Groupe de travail "théorie ergodique"

Groupe de travail de théorie ergodique

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 : le vendredi 13 février, 10:00, salle 1013, bâtiment Sophie Germain, diffusée sur BBB, On the space of subequivalence relations (François Le Maître).

The space of subequivalence relations of a given non-singular equivalence relation is a Polish space whose study was initiated by Kechris. He rose the following natural question: when is the action of the full group (or the automorphism group) of a given ergodic non-singular equivalence relation on its space of subequivalence relations topologically transitive? When does this action have meager orbits? I will explain why the full group of the ergodic pmp equivalence relation acts topologically transitively with meager orbits on its set of subequivalence relations, and discuss the many remaining questions.

Prévisions : On the space of subequivalence relations II (François Le Maître), le 20 février (à confirmer).

Séances précédentes

30 janvier : Some (more) ergodic properties of Poisson boundaries and applications II (Corentin Le Bars). Abstract
Poisson boundaries represent the asymptotic significant behaviour of a stochastic process on a group. I will present some of their strong ergodic properties, and show that they naturally appear in some superrigidity problems in higher rank. This will be a sort of continuation of Antoine Derimay's talks, but I will introduce all the concepts.
9 janvier : Some (more) ergodic properties of Poisson boundaries and applications I (Corentin Le Bars). Voici les notes de l'exposé (en français). Le lien pour l'enregistrement n'est pas encore disponible suite à un souci technique, mais devrait finir par apparaitre.
3 octobre : Random walks and Poisson boundaries in ergodic theory I (Antoine Derimay). Voici l'enregistrement et les notes. Abstract
To a random walk on a group, one can associate a measured space on which the group acts by measure-class preserving automorphisms, called the Poisson boundary of the walk. This action is the equality case of entropy inequalities, and it satisfies strong ergodic properties and is amenable, which makes it a boundary in the sense of Bader-Furman. As such, a good understanding of this action can lead to various interesting rigidity results.
10 octobre : Random walks and Poisson boundaries in ergodic theory II (Antoine Derimay). Voici l'enregistrement et les notes.
14 novembre : The Poisson point process from scratch I (Sam Mellick) Voici l'enregistrement et des notes détaillées. Abstract

The Poisson point process is a fundamental object from stochastic geometry, with many real world applications. I will present this object from the ergodic theoretic perspective, and show in full detail how it is constructed, as well as prove many of its basic properties. Some probability theory knowledge will be assumed (but only a first undergrad probability course, and I will remind everyone of the key tools needed as they come up).

Whilst there is no particular guiding goal theorem, one should note that the Poisson point process has played an integral role in recent breakthroughs for proving fixed price one for higher rank semisimple Lie groups and products of groups, and this hopefully serves as sufficient motivation.
5 décembre : The Poisson point process from scratch II (Sam Mellick) Voici l'enregistrement et des notes détaillées.

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