Before his work on geometrization, Thurston introduced the Thurston norm of 3-manifolds and related it to taut foliations. Based on his work, it was proved that Heegaard Floer homology determines the Thurston norm. Yi Ni of the California Institute of Technology discusses an analogue of Thurston norm for rational homology spheres, and its lower bound from Heegaard Floer homology, June 24, 2014 at the Bill Thurston Legacy Conference.
The conference, "What's Next? The mathematical legacy of Bill Thurston," held at Cornell June 23-27, 2014, brought together mathematicians from a broad spectrum of areas to describe recent advances and explore future directions motivated by Thurston's transformative ideas.