Peter J. Olver (University of Minnesota)
The classical method of moving frames was developed by Elie Cartan into a powerful tool for studying the geometry of submanifolds under certain geometrical transformation groups. In this talk, I will present a new foundation for moving frame theory based on equivariant maps. The method is completely algorithmic, and applies to very general Lie group actions and even infinite-dimensional pseudo-groups. It has led to a wide variety of new applications, ranging over classical differential geometry, differential equations, the calculus of variations, geometric flows, image processing, invariant numerical algorithms, invariant theory, and elsewhere. The talk will survey the key ideas, and present some of the principal applications.