IRMAR, Université Rennes, France

ulmer@univ-rennes1.fr

http://www.maths.univ-rennes1.fr/~ulmer

To decide if a given equation has Liouvillian solutions (solutions that can be written down using integrals, exponential functions and algebraic extensions) or to apply the result of Morales-Ramis to test the integrability of a Hamiltonian system one needs to decide if the differential Galois group has special properties. We will discuss some approaches and problems in the particular case of irreducible differential Galois groups.