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.