7 problems

Let $\mathcal{K}_{\tau}$ be a knot in $S^3$ with framing $\tau\in\mathbb{Z}$, and let $Z_{CS}^{(S^3,\mathcal{K}_{\tau})}(q,a,\mathbf{x})$ be its Chern–Simons partition function. De…

LMOV conjecture. For every $\mu\in\mathcal{P}_+$, the function $F_{\mu}^{(X,\mathcal{D})}$ has the integral expansion given by the right-hand side of the open multiple-covering for…

Let $\mathbb{P}$ be a smooth projective surface, let $\widehat{\mathbb{P}}$ be the blow-up of $\mathbb{P}$ along $L$ with exceptional curve $C$, and let…

Gaussian/binomial distribution conjecture. The absolute values $|N_{\mu,g,Q}^{\mathcal{K}}|$ approach a Gaussian or binomial distribution as a function of $g$, with only three para…

Revised framed LMOV conjecture. For every partition $\mu$,

Let $\mathcal{K}_{\tau}$ be a framed knot with $\tau\in\mathbb{Z}$, and let $f_m(\mathcal{K}_{\tau};q,a)$ be the reduced free-energy coefficients defined from the reduced Chern–Sim…

Let $\tau\in\mathbb{Z}$ be a framing and let … be the reduced open string partition function of $(\mathbb{C}^3,D_{\tau})$. The reduced LMOV conjecture. There exist nonnegative inte…