6 problems

Let $U$ be an unknot in $\mathbb{R}P^3$ colored by an $n$-dimensional skew-symmetric or symmetric representation $R$ of $su(2)$. Let $Z_{R\emptyset}(U;Q,q)$ be its invariant, and l…

Let $\boldsymbol\mu=\{\mu_a\}_{a=1}^{4}$ be plane partitions with no PT$_0$ moduli, and let $\mathsf V^{\mathrm{DT}}_{\mu_1\mu_2\mu_3\mu_4}(q)$ and…

Fix plane partitions $\boldsymbol{\mu}=\{\mu_a\}_{a=1}^{4}$ corresponding to $(\mathbb C^*)^3$-fixed subschemes of $\mathbb C^3$ of dimension at most one, viewed as asymptotic cros…

Framed ADKMV conjecture. The framed topological vertex is given by

Let $\mu^1,\mu^2,\mu^3$ be partitions, and let $W_{\mu^1,\mu^2,\mu^3}(q)$ denote the topological vertex. For $i,j\in\{1,2,3\}$ and $m,n\geq 0$, let $A_{mn}^{ij}(q)$ be the explicit…

Let $V_{,,}$ be the DT topological vertex and let $W_{,,}$ be the weighted labelled-box vertex. Let … be the plane-partition generating function. Pandharipande–Thomas topological v…