9 problems

Let $f_\infty(y)$ be the generating function in Eq., and let $\tilde{f}_\infty(y)$ be its asymptotic expansion as $y\to0$ with $\Im(y)>0$. Strong-coupling median-resummation conjec…

Let $\mathbf{T}$ be the set of 2-functions and let $W\in\mathbf{T}$. Construct a spectral curve $\mathcal{C}_W$ associated with $W$, apply topological recursion to obtain symplecti…

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 $q$ and $x$ be formal variables, and for each fixed integer $m\geq1$ let $n_{m,k}$ be positive integers indexed by finitely many $k\in I_m$. Refined Rogers–Ramanujan conjecture…

Let $\tau\in\mathbb{Z}$ be a framing, let $Z^{(\mathbb{C}^3,\mathcal{D}_\tau)}(\mathbf{x};q)$ be the framed open-string partition function, and let $f_n^\tau(q)$ be the coefficient…

Ooguri–Vafa integrality conjecture. One has

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…

Let $\rho_S$ be the inverse of the quantized mirror-curve operator acting on $L^2(\mathbb R)$, let $\Xi_S(\kappa,\boldsymbol{\xi},\hbar)$ denote its Fredholm determinant, and write…