Tudor Ratiu
Chair, Geometrical Analysis, Mathematics Section
Director, Bernoulli Center
Ecole Polytechnique Federale de Lausanne
Invariant higher order variational problems
Motivated by the problem of longitudinal data assimilation, e.g., in the registration of a sequence of images, we develop the higher-order framework from Langrangian and Hamiltonian reduction by symmetry. In particular, we obtain the reduced variational principles and the associated Poisson brackets. Applications to higher-order geometric k-splines for interpolation on Lie groups will be presented. This is motivated by the need to develop methods for applying template matching to a series of images.