Presentations for sisters of one-cusped Picard modular groups

Arithmetic lattices form a rich class of lattices in negatively-curved symmetric spaces. However, certain information about the geometry of these groups is often complicated to compute. Group presentations, in particular, can provide a plethora of important group-theoretic and geometric information. Recently, Mark and Paupert devised a method for computing group presentations of the single-cusped Picard modular groups in complex hyperbolic space. In this talk, we will discuss their method and its generalization to a larger class of lattices in complex hyperbolic space, which includes the so-called sister lattices of the Picard modular groups.