Infinite dimensional sub-Riemannian geometry - Erlend Grong

Title: Infinite dimensional sub-Riemannian geometry.

Abstract: We will talk about different attempts to study sub-Riemannian geometry in infinite dimensional manifolds.
We will first to look at the development of the metric approach to study the space of shapes. Then I will talk about my recent work (joint work with Irina and Alexander), where I try to use the previous ideas in order  to study the space of holomorphic functions. It turns out that many of the properties from sub-Riemannian geometry on finite dimensional principal bundles are generalized to this case.