It is therefore a common practice in mathematics to develop theories of invariants as extensively as possible. The theory of isomonodromic deformations falls within this context, where the main invariant is the monodromy of linear differential equations.

Isomonodromic deformations, indeed, consist of families of linear differential equations whose coefficients exhibit singularities, leading to multi-valued solutions and monodromy properties. Understanding and characterizing these deformations play a crucial role in various areas of mathematics and theoretical physics. The main areas of research developed within the context of the GENIDE project encompass the following applications: