This project is about group actions on low-dimensional manifolds. This is a subject of intense development nowadays and its aim is to find relations between the algebraic or geometric data of a given group (or class of groups) with the dynamical features that an action of this group (or class of groups) can possibly display.

We will focus in two types of problems:
- Realization problems: Given a manifold, what are the groups that can act on it?
- Dynamical quality problem: Given an action of a group, how smooth can this action be made? Can we characterize the dynamics of group actions when a representation exists?.

This project will gather together a list of world-leader specialists in the field as well as young PhD and master students. The plan is to strengthen ongoing international collaboration and to engage into new ones as well. Besides small missions covered by this project we will also organize a graduate school in France in 2022 and a Workshop in Chile in 2023.