Pleated surfaces and surface group representations inside PSL (n,C)

Since their introduction by Thurston, pleated surfaces have been extensively deployed to study the geometry of hyperbolic 3-manifolds and representations of the fundamental group of a closed surface of genus larger than 1 (in short, a surface group) inside PSL(2,C). In this talk, we will see how the notion of pleated surface can be suitably generalized to investigate wide classes of surface group representations inside PSL(n,C) for every n larger than 1. We will also discuss applications and questions that arise naturally from their study. This talk is based on an upcoming work with S. Maloni, G. Martone, and T. Zhang.