Isomonodromic Deformation Theory

• Isomonodromic deformation theory is the study of parametrized families of meromorphic differential systems with preserved monodromy, connection, and Stokes data.
• It provides a conceptual bridge linking differential equations with geometric aspects, highlighting the role of regular and irregular singularities.
• The theory is applied to analyze stability and transitions in complex systems, offering insights into both theoretical and practical challenges.

Isomonodromic deformation theory is the study of parametrized families of meromorphic differential systems (or flat connections) for which the generalized monodromy data—encompassing conventional monodromy matrices at regular singularities and Stokes matrices, connection matrices, and formal monodromies at irregular singularities—are preserved under deformation. The field provides a conceptual bridge between