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Asymptotic geometry of non-abelian Hodge theory and Riemann--Hilbert correspondence, rank three $\widetilde{E}_6$ case

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arxiv 2407.20638 v2 pith:JEU5VN6H submitted 2024-07-30 math.AG

Miklos Eper , Szilard Szabo This is my paper · ORCID
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We prove the Geometric P=W conjecture in rank 3 on the three-punctured sphere. We describe the topology at infinity of the related character variety. We use asymptotic abelianization of harmonic bundles away from the ramification divisor and an equivariant approach near the branch points to find the WKB (also known as Liouville--Green or phase-integral) expansion of the involved maps. We analyze the Stokes phenomenon governing their behavior.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Rank three representations of Painleve systems: III. Dolbeault structure, spectral correspondence

    math.AG 2025-08 conditional novelty 7.0 of 10

    Algebraic Nahm transformation gives a holomorphic symplectic isomorphism between the rank-2 and rank-3 (JKT) Dolbeault moduli spaces for all six Painleve systems, realized by explicit elliptic fibrations of types I*_0...

  2. Rank three representations of Painlev\'e systems: I. Wild character varieties

    math.AG 2025-05 conditional novelty 6.0 of 10

    The six rank 3 Joshi-Kitaev-Treharne wild character varieties are affine cubic surfaces, each isomorphic to the corresponding rank 2 Painlevé wild character variety.

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