In this mini-course, we explore the relationship between the properties of Right-angled Artin groups (RAAG) and the properties of their defining graphs, which we then use to explore the properties of R-infinity for RAAG. In the first part, we will define RAAG and provide a (non-exhaustive) vocabulary to understand how graph theoretical properties translate to algebraic group properties and vice versa. In the second part, we define twisted conjugacy and the R-infinity property, after which we use the above vocabulary to prove that some RAAG families have the R-infinity property. Of course, both parts will be illustrated with specific examples.
