On invariants and equivalence differential operators under algebraic Lie pseudogroups actions

It is the concluding talk on invariants and the equivalence of differential operators under actions of Lie pseudogroups. We'll show, that under some natural algebraic restrictions on Lie pseudogroups and nonlinearities of differential operators under consideration, there is a reasonable description of their orbits under the Lie pseudogroups, as well as local model forms. Then, the general approach will be applied to the Cartan list of primitive Lie pseudogroups.