Abstract: The study of Einstein metrics has a rich history in differential geometry with origins in general relativity. Ricci soliton metrics are a generalization of Einstein metrics that arise as self-similar solutions to the Ricci flow. An important subclass of Ricci solitons is given by the so-called algebraic solitons. More specifically, a Lie group S with a left invariant metric is said to be an algebraic Ricci soliton if the \((1,1)\) Ricci tensor Ric satisfies an equation of the form: \( Ric= cId+ D\) for some derivation \(D \in Der(\frak{s})\). Motivated by the Alekseevskii conjecture, an active area of research in recent years has been the study of submanifolds of symmetric spaces and their connections to homogeneous Einstein and Ricci-soliton metrics. In this talk I will explain some of these ideas and talk about a recent work by Sanmartin-Lopez, which claims to classify Ricci soliton codimension one subgroups of nilpotent Iwasawa groups.