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Rank three representations of Painlevé systems: II. de Rham structure, Fourier--Laplace transformation
Miklos Eper, Szilard Szabo
We use formal microlocalization to describe the Fourier--Laplace transformation between rank 3 and rank 2 D-module representations of Painleve systems. We conclude the existence of…
Rank three representations of Painleve systems: III. Dolbeault structure, spectral correspondence
Miklos Eper, Szilard Szabo
We prove that there exists a holomorphic symplectic isomorphism between the rank 2 and 3 representations of the Painleve systems in the Dolbeault complex structure, and give explic…
Rank three representations of Painlevé systems: I. Wild character varieties
Miklos Eper, Szilard Szabo
We give explicit cubic equations for the wild character varieties corresponding to the rank 3 representations of Painlevé equations, and compare them to the ones of their classical…
Asymptotic geometry of non-abelian Hodge theory and Riemann--Hilbert correspondence, rank three case
Miklos Eper, Szilard Szabo
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 abelianizati…