13 problems

Borel summability conjecture. The series $h_{\mathrm{s}}(\varphi)$ might be Borel-summable in the variable $e^{-\beta\varphi}$. Since the coefficient ratio exhibits factorial growt…

Let the fermionic matrix integral be defined by the matrix model in the source, with matrix size $N$, and consider its genus expansion in the large $N$ limit. Borel summability con…

The Borel-summability and connection-formula conjecture. If the Stokes graph is saddle-free, then $Z$ is Borel summable, the displayed discrete Fourier series converges and defines…

Let $\cQ$ be an $\hbar$-differential operator, lifted to an $\hbar$-connection after fixing a spin structure, and assume WKB-regularity. Let $L$ be the characteristic variety of…

Let $\cQ$ be an $\hbar$-differential operator, lifted to an $\hbar$-connection after fixing a spin structure, and assume WKB-regularity. Let $L$ be the characteristic variety of…

Let $C=C_{0,2}$ and restrict the coordinate function $\sigma$ on the space of quantum curves to the subspace represented by opers. Consider the Voros symbol associated to this rest…

Fix $(t,\nu)\in D_{t_\ast}\times D_{\nu_\ast}$ and suppose that the Stokes graph for $(t,\nu)$ has no Stokes segment. Let $U$ be a Stokes region, and let…

Absence-of-IR-renormalons conjecture. Four-dimensional $\mathcal{N}=2$ theories do not have infrared renormalon-type singularities.

Let $k\geq 3$, set $m=k-1$, and let $Z_k(\lambda,N)$ and $F_k(\lambda,N)$ denote the partition function and free energy for the positive matrix interaction of order $k$. The paper…

The paper studies positive matrix and tensor models with coupling constant $\lambda$ and matrix size or tensor rank parameter $N$. Their perturbative expansions are Borel--Le Roy s…

The Bremsstrahlung function $B$ is defined by the small-boost expansion of the cusp anomalous dimension, … where $\varphi$ is the boost parameter. In the localized description, let…

Let $R_{\rm odd}$ be the odd part of the formal WKB solution, and let $\lambda(t,{\bf c},\eta;\alpha)$ be the corresponding transseries solution of $(P_{\rm III'})_{D_{6}}$, with f…

Let $S_2$ denote the two-point function defined by the paper's non-perturbative formula for the $bbda \phi^4_D$ theory, and let a Nevanlinna–Sokal disk be given by the condition…