5 problems

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 $K\subset S^3$ be a knot, and let $\mathbf{A}_K(e^x,e^p,Q)$ denote the three-variable $Q$-deformed $A$-polynomial associated with the mirror construction for the resolved conif…

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…