Explore the mathematical concept of group actions on the line in this 52-minute lecture by Michele Triestino from Université de Bourgogne. Delve into the description of all possible actions of a finitely generated group G on the line, focusing on the compact lamination formed by these actions up to pointed semi-conjugacy. Learn about the Deroin space of G and examine specific examples where such spaces can be described. Gain insights from this collaborative work involving Brum, Matte Bon, and Rivas, presented as part of the Workshop on Orderable Groups at the Centre de recherches mathématiques (CRM).