14 problems

Let $L\subset(\mathbb{C}P^2,\omega_{\operatorname{FS}})$ be an embedded monotone Lagrangian two-torus, and let $\Lambda$ be the Legendrian lift of its canonical threefold Bohr–Somm…

Let $K$ be a knot in $S^3$. Its augmentation variety is the locus in $(\mathbb{C}^*)^2$ of pairs $(\lambda_0,\mu_0)$ for which the framed knot DGA of $K$, specialized at…

Let $L$ be a link, let $I_q(L)$ be the ideal of quantum relations annihilating the distinguished class $[L]$, let $I_q'(L)$ be the annihilator of its evaluation in antisymmetric co…

Let $L$ be a link, let its three-variable augmentation variety denote the algebraic variety associated to the degree-zero abelianized knot contact homology of $L$, and let…

Let $\Sigma$ be an algebraic weave, let $\mathcal{M}(\Sigma)$ be the correspondence it induces between two augmentation varieties of Legendrian links, and let…

Disk-potential deformation conjecture. For any knot $K$, there is a collection of functions $\epsilon=\{\alpha_{ij}(t,p)\}$ such that $U_{K}^{0,\epsilon}(p,t)$ is invariant under d…

For a knot $K$, let $A_K(\lambda,\mu)$ denote its $A$-polynomial and let $Aug_K(\lambda,\mu)$ denote its augmentation polynomial; their vanishing loci define the corresponding char…

Let $\mathcal{K}$ be a non-torus knot with an augmentation curve, and let $\widehat{B}_\mathcal{K}(p_1,p_2)$ denote the annulus kernel associated with that curve. The source does n…

Let $\mathcal{K}$ be a knot, and let $N_\mathcal{K}$ be its appropriate normalization factor. The variational formula referred to in the source is the formula governing the variati…

Let $K$ be a non-split link, let $K_n$ be its $n$th component, and let $K-K_n$ be the remaining link. Let $V_K(n)$ and $V_{K_n}(1)$ be the corresponding augmentation varieties, and…

Let $K$ be an $n$-component link. For each primitive partition $P$ of its components, let $V_K(P)$ be the corresponding augmentation-variety component, and let $\Gamma_K$ be the gr…

Let $K$ be a non-split $n$-component link, let $V_K(P)$ denote the $n$-dimensional variety associated with a primitive partition $P$, and let $\Gamma_K$ be the graph whose vertices…

Let $K$ be a knot, let $L_K$ be its associated Lagrangian, and let the augmentation variety be the curve parametrizing one-dimensional representations of the knot's differential gr…

Let $K$ be a link, let its augmentation variety encode the relevant large-$N$ data, and let the colored HOMFLY polynomial be considered in the large-$N$ limit. Large-$N$ colored HO…