Classifying Anosov flows in dimension 3 by geometric types

In this talk, I will introduce a new approach to the problem of classification of transitive Anosov flows in dimension 3 up to orbital equivalence. To every transitive Anosov flow on a 3-manifold, we can associate a group action on a bifoliated plane characterizing completely the original flow up to orbital equivalence. During my thesis, I proved that all the information of the previous action can be stored inside a combinatorial object, called a geometric type, and thus that geometric types can be used to classify Anosov flows in dimension 3. In this talk, I will explain how one constructs geometric types for any Anosov flow and I will also mention some recent applications of this classification method in the theory of Anosov flows.