14 Nov 2003; Mat-Nat Faculty (UITO), room U7, 10:15-12:00

Cathrine V. Jensen "Structures on Ordinary Differential Equations: Model equations and Decomposition by symmetries." 

We shall recall and consider different views on linear ODEs, i.e. ODEs as D-modules, ODEs in terms of operators, and, briefly, geometric realization of D-modules and equations in jet-space. The algebraic apparatus helps us determine precise conditions for what invariant structures an equation posesses, such as symmetries, invariant bilinear forms etc. We shall see examples of equations with product and Lie-algebra structure on the space of solutions, that arise as symmetry equations.

We shall discuss symmetries as operators, and strategies to decompose and solve equations with known symmetry algebras in terms of model equations.