Seminarium Gamma

AbstractIn these two seminar talks I will survey the Lie group theoretic approach to the classical integration method of Darboux -- based on the symmetry reduction of pairs of differential systems admitting a common symmetry group. Topics include:Differential Equations via Differential SystemsFundamental ConstructionsSymmetry Reduction of Differential Systems.Lie EquationsSymbolic ToolsExamplesDarboux Integrable (DI) SystemsThe Equivalence Problem for DI SystemsClassificationsFurther Applications