Overtwisted contact structures

In this talk we discuss a criterion that characterizes overtwisted contact structures. The result establishes seven equivalent properties that relate overtwistedness to loose Legendrians, adapted open books decompositions and thick neighborhoods of overtwisted submanifolds. We first provide the necessary definitions and properties involved in the criterion, and then present the proof of (part of) these equivalences. Finally, we explore possible consequences and applications. This is joint work with E. Murphy and F. Presas.