9 problems

Let $K$ be a hyperbolic knot or link, so that $S^3\setminus K$ admits a hyperbolic structure. Let $J_{N-1}(K)$ be the normalized colored Jones polynomial at $q=\exp(\pi i/N)$, and…

Let $k=\overline{k}\subset\mathbb{C}$ be a conjugation-stable number field, let $\mathcal B(k)$ be its Bloch group, and let $vol:\mathcal B(k)\to\mathbb{R}$ and…

Let $M$ be a hyperbolic $3$-manifold with invariant trace field $k=k(M)$, and let $\overline{k}$ denote its complex conjugate. The Chern–Simons invariant $CS(M)$ lies in…

Neumann–Yang conjecture. The normalized Chern–Simons invariant

Let $L$ be a hyperbolic link, and let $J_N(L)$ be its colored Jones polynomial evaluated at $\exp\left(2\pi\sqrt{-1}/N\right)$. Write $\operatorname{vol}(L)$ for the hyperbolic vol…

Let $M$ be the relevant hyperbolic three-manifold, let $X=\tilde{X}(M)_0^{\mathrm{sm}}$, and let $P$ be an ideal point of $X$. Choose a local uniformizer $z$ at $P$ with…

Large-genus torsion conjecture. The imaginary part of the logarithm of this torsion satisfies

Let $L$ be a hyperbolic knot or link, and let $x_{M,N}(L)$ and $y_{M,N}(L)$ denote the real and imaginary parts, respectively, of the normalized colored HOMFLY quantity…

Let $M$ be a closed oriented $3$-manifold and consider finite Skyrme-energy, distributionally flat $SU(2)$ connections on $M$. Their Chern–Simons invariants are defined by the corr…