Abstract: In 1970, Ebin introduced a natural L2-type metric on the infinite-dimensional space of Riemannian metrics over a given manifold. Though the infinite dimensional geometry of this space has been extensively-studied, a new metric perspective emerged in 2013 when Clarke showed that the completion with respect to the Ebin metric turns out to be a CAT(0) space.
Recently, Cavallucci provided a shorter and more conceptual proof of a strengthened result that in addition to being CAT(0) establishes the completion of the space of Riemannian metrics to depend only on the dimension of the underlying manifold.
In this talk I will sketch some of this recent progress and present new results which provide a complete characterization of the self-isometries of the space of Riemannian metrics with respect to the Ebin metric.
The seminar takes place every Friday at 09:45 am in SE 07 and is streamed via moodle.