12 papers
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…
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…
The Painlevé I hierarchy: Correspondence between the isomonodromic approach and the minimal models of the KP hierarchy
Mohamad Alameddine, Nathan Hayford, Olivier Marchal
Two approaches to the Painlevé I hierarchy are discussed: the isomonodromic construction based on meromorphic connections, and the minimal models construction based on a reduction…
A Twisted sl_2(C) Isomonodromic-Isospectral Correspondence
Mohamad Alameddine
The aim of this article is to generalize the isomonodromic-isospectral correspondence for meromorphic connections of rank over to the twisted case. More specific…
Resurgence of Tritronquées Solutions of the Deformed Painlevé I Equation
Mohamad Alameddine, Olivier Marchal, Nikita Nikolaev +1
We prove that the formal -power series solution of the deformed Painlevé I equation is resurgent, which means it is generically Borel summable and its Borel transform admits…
On the geometry of isomonodromic deformations on the torus and the elliptic Calogero-Moser system
Mohamad Alameddine
We consider isomonodromic deformations of connections with a simple pole on the torus, motivated by the elliptic version of the sixth Painlevé equation. We establish an extended sy…
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…
Isomonodromic and isospectral deformations of meromorphic connections: the case
Olivier Marchal, Mohamad Alameddine
We consider non-twisted meromorphic connections in and the associated symplectic Hamiltonian structure. In particular, we provide explicit expressions…
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 construct the Hamiltonian systems attached to generic meromorphic connections with an arbitrary number of unramified poles of arbitr…