Drilling veering triangulations and applications to pseudo-Anosov flows

By a result of Agol and Guéritaud, a transitive pseudo-Anosov flow F on a closed three-manifold N, along with a certain collection O of its closed orbits, determines a veering triangulation V of N - O that encodes F. Together with Henry Segerman, we devised and implemented an algorithm that takes as an input V and a closed orbit c of F that is not in O, and returns a veering triangulation of N - O - c that also encodes F. I will discuss the main ideas behind the algorithm, its key challenges, and its role in collecting experimental evidence for certain conjectures about pseudo-Anosov flows.