## University of Sydney Algebra Seminar

# Boris Kruglikov (University of Tromsų, Norway)

## Friday 16 March, 12:05-12:55pm, Carslaw 175

### Global Lie-Tresse theorem

Consider an algebraic pseudogroup transitively acting on a smooth manifold (more generally on a geometric structure, more generally on an algebraic differential equation). This action naturally extends to the space of infinite jets (partial case: actions by Lie groups). By differential invariant we will understand a rational function on this space, which is invariant with respect to the prolonged action. Alternatively this is a non-linear scalar differential operator (defined globally except for singularities). The main theorem states that the algebra of all scalar differential invariants is generated by a finite number of differential invariants and invariant derivatives. This is the base for solution of the equivalence problem. A number of examples and counter-examples from geometry, algebra and physics (with both finite- and infinite-dimensional groups) will be presented.

The talk is based on joint work with Valentin Lychagin.