Taut foliations from knot diagrams

Taut foliations have been a classical object of study in 3-manifolds theory. Recently, new interest in them has come from the investigation of the so-called "L-space conjecture", that predicts that Heegaard Floer L-spaces can be characterised as those 3-manifolds that do not admit coorientable taut foliations. A possible approach to the study of this conjecture is analysing surgeries on knots and links. Most of the techniques employed for constructing taut foliations on Dehn surgeries usually make use of some property of the exterior of the link, for example its fiberedness. It is interesting to address this study from a different perspective, using other types of properties of knots and links. In this talk I will introduce the L-space conjecture and present a result about the existence of taut foliations on all non-trivial surgeries on knots with a special diagram.