Wilfrid Kendall. Riemannian barycentres: from harmonic maps and
statistical shape to the classical central limit theorem

The subject of Riemannian barycentres has a surprisingly long history,
tretching back to work of Frechet and Cartan. The first part of this talk
will be a review of the fundamental ideas and a discussion of the work of
various probabilists and statisticians on applications of the concept to
probabilistic approaches to harmonic map theory and statistical shape
theory. I will then present some recent joint work with Huiling Le
concerning central limit theory for empirical barycentres, which to our
considerable surprise has led us to a new perspective on the classical
Lindeberg-Feller central limit theorem.