Asuka Takatsu. Wasserstein geometry of the space of Gaussian measures.

In this talk, I shall describe the Riemannian/Alexandrov geometry of
Gaussian measures from the view point of the Wasserstein geometry.
Wasserstein geometry is a metric geometry on a space of probability
measures, which has its root in the optimal transport theory. The space of
Gaussian measures is of finite dimension, which allows to write down the
explicit Riemannian metric which in turn induces the Wasserstein distance.
I also give an expression of its sectional curvatures. Its completion as a
metric space provides a complete picture of the singular behavior of the
Wasserstein geometry. In particular, the singular set is stratified
according to the dimension of the support of the Gaussian measures.