Coorganisé avec Matthieu Joseph. Le groupe de travail se réunit tous les vendredis à 10h en salle 1013 du bâtiment Sophie Germain.
Si vous êtes intéressés, inscrivez-vous à la liste de diffusion pour recevoir les annonces.
Selon la demande, il est possible que nous diffusions les exposés sur BBB.
Prochain exposé: vendredi 25 octobre, 10:00, salle 1013, bâtiment Sophie Germain, diffusée sur BBB :
Around the commensurating full group II. (Antoine Derimay).
Résumé. Deciding whether two automorphisms of a standard Borel space are conjugate is a historically challenging problem, creating numerous new methods in an attempt at solving it.
Recently however, it has been shown by Foreman-Rudolph-Weiss that this equivalence relation is not Borel, meaning we have little chance of understanding it, ever.
A half-century before this result was known, Belinskaya showed that if two ergodic pmp automorphisms have the same orbits, and one has an integrable cocycle with respect to the other, then they are flip-conjugate.
This result encouraged Le Maître in 2018 to introduce the L1 full group of a pop automorphism T, defined as the group of automorphisms preserving the T-orbits such that their cocycle is integrable. This group has proven to have a number of nice properties: it is Polish, its quasi-isometry type is known, it is an algebraic invariant of flip-conjugacy etc.
However, those results can only hold when T is pmp, which is a restricted setting. A solution to this problem, inspired by an alternative proof of Belinskaya’s theorem by Katznelson is to consider instead the commensurating full group.
In my talk, I will define the important notions of this area of research, before defining the commensurating full group and proving that many of the properties of the L1 full group still hold, and, if time allows it, I will also give some extra properties that the L1 full group doesn’t have.
Prévisions : Vacances ! Reprise le 8 novembre.