Deformations with a resonant irregular singularity

I review topics of my talk in Alcalá, inspired by the paper [1]. An isomonodromic system with irregular singularity at z=∞ (and Fuchsian at z=0) is considered, such that z=∞ becomes resonant for some values of the deformation parameters. Namely, the eigenvalues of the leading matrix at z=∞ coalesce along a locus in the space of deformation parameters. I give a complete extension of the isomonodromy deformation theory in this case.