16 problems

Borel summation conjecture. It should be possible to restore $P(z)$ from its Gevrey expansion $\widehat{P}(z)$ using Borel summation as above.

Let a formal series be Borel–Écalle resummed using a choice of well-behaved average. A well-behaved average is the averaging choice used to define the resummed function across the…

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 $\tilde G_{\rm reg}$ and $\tilde b$ be the trans-series for the regular quantity $G_{\rm reg}$ and the physical coupling relation, respectively, and let $S^+$ denote lateral Bo…

Let $F(v)$, $u(v)$, $w_1(v)$, and $\sigma(v)$ be the physical quantities, and let $\tilde F$, $\tilde u$, $\tilde w_1$, and $\tilde\sigma$ denote their corresponding normalized tra…

Let a Borel integral be one of the integrals considered in the paper, and let the resurgent analytic continuation procedure be the decomposition procedure whose uniqueness is prove…

Let $F_{\rm coni}^{\rm resum}(\lambda,t)$ be the analytic function considered in the source, and let $F_{\mathbb R_{>0}}(\lambda,t)$ denote the Borel summation along the positive r…

Let $F_{\rm GV}(\lambda,t)$ be the Gopakumar–Vafa free energy of the resolved conifold, and let $F_{\rm np}(\lambda,t)$ be the non-perturbative completion defined by … Here…

Let $\phi^{0,u}$ and $\phi^{0,s}$ denote the stable and unstable solutions obtained through the Lyapunov–Perron approach, and let $C_{\mathrm{in}}$ be the constant in their leading…

Consider the asymptotic power series arising in topological string theory from conifold free energies and quantized flat coordinates. A peacock pattern is an infinite tower of sing…

A chain-link is a function of the integration scale $hell$. A renormalon is a singularity in the Borel transform associated with the divergent perturbative sum of a set of chains.…

A formal series is resummed by the Borel-Ecalle method using a choice of a well-behaved average, and different well-behaved averages may be used in this construction. Average-indep…

Let ${\rm e}^{{\rm i}\vartheta}\mathbb R_+$ be the ray associated with the phase $\vartheta$, and let ${\mathcal X}_\gamma^\vartheta$ have the asymptotic expansion given by. On the…

In the Gauding--Yang model, let $e(\gamma)$ denote the ground-state energy and write its trans-series as … Here $C_\ell$ and $b_\ell$ are trans-series parameters, and the ambiguity…

First Borel-plane singularity conjecture. The first singularity in the Borel plane of the coupling constant is given by $A$.

Borel resummation conjecture. The Borel resummation of the WKB expansion reproduces the exact values: