13 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…

Spectral-network stability-condition conjecture. The collection $\mathcal{P}$ forms a pre-slicing of the standard $\mathbb{V}_{\mathcal{S}}$-collection, and $(Z,\mathcal{P})$ is a…

Let $C$ be the underlying curve, let $\Sigma$ be a real exact Lagrangian in $T^*C$, and let $q_1,\dots,q_\kappa$ be points of $C$. The maps … and … are respectively defined by holo…

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…

Spectral-network stability conjecture. There is a stability condition on the homotopy category of $\mathcal F(S,M;\mathcal E)_{\mathbf K}$ with central charge $Z$, whose semistable…

Let $\mathcal A$ be the Hitchin base. A basic WKB cameral network associated to $a\in\mathcal A$ consists of a suitable homotopy-equivalent open subset of the curve together with f…

Let $P$ be a polynomial with only simple zeroes, and let $Y(P)$ be the convex polygon associated to the minimal harmonic map determined by $P$. Let $\zeta$ be the variable on which…

WKB spectral-network determination conjecture. The WKB exponents determined by the process coincide with the exponents constructed by the spectral network procedure of Gaiotto, Moo…

Pre-building Finsler isometric-embedding conjecture. The factorization $f:B^{\rm pre}_{\phi}\rightarrow B$ is an isometric embedding for the Finsler distance.

Bounded-region finiteness conjecture. On bounded regions, the process stabilizes in finitely many steps.

No-BPS finite stabilization conjecture. The sequence $Z_i$ is well-defined until it reaches a construction with no more fourfold points or sixfold points with triple fold lines; th…

Let $X$ be a Riemann surface and let $\phi$ be a spectral cover. Let $\mathcal W$ be the spectral network associated to $\phi$, and let $\widetilde{\mathcal W}$ be its lift to…

In the $(p,q)$-system, let $\mathfrak g$ be defined by $2\mathfrak g=(p-1)(q-1)$, and let $\{\theta_a\}_{a=1}^{2\mathfrak g}$ denote the D-instanton and ghost D-instanton fugacitie…