Taut foliations through a contact lens

Abstract

This survey explores the rich interplay between (taut) foliations and (tight) contact structures in dimension three, highlighting recent work of the author. We outline a new method for constructing taut foliations from suitable pairs of contact structures, and discuss some applications and future research directions. In particular, we give a brief account of work in progress with Jonathan Zung on ziggurats for taut foliations transverse to pseudo-Anosov flows, and we propose a (mostly speculative) contact perspective on the $L$-space conjecture.