6 problems

Let $K\subset S^{3}$ be a knot, let $L_{K}$ be the corresponding Lagrangian in the resolved conifold $X$, and let $A_{K}(x,p,Q)$ be the augmentation polynomial of $K$, where $x$,…

Aganagic–Vafa conjecture. For each choice of knot, there is a corresponding mirror $\hat{X}_{K}$ describing the moduli space of Lagrangian fibers with geometry $L_{K}$ along the si…

Let $\{P_{K;n}(a,q)\}$ be the colored HOMFLY-PT polynomials of $K$, colored by the $n$-th symmetric power of the fundamental representation. Define operators by … Suppose these pol…

Let $K$ be a knot in $S^3$, and let $f(U)$ be the polynomial determined by the branch of the zero locus of $\operatorname{Aug}_K$ near $(\lambda,\mu,U)=(0,U,U)$ through … Here…

Let $K$ be a knot, and let $\operatorname{Aug}_K(\lambda,\mu,U)$ be its three-variable augmentation polynomial. When the $U=1$ slice of the augmentation variety has a maximal-dimen…

Let $K$ be a knot. The augmentation variety $V_K$ is the set of augmentation values in $(\mathbb{C}^*)^3$, and the augmentation polynomial is defined when the maximal-dimensional p…