My life in manifolds

The talk will contain some informal reflections on the roles manifolds have played in statistics historically, Including what I like to call the “Evil Manifold”, the “Casino Manifold” and the "Surprisal Manifold.” I will also alert us to some exciting developments in recent years on optimization over manifolds, including over linear finite element surfaces. It will be argued that we have hardly begun to escape “Decartes/Hilbert Box”, and that exciting times are just around the corner.