22 problems

Let $A$ be the annulus, and let $L\subset A\times I$ be an annular link. Let $\mathrm{wrap}(L)$ be the minimal geometric intersection number between $L$ and a meridional disk in…

Let $A$= $S^1\times[0,1]$ be the annulus, let $L\subset A\times I$ be an annular link, and let $\mathrm{wrap}(L)$ be the minimal geometric intersection number between $L$ and a mer…

Morton's conjecture. These central elements generate the entire center $Z(B_{r,s})$.

Let $\mathcal{T}ang$ be the category of tangles, let $\Lambda\mathbf{Grp}$ be the category of groups, and let $\Gamma\colon\mathcal{T}ang\to\Lambda\mathbf{Grp}$ be the tangle group…

Let $H_{n,p}$ be the Homfly skein algebra with $n$ positive and $p$ negative boundary points, let ${\cal C}$ be the skein of the annulus, and let … be the algebra homomorphism obta…

Let $\Sigma_g$ be a closed surface of genus $g$, let $L_{WRT}$ be the Witten–Reshetikhin–Turaev projective representation of the mapping class group, and let…

Blanchet–Costantino–Geer–Patureau Mirand faithfulness conjecture. The projective representation $L_{r_{\omega}}$ is injective. These representations were introduced to obtain mappi…

Let $N$ and $n$ be parameters for the skein algebra $\mathrm{SkAlg}_{\mathrm{SL}_N,n}$, and let $\overline{\pi}$ denote the element defined in the surrounding discussion. Central p…

Let $N$ be a positive integer, let $T^2$ be the torus, and let $\mathrm{SkCat}_{\mathrm{SL}_N}(T^2)$ and $\mathrm{SkAlg}_{\mathrm{SL}_{N/d}}$ denote the corresponding skein categor…

Let $G$) be a reductive group, let $\Sigma$ be a closed compact surface, and let $\mathrm{SkCat}_G(\Sigma)$ denote the $G$-skein category at a generic value of the quantization par…

Let $\lambda$ range over partitions, let $c(\square)$ and $h(\square)$ denote the content and hook length of a box $\square\in\lambda$, and let ${\mathsf{W}}_{\lambda,\emptyset}$ b…

Let $L_{st}$ be a Lagrangian filling of the Hopf link conormal, with $s,t\in\{l,m,d\}$ and $|s|=|t|$. Let ${\mathsf{Z}}_{L_{st}}$ denote its skein-valued partition function, and le…

Haioun's boundary-condition conjecture. Such a boundary condition on the invertible TQFT associated with $\mathcal{C}$ should recover the non-semisimple $(2+1)$-TQFT constructed in…

Yang–Baxter homology conjecture. The homology groups satisfy

Let $\mathrm{BSk}_n(T^2,*)$ be the braid skein algebra of the punctured torus with $n$ strands, and let $\mathrm{Sk}_n(T^2,*)$ be the corresponding full framed Homflypt tangle skei…

Let $\mathrm{Sk}(T^2-D^2)$ be the Homflypt skein algebra of the punctured torus, and let $\mathcal{E}_{\sigma,\bar\sigma}$ be the elliptic Hall algebra with generators…

Let $L$ be a link, and write its colored Jones polynomial in the form … where $S_{n,i}$ is the corresponding skein element and $C_{n,i}$ is its coefficient. Integrality conjecture.…

Let $L$ be a singular link with $k$ singular crossings, let $[L]_{2n}$ be its invariant, and let $C_{2n,n}$ be the Laurent polynomial defined in the source. Integrality conjecture.…

Let $L_1$ and $L_2$ be links with three components. For each $c$, let $\Sigma^c(L)$ denote the sum of the elements of the set $\mathbf{F}^c_p$ associated with $L$, where $p$ record…

Skein action conjecture. The operators $\{\tau_p:p\in M\}$ define an action of

Let $\gamma$ be a multicurve, let $f_\gamma$ be its trace function, and let $(\tau,\theta)$ be action-angle coordinates on the relevant open subset of $\mathcal M(\Sigma,t)$, with…

Let $t=(t_1,\ldots,t_n)$ be a family in $([0,\pi]\cap\mathbb{Q}\pi)^n$, let $D$ be the common denominator of the rational numbers $t_j/\pi$, and let…