8 problems

Let $C$) be a Riemann surface with a compatible $\mathbb{CP}^1$-structure and a spin structure. Let $u=(u_2,\ldots,u_n)\in\bigoplus_{i=2}^n \mathrm{H}^0(C,K^{\otimes i})$, let…

Let $Z(t,\nu,\hbar)$ be the perturbative partition function for the Painlevé I system, and let $\mathfrak S$ denote the Stokes automorphism associated with the $B$-periods. Write…

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 $\cQ$ 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…

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…

Stokes triangulation–seed correspondence conjecture. We have $T=T'$ if and only if $(B',x',y')=(B,x,y)$. This conjecture asserts that the seed obtained from signed mutations record…