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# Welcome to GDAR

Franco-Brazilian-Chilean Mathematical Project

on Geometry, Dynamics and Anosov Representations.

MATH-AMSUD 2017 Project N° 38888QB

The goal of the project is to generate and enhance the contact between Brazil, Chile and France, and to establish a network of scientific investigation and development in the area of Anosov aspects of lorentzian and complex geometry, and related questions of piecewise projective actions on the circle. Another important aspect is to encourage the participation of young researchers to ensure the continuity of the collaboration network initiated by this project.

**Scientific proposal **

In the last decade, Anosov representations appeared to be an important tool in the study of several geometric notions. This project will allow the collaboration between the scientific teams of the various partners, particularly for their young members, assisted by several international experts in other places in France, Chili or Brazil. A central idea will be to apply the notion of Anosov representations in the following area:

- Conformally flat lorentzian geometry,
- Complex geometry.

More precisely, the main goal will be:

- To establish a correspondence between Anosov representations into \(\mathrm{SO}(2,n+1)\) and conformally flat globally hyperbolic spacetimes of dimension \( n+1,\)
- To study the dynamics of Anosov representations of surface groups into \(\mathrm{SL}(3,\mathbb{R} )\) or \(\mathrm{PU}(1,2)\),
- To study the connection between the group of piecewise projective transformations of the circle and singular space-times.