**Description:**
Group actions on manifolds constitute a very active subject nowadays,
which lies at the interface between geometry, dynamical systems and
geometric group theory. Actions of fundamental groups of closed
surfaces are by far the most studied objects, because of the deep
relationship with hyperbolic geometry and more generally Teichmüller theory.
Although of similar geometric nature, actions of fundamental groups of
hyperbolic 3-manifolds have not received much attentions. From a geometric
and group-theoretical point of view, these groups have been a very central
object in the last decade, so the time seems appropriate to investigate more
their low dimensional dynamics. The aim of this workshop is to gather international
experts of the fields to describe the state of the art, and to try settling the
basis for a more general theory.

The workshop will feature introductory mini-courses and few extra talks. **tentative schedule**

**Mini-courses (tentative titles):**

- On Anosov flows and universal circle

by Harry Baik (Korea Advanced Institute of Science & Technology) - Orderability of 3-manifold groups

by Steve Boyer (Université du Québec, Montréal) - An introduction to arithmetic lattices of \(\mathsf{PSL}(2,\mathbb{C})\)

(TBA) - An introduction to (hyperbolic) 3-manifolds and their fundamental groups

by Luisa Paoluzzi (Université d'Aix-Marseille)

**Research talks:**

- Thierry Barbot (Université d'Avignon):

Orbital equivalence classes of Anosov flows on circle bundles over surfaces

Abstract: in 1981, E. Ghys proved that any Anosov flow on a circle bundle over a surface S is a finite covering of the geodesic flow of S. In this talk, I will present the proof of the following fact: if the index of the covering is odd, then all these flows on a given manifold are orbitally equivalent one to the other. If not, there are two orbital equivalence classes. This is a joint work with S. Fenley. - Michel Boileau (Université d'Aix-Marseille)
- Yan Mary He (University of Toronto and Université du Luxembourg)
- Alain Reid (Rice University)

**Organizers:**

- Christian Bonatti (CNRS & Université de Bourgogne)
- Sang-hyun Kim (Korea Institute for Advanced Study)
- Michele Triestino (Université de Bourgogne)
- Gioia Vago (Université de Bourgogne)

**Practical information:** The workshop will take place at the
Institut de Mathématiques de Bourgogne
of Université of Bourgogne (Dijon, France).
We can offer accommodation for most participants that register, giving priority to the youngest.

See the **list of registered participants**

**Supports:**

Université de Bourgogne

Institut de Mathématiques de Bourgogne (UMR CNRS 5584)

Région Bourgogne-Franche-Comté

Korea Institute for Advanced Study

National Research Foundation Grant, Korean Government

Projet ANR Gromeov