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On the monodromy of the deformed cubic oscillator

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arxiv 2006.10648 v2 pith:BZSDHRQB submitted 2020-06-18 math.CA math.AG

Tom Bridgeland , Davide Masoero This is my paper · ORCID
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keywords equationmonodromycubicdeformedfirstknownoscillatorproblems
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We study a second-order linear differential equation known as the deformed cubic oscillator, whose isomonodromic deformations are controlled by the first Painlev{\'e} equation. We use the generalised monodromy map for this equation to give solutions to the infinite-dimensional Riemann-Hilbert problems arising from the Donaldson-Thomas theory of the A2 quiver. These are the first known solutions to such problems beyond the uncoupled case. The appendix by Davide Masoero contains a WKB analysis of the asymptotics of the monodromy map.

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  1. K3 atoms of the cubic fourfold and the BPS structure of the Painlev\'e I determinant line

    math.AG 2026-08 conditional novelty 6.0 of 10

    In solvable models the quantum stability path enters the semiorthogonal selection region at finite time and never leaves; the cubic-fourfold chamber theorem and the full determinant dictionary remain conjectural.

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