104 citations · 576 across the 29 of their papers we have counts for
23 papers
The generalized Chebotarev problem in higher genus
Marco Bertola
We consider the extension to higher genus Riemann surfaces of the classical Chebotarev problem, with a view towards the development of the theory of Padé\ approximants on algebraic…
New systems of log-canonical coordinates on character varieties of compact Riemann surfaces
Marco Bertola, Dmitry Korotkin, Jordi Pillet
We construct new sets of log-canonical coordinates on the character variety of compact Riemann surfaces. These are labelled by families of no…
Rational Solutions of Painlevé V from Hankel Determinants and the Asymptotics of Their Pole Locations
Malik Balogoun, Marco Bertola
In this paper, we analyze the asymptotic behaviour of the poles of certain rational solutions of the fifth Painlevé equation. These solutions are constructed by relating the corres…
Chebotarov continua, Jenkins-Strebel differentials and related problems: a numerical approach
Marco Bertola
We detail a numerical algorithm and related code to construct rational quadratic differentials on the Riemann sphere that satisfy the Boutroux condition. These differentials, in sp…
Szegő Kernel and Symplectic Aspects of Spectral Transform for Extended Spaces of Rational Matrices
Marco Bertola, Dmitry Korotkin, Ramtin Sasani
We revisit the symplectic aspects of the spectral transform for matrix-valued rational functions with simple poles. We construct eigenvectors of such matrices in terms of the Szegő…
Tau-functions and monodromy symplectomorphisms
Marco Bertola, Dmitry Korotkin
We derive a new Hamiltonian formulation of Schlesinger equations in terms of the dynamical -matrix structure. The corresponding symplectic form is shown to be the pullback, unde…