15 citations · 69 across the 13 of their papers we have counts for
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Modular transformations of tau functions and conformal blocks on the torus
Fabrizio Del Monte, Harini Desiraju, Pavlo Gavrylenko
The connection problem for isomonodromic tau functions on the one-punctured torus concerns the ratio between the tau function and its modular transform, associated to dual pants de…
Riemann-Hilbert problems, Fredholm determinants, explicit combinatorial expansions, and connection formulas for the general -Painlevé III tau functions
Pavlo Gavrylenko
We reformulate the -difference linear system corresponding to the -Painlevé equation of type as a Riemann-Hilbert problem on a circle. Then, we consider the Fred…
Monodromy dependence and symplectic geometry of isomonodromic tau functions on the torus
Fabrizio Del Monte, Harini Desiraju, Pavlo Gavrylenko
We compute the monodromy dependence of the isomonodromic tau function on a torus with Fuchsian singularities and residue matrices by using its explicit Fredholm determi…
Quantum spectral problems and isomonodromic deformations
Mikhail Bershtein, Pavlo Gavrylenko, Alba Grassi
We develop a self-consistent approach to study the spectral properties of a class of quantum mechanical operators by using the knowledge about monodromies of linear sys…
Isomonodromic tau functions on a torus as Fredholm determinants, and charged partitions
Fabrizio Del Monte, Harini Desiraju, Pavlo Gavrylenko
We prove that the isomonodromic tau function on a torus with Fuchsian singularities and generic monodromies in can be written in terms of a Fredholm determinant…
Irregular conformal blocks, Painlevé III and the blow-up equations
Pavlo Gavrylenko, Andrei Marshakov, Artem Stoyan
We study the relation of irregular conformal blocks with the Painlevé III equation. The functional representation for the quasiclassical irregular block is shown to be consiste…
Crossing invariant correlation functions at from isomonodromic functions
Pavlo Gavrylenko, Raoul Santachiara
We present an approach that gives rigorous construction of a class of crossing invariant functions in CFTs from the weakly invariant distributions on the moduli space $\mathc…
Higher rank isomonodromic deformations and W-algebras
P. Gavrylenko, N. Iorgov, O. Lisovyy
We construct the general solution of a class of Fuchsian systems of rank as well as the associated isomonodromic tau functions in terms of semi-degenerate conformal blocks of $…