At the base of the topic of the workshop is the Galois theory of linear differential equations, the origins of which lie in the 19th century, but which was put on a solid foundation by Ellis Kolchin in the 1940-50's. The Galois group of a homogeneous linear differential equation with coefficients in a differential field is a linear algebraic group defined by equations with coefficients in the field of constants of the differential field. Typically this Galois theory (usually called the Picard-Vessiot theory) does not help to solve the equation or describe solutions, but rather provides invariants of the equation such as the transcendence degree over the base field of a fundamental system of solutions. So, not surprisingly, differential Galois theory is closely related to problems of functional transcendence, namely the study of algebraic relations between functions. The extension of this theory to logarithmic differential equations on (not necessarily linear) algebraic groups is the strongly normal theory of Kolchin. It plays a role in accounts, by the Japanese school, of Painlevé's notion of irreducibility of an ODE, and of new special functions.

Another important contribution of Ellis Kolchin was the theory of differential algebraic groups. These groups are related to differential polynomial equations in the same way that algebraic groups are related to polynomial equations. Although differential algebraic groups can and will (in the workshop) be studied in their own right, the workshop plans to stress the inter-relation of differential algebraic groups and differential Galois theory.

The workshop will also include difference (functional) analogues of the objects mentioned above.

The aim of the workshop is to exchange ideas among the main researchers, give a clear picture of the current state-of-the art to beginning researchers, and discuss new directions.