I will explain how the recent developments in the theory of birational geometry of rank 2 foliations on 3-folds have find quite a few applications in the study of the structure of such foliations and their singularities.
In this talk that is a complement to the course of Cascini and Spicer, but which will be self-contained, I shall briefly explain why the MMP terminates and then proceed to illustrate a few applications of these techniques, e.g., to the classification of canonical singularities, to the study of adjunction theory, and to the study of hyperbolicity properties of foliated 3-folds.
The work is in collaboration with Calum Spicer.[-]