8 problems

Let $K$ be a hyperbolic knot in ${\mathbb S}^3$. An ideal triangulation $X$ of ${\mathbb S}^3{\smallsetminus} K$ has a nonempty angle-structure space $\mathcal{A}_X$, and let…

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

Let $M$ be a closed, oriented $3$-manifold and $K$ a hyperbolic knot in $M$ with a suitably decorated triangulation. Let $\mathcal{Z}_{\mathrm{b}}^{(N)}(X)$ be the corresponding Te…

Let $K\subseteq M$ be a knot inside a closed, oriented $3$-manifold, with hyperbolic complement. Let $\widehat{A}^{\mathbb{C}}_{K}$ denote the non-commutative polynomial arising fr…

Let $W$ be a three-manifold and let $\mathcal{S}_{y_0}\subset\Omega_{\mathcal{A}}$ be the space of fields reached at $y=y_0$ by Kapustin–Witten flows on $W\times\mathbb{R}^+_y$ sta…

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…