Flows, triangulations and algorithms on 3-manifolds

Pseudo-Anosov flows are a rich class of dynamical systems on 3-manifolds which are studied for their deep connections to the geometry and topology of the underlying space. A modern tool for studying these flows is to capture them with combinatorial objects called veering triangulations. This correspondence lets us study the flows from a computational perspective. In this talk, I will first give an introduction to pseudo-Anosov flows and how they are captured by these ‘old’ triangulations. I will then give a ‘new’ triangulation which captures these flows in greater generality, giving us many new explicit examples. I will finish by discussing how to algorithmically pass between the old and the new.