In Galois theory, one asks for the smallest number of parameters needed to write down a generic Galois extension with Galois group G which specializes to all other Galois extensions with Galois group G (when it exists). One uses the essential dimension of G to give a lower bound to this number.
Similarly in differential Galois theory, one asks for the smallest number of parameters needed to write down a generic differential Galois extension for a given differential Galois group. The goal of this talk will be to introduce the analogous notion of differential essential dimension to bound this number, and to compute the differential essential dimension in some examples.