4 problems

The volume conjecture for the Teichmüller TQFT. There exists a smooth function $J_{M,K}(\hbar,x)$ on $\mathbb{R}_{>0}\times\mathbb{R}$ such that

Akutsu–Kashaev conjecture. There exists such a family with the following properties:

Let $X$ be a levelled shaped triangulated oriented pseudo 3-manifold, and let $Z_{\hbar}^{\mathrm{new}}(X)$ be the partition function defined from the Boltzmann weights in the prop…

Let $M$ be a closed oriented 3-manifold. For any hyperbolic knot $K\thinspace\subset M$, consider fully balanced shaped ideal triangulations $X$ of the complement of $K$ in $M$ and…