with Charlotte Hardouin and Michael Wibmer. Advances in Mathematics, 260 (2014), Pages 1--58. 
Abstract:
We develop a Galois theory for linear differential equations equipped with the action of an endomorphism. This theory is aimed at studying the difference algebraic relations among the solutions of a linear differential equation. The Galois groups here are linear difference algebraic groups, i.e., matrix groups defined by algebraic difference equations.
DOI: 10.1016/j.aim.2014.04.005
ArXiv: 1302.7198
HAL: hal-00997318v1