9 papers
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 realizat…
Universal Correlators on Exponentially Ramified Spectral Curves
Mohamad Alameddine, Alexander Hock
We investigate generalized topological recursion on compact spectral curves admitting exponential, and more generally essential, singularities as ramification points. Exploiting th…
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…
Explicit Hamiltonian representations of meromorphic connections and duality from different perspectives: a case study
Mohamad Alameddine, Olivier Marchal
In this article, we present an explicit study of -deformed meromorphic connections in with an unramified irregular pole at infinity of order $r…
Hamiltonian representation of isomonodromic deformations of twisted rational connections: The Painlevé hierarchy
Olivier Marchal, Mohamad Alameddine
In this paper, we build the Hamiltonian system and the corresponding Lax pairs associated to a twisted connection in admitting an irregular and ramifi…
Hamiltonian representation of isomonodromic deformations of general rational connections on
Olivier Marchal, Nicolas Orantin, Mohamad Alameddine
In this paper, we study and build the Hamiltonian system attached to any meromorphic connection with an arbitrary number of non-ramified poles of arbi…