László Lempert (Purdue University): On the geometry of the space of Kähler metrics

On a fixed Kahler manifold all possible Kahler metrics form an infinite dimensional manifold H. In the 1980s Mabuchi introduced a Riemannian metric on H, and computed its curvature. The computation suggested that H with its Mabuchi metric is a so called locally symmetric space. I will discuss what this suggestion means, and to what extent it is justified.