Selim Ghazouani

Representations of surface groups into SL(2,R) and simple closed curves

A hyperbolic structure on a surface naturally gives rise to a representation of its fundamental group into SL(2,R). However not all such representations come from a hyperbolic structure. The geometry of such representations is still somewhat mysterious. I will try and present the history of the topic, motivations and interesting open problems.

If time permits, I may mention recent work joint with Florestan Martin-Baillon, about the role played by the images of simple curves of such representations.