3 problems

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Ooguri–Vafa local model conjecture for singular Hitchin fibers
Let $\bar{\mathcal{M}}^{0}=\mathcal{M}^{0}/Q$ be the SYZ mirror of the local model, and let $\Omega(\xi)$ be the holomorphic symplectic form of its hyperkähler metric. Let $u_0$ be…
Conjecturesolvedhitchin-moduli-spaces hyperkahler-geometry ooguri-vafa-spacesarXiv posted 2 days ago
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Smooth splitting conjecture for the twisted bundle over Hitchin's moduli space
Let $V_z$ be the twisted bundle obtained as the globally defined direct sum of the two locally defined bundles $V_z^1$ and $V_z^2$ over the relevant cover of the Hitchin moduli spa…
Conjecturesolvedhitchin-moduli-spaces hyperholomorphic-connections vector-bundlesarXiv posted 2 days ago
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Riemann–Hilbert uniqueness conjecture for Gaiotto–Moore–Neitzke coordinates
Let $\mathcal{Y}^{RH}_{\gamma}(\xi)$ be the piecewise holomorphic function on the $\xi$ -plane obtained from the Fock–Goncharov coordinate data, with discontinuities on BPS…
Conjecturesolvedhitchin-moduli-spaces riemann-hilbert-problems wall-crossingarXiv posted 2 days ago

Ooguri–Vafa local model conjecture for singular Hitchin fibers