Abstract: (joint work with E. Piguet-Nakazawa) In 2014, Andersen and Kashaev defined an infinite-dimensional TQFT from the Quantum Teichmüller theory. This Teichmüller TQFT is an invariant of triangulated 3-manifolds, in particular knot complements.
The associated volume conjecture stated that the Teichmüller TQFT of an hyperbolic knot complement contains the volume of the knot as a certain asymptotical coefficient, and Andersen-Kashaev proved this conjecture for the first two hyperbolic knots.
In this talk I will present the construction of the Teichmüller TQFT and how we approached this volume conjecture for the infinite family of twist knots : in particular, we proved the conjecture for several new examples of knots, up to 13 crossings.
No prerequisites from quantum topology will be necessary.