Felix Ulmer: "Methods to compute properties of the differential Galois group of a given linear differential equation"
IRMAR, Université Rennes, France

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.