Markov partitions for geodesic flows

Geodesic flows of negatively curved surfaces are one of the two classical families of Anosov flows on 3-manifolds. These are interesting objects to study, because, among other reasons, their periodic orbits are in one-to-one correspondence with the isotopy classes of closed curves of the surface. In this talk, we will start by introducing these geodesic flows, then explain the concept of Markov partitions, which is a useful tool for studying periodic orbits of Anosov flows in general. We will then illustrate a way of obtaining Markov partitions for these geodesic flows, via something called veering branched surfaces.