Title:
Some progress on the volume conjecture for the Turaev-Viro invariants
Abstract:
In 2015, Qingtao Chen and I conjectured that at the root of unity exp(2πi/r) instead of the usually considered root exp(πi/r), the Turaev-Viro and the Reshetikhin-Turaev invariants of a hyperbolic 3-manifold grow exponentially with growth rates respectively the hyperbolic and the complex volume of the manifold. In this talk, I will present a recent joint work with Giulio Belletti, Renaud Detcherry and Effie Kalfagianni on an infinite family of cusped hyperbolic 3- manifolds, the fundamental shadow links complement, for which the conjecture is true.