimality of Belinskaya’s theorem. 

Belinskaya proved that orbit equivalence with integrable cocycles boils down to flip-conjugacy. We prove that it is optimal for all the odometers, namely for every odometer, we find a odomutant which is almost-integrably orbit equivalent to it but not flip-conjugate. This yields an extension of a theorem by Carderi, Joseph, Le Maître and Tessera.