Bethe ansatz and Isomonodromic deformations
  We study symmetries of the Bethe equations for the Gaudin model appeared naturally in the framework of the geometric Langlands correspondence under the name of Hecke operators and under the name of Schlesinger transformations in the theory of isomonodromic deformations, and particularly in the theory of Painlev\'e transcendents. 
D. Talalaev