Representations of Algebraic Groups in Differential and Difference Galois Theory

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To a differential or difference equation one associates an algebraic group which describes the symmetries and encodes a lot of information about the solutions of the equation. By Tannakian theory, this group is determined by the structure of its representations on objects of the tensor category generated by the solution space. The aim of this project is to apply methods from the structure and representation theory of algebraic groups to study differential (or difference) equations. The first application is the computation of the symmetry group (Galois group) of a given equation. A second goal is the construction of objects with interesting symmetry groups.