Flows and ideal triangulations of three-manifolds

Pseudo-Anosov flows are a class of dynamical systems on three-manifolds that have been extensively studied due to their deep connections with the topology and geometry of their underlying spaces. These include relationships with hyperbolic geometry, embedded surfaces, and fundamental groups. A modern approach to studying these flows is through veering triangulations, which are rigid combinatorial objects. Among their many applications, these triangulations have led to new computational and algorithmic techniques for studying pseudo-Anosov flows. In this talk, I will first give a broad overview of the correspondence between pseudo-Anosov flows and veering triangulations. I will then discuss my ongoing work on using related, but more flexible, combinatorial objects to study pseudo-Anosov flows.