5 problems

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…

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…

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 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…