The study of rational curves on a variety is a powerful tool to study the variety itself, and provides examples of many of the more abstract tools of algebraic geometry (e.g., cohomology, deformation theory, moduli spaces, and so on). In this talk, I'll give an elementary introduction to the study of rational curves on varieties: when do they exist, how do they fit together into "families", and what does this tell us about the variety? The focus will be on examples and ideas rather than technical details, and should be accessible to anyone who's taken a first course in algebraic geometry. There will also be some cool Desmos graphs to help make things concrete! Speaker(s): Devlin Mallory (UM)