Jones polynomials, volume, and essential knot surfaces: a survey
  This paper is a brief overview of recent results by the authors relating colored Jones polynomials to geometric topology. The proofs of these results appear in the papers [arXiv:1002.0256] and [arXiv:1108.3370], while this survey focuses on the main ideas and examples. 
David Futer, Efstratia Kalfagianni, Jessica S. Purcell
math.GT