Taut Foliations Through a Contact Lens

In the late '90s, Eliashberg and Thurston established a remarkable connection between foliations and contact structures in dimension three: any co-oriented, aspherical foliation on a closed, oriented 3-manifold can be approximated by positive and negative contact structures. Additionally, when the foliation is taut, its contact approximations are (universally) tight. In this talk, I will present a converse result concerning the construction of taut foliations from suitable pairs of contact structures. I will also describe a comprehensive dictionary between the languages of foliations and of (pairs of) contact structures. Although taut foliations are usually considered rigid objects, this contact viewpoint reveals some degree of flexibility. As an application, I will show that taut foliations survive after performing large slope surgeries along transverse knots.