0 Isomonodromic deformations in genus zero and one : algebrogeometric solutions and Schlesinger transformations

@inproceedings{Korotkin20080ID,
  title={0 Isomonodromic deformations in genus zero and one : algebrogeometric solutions and Schlesinger transformations},
  author={Dmitry Korotkin},
  year={2008}
}
Here we review some recent developments in the theory of isomonodromic deformations on Riemann sphere and elliptic curve. For both cases we show how to derive Schlesinger transformations together with their action on tau-function, and construct classes of solutions in terms of multi-dimensional theta-functions. The theory of isomonodromic deformations of ordinary matrix differential equations of the type dΨ dλ = A(λ)Ψ , (1.1)