66 citations · 86 across the 13 of their papers we have counts for
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The WKB Riemann-Hilbert Problem for the Painlevé I System
Mohamad Alameddine, Olivier Marchal, Nikita Nikolaev +1
In this paper, we solve the direct monodromy problem for the Borel-summed -parameter solution of Painlevé~I. Using the auxiliary time equation, we first construct formal WKB wav…
Explicit Hamiltonian structure of the Flaschka-Newell Painlevé II hierarchy via symmetry reduction of the Painlevé IV hierarchy
Olivier Marchal, Mohamad Alameddine, Sergej Laub
We study the Hamiltonian structure of the Flaschka-Newell Painlevé II hierarchy via symmetry reduction of the associated space of meromorphic connections. Building on the realizati…
A symmetry reduction of the Painlevé IV hierarchy to the Flaschka-Newell Painlevé II hierarchy
Mohamad Alameddine, Olivier Marchal
We study the isomonodromic deformation problem associated with rank-two meromorphic connections on the Riemann sphere having one regular singularity and one irregular singularity o…
Geometry of Logarithmic Topological Recursion: Dilaton Equations, Free Energies and Variational Formulas
Alexander Hock, Olivier Marchal, Nicolas Orantin
One of the most important applications of topological recursion concerns spectral curves for which the functions defining the spectral curve are allowed to have logarithmic…