The Newton polygon of the quantum curve for a 3d N=2 brane configuration is conjectured to equal the toric diagram dual to its (p,q) 5-brane web, with derivations for Lagrangian cases and new matrix models for p>=2.
q-Painleve equation from Virasoro constraints
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abstract
The q-Painleve equation, satisfied by the Fourier transform of the q-Virasoro conformal blocks at c=1, is interpreted as a reformulation of the string equation and two other Virasoro constraints in the $5d$ Dotsenko-Fateev matrix model.
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Five-brane webs, 3d $\mathcal{N}=2$ theories and quantum curves
The Newton polygon of the quantum curve for a 3d N=2 brane configuration is conjectured to equal the toric diagram dual to its (p,q) 5-brane web, with derivations for Lagrangian cases and new matrix models for p>=2.