||In the recent years, the nature of the generating series of the walks in the quarter plane have attracted the attention of many authors. The main questions are: are they algebraic, holonomic (solutions of linear differential equations) or at least differentially algebraic (solutions of algebraic differential equations)?
In this talk, I will review what is known and show how difference Galois theory can be used to decide some of these questions. No previous knowledge of this Galois theory is necessary. This is joint work with T. Dreyfus, C. Hardouin and Julien Roques.