The method of equivariant moving frames, computation of invariants, and applications

Peter J. Olver

University of Minnesota

Abstract:

The course will center on the theory and applications of the new, equivariant approach to the classical method of moving frames. The lectures will begin with the case of finite-dimensional Lie group actions, and then move on to more recent developments for infinite-dimensional pseudo-groups. A variety of applications, including structure theory for pseudo-groups, explicit construction and classification of differential invariants, differential invariant algebras, symmetry groups of differential equations, invariant variational problems, and equivalence problems arising in geometry, computer vision, invariant theory and elsewhere will be presented, time permitting.

Prerequisites are basic knowledge of differential geometry and Lie groups. The required aspects of jets, contact structures, prolongation, the variational bicomplex and Lie pseudo-groups will be developed during the course of the lectures. First two chapters of the book P.Olver "Applications of Lie Groups to Differential Equations" (Springer Graduate Texts in Mathematic, 1993) are good, but the key points of the second chapter will be reviewed. Also the material on contact structures in Chapter 4 of the book P.Olver "Equivalence, Invariants, and Symmetry" (Cambridge University Press, 1995) will be useful, but again will be reviewed.