Applied Mathematics Seminar: Moving Frames in Applications

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 can be readily applied to completely general Lie group and even infinite-dimensional pseudo-group actions. The resulting theory and applications are remarkably wide-ranging, and include classification of differential invariants, construction and analysis of invariant variational problems and invariant differential equations, the design of symmetry-preserving numerical algorithms, and symmetry and object recognition in computer vision.