# ANR Project AGRUME – Group actions and model theory

coordinated by Itaï Ben Yaacov

## Description

The main goal of the project is to study interactions between dynamical systems and model theory. We are going to concentrate on four main themes:

- Relations between Ramsey properties of a Fraïssé class and topological dynamical properties of the automorphism group of the Fraïssé limit. One of our main goals is to find a useful sufficient condition for an automorphism group to have a metrisable universal minimal flow (which will have many Ramsey-theoretic applications).
- A model-theoretic approach to ergodic theory. We are intersted in applications of continuous logic to ergodic theory and orbit equivalence. One of our main goals is to develop a model-theoretic approach to the theory of entropy (for both amenable and non-amenable groups).
- Correspondences between model-theoretic properties (of structures, or formulas) and dynamical properties (of automorphism groups, or of functions defined on them). In particular, the extension of several existing such correspondences beyond the ω-categorical setting, or beyond the discrete setting.
- A study of the normal subgroup structure of automorphism groups. In particular, the study of the subgroup of “bounded automorphisms”, and its subgroups, both in several specific cases and under general hypotheses.

## Announcements and events

- Special semester: Descriptive set theory and Polish groups, Bernoulli Center, Lausanne, 2018.
- Conference: Measurable, Borel and topological dynamics, CIRM, Luminy, 7–11 October 2019.
- Kostya Slutsky started as a one-year postdoc in Paris funded by the project in September 2019.
- AGRUME meeting in Colmar, 1–4 September, 2021.
- Conference: Model theory and applications 2022, Cetraro, Italy, 20–25 June, 2022.

## Members

The project has two nodes, based in Lyon and in Paris.

### Lyon

- Tuna Altınel (Univ. Lyon 1)
- Gianluca Basso (Univ. Lyon 1)
- Itaï Ben Yaacov (Univ. Lyon 1), coordinator of the project
- Thomas Blossier (Univ. Lyon 1)
- Charlotte Hardouin (Toulouse)
- Julien Melleray (Univ. Lyon 1)
- Lionel Nguyen Van Thé (Aix-Marseille)
- Todor Tsankov (Univ. Lyon 1)
- Frank Wagner (Univ. Lyon 1)

### Paris

- Élisabeth Bouscaren (CNRS, Univ. Paris Sud)
- Zoé Chatzidakis (CNRS, ENS Paris)
- Tomás Ibarlucía (Univ. Paris Diderot), coordinator of the node
- François Le Maître (Univ. Paris Diderot)
- Kostya Slutsky (IMJ-PRG)
- Alessandro Vignati (Univ. Paris Diderot)
- Andy Zucker (IMJ-PRG)

## Information for members

- Please acknowledge support in your papers by mentioning the name of the project (AGRUME) and the ANR code (ANR-17-CE40-0026).
- The duration of the project is four years: from October 2017 to September 2021.