Séminaires : Séminaire des Thésards

Le séminaire des thésards est l'occasion pour les doctorants de présenter des résultats et des problématiques dignes d'intérêt devant un public de non-spécialistes. L'ambiance y est informelle ; poser des questions naïves est encouragé, et les questions moins naïves sont bienvenues dans la mesure où elles n'entravent pas le bon déroulement de l'exposé.

Un jeudi sur deux à 18h00, en alternance entre Jussieu et Sophie Germain.

At the level of ergodic probability measure-preserving bijections, quantitative orbit equivalence aims at bridging the gap between the well-studied but very complicated relation of conjugacy, and the trivial relation of orbit equivalence, which is equality of orbits up to conjugacy. Indeed, Dye’s theorem states that orbit equivalence cannot distinguish between ergodic transformations. In order to obtain an interesting theory, quantitative orbit equivalence proposes to add quantitative restrictions to the cocycles associated to an identification of orbits.

The goal of this talk is to understand the statement of a recent theorem by David Kerr and Hanfeng Li : "every odometer is Shannon orbit equivalent to the universal odometer". After an overview of the state of the art in quantitative orbit equivalence (with a recall of basic notions in ergodic theory), I will introduce the odometers (a class of systems with an interesting combinatorial structure given by the cutting-and-stacking construction).

If time permits, I will end with an extension of this result, also using the cutting-and-stacking method but for the larger class of rank-one systems.