9 problems

Fix $u_1,\ldots,u_n\in{\mathds C}$, $\xi\in S^1$ with $\Re((u_i-u_j)/\xi)<0$ for $i<j$, and $T\in M(n\times n,{\mathds R})$ upper triangular with $T_{ii}=1$ and $T+T^{tr}$ positive…

Let $(w,u_1,\ldots,u_n,\xi,T)$ be data with $w\in{\mathds Z}$, $u_i\in{\mathds C}$ pairwise distinct, $\xi\in S^1$ satisfying $\Re((u_i-u_j)/\xi)<0$ for $i<j$, and…

Let $(H,\nabla,H'_{\mathds R},P)$ be a TERP-structure. It requires no ramification when its formal decomposition can be made without ramification; it is a mixed TERP-structure when…

Let $(\nu^\pm,\rho^\pm)$ be two parameter pairs, and let $\mathscr T^\pm(t,\nu^\pm,\rho^\pm,\hbar)$ be analytic $\tau$-functions of $(P_{\rm I})$ defined on domains containing…

Let $\nabla$ be a WKB-regular $\hbar$-flat connection with strongly GMN spectral curve, let $\Psi$ be a WKB formal solution, and let $\cL\Psi$ be its Borel–Laplace dual. Let…

Let $\alpha$ and $\beta$ be critical points, let $\tau(\alpha)$ and $\tau(\beta)$ denote their corresponding torsions, and let $\mathcal{S}_{\alpha}^{\beta}$ be the Stokes coeffici…

Fix $(t,\nu)\in D_{t_\ast}\times D_{\nu_\ast}$ so that the Stokes graph has no Stokes segment. Let $C$ be a Stokes curve connecting a branch point $e$ and $\infty$, forming a commo…

Let $M>1/2$, let $k$ be any value, and let $\psi^{(1)}_{[k]}(z,\overline{z};\theta)$ denote the Symanzik-rescaled solution of the differential equations for $\psi^{(1)}$ and…

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…