Homology of curves and surfaces in hyperbolic 3-manifolds

Vlad Markovic of the University of Cambridge shows that every second homology class in a closed hyperbolic 3-manifold can be realized by a nearly geodesic immersed surface, answering a question that Thurston asked two years ago, June 26, 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.