Recent developments in pseudo-Anosov flows

Pseudo-Anosov flows on 3-manifolds are dynamical systems generalizing the behavior of geodesic flow on the unit tangent bundle of a hyperbolic surface. Like geodesic flows, they come with two transverse, invariant 2-dimensional foliations (possibly with some prong singularities) which meet along the 1-dimensional foliation by orbits. Because of various surgery techniques, there are many examples known, and their "topological" classification is an interesting and important problem both in low-dimensional geometric topology and dynamics. I will describe some of this framework, and then some joint work with T. Barthelmé, S. Frankel, S. Fenley and C. Bonatti, on describing the structure and classification of such flows and their associated foliatoins.