Tau Functions as Widom Constants
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DOI: 10.1007/s00220-018-3230-9
Abstract: We define a tau function for a generic Riemann–Hilbert problem posed on a union of non-intersecting smooth closed curves with jump matrices analytic in their neighborhood. The tau function depends on parameters of the jumps… read more here.
Keywords: riemann hilbert; tau; tau functions; tau function ... See more keywords
Quantum curves and q-deformed Painlevé equations
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DOI: 10.1007/s11005-019-01174-y
Abstract: We propose that the grand canonical topological string partition functions satisfy finite-difference equations in the closed string moduli. In the case of genus one mirror curve, these are conjectured to be the q-difference Painlevé equations… read more here.
Keywords: quantum curves; painlev equations; tau functions; topological string ... See more keywords