Rémi Reboulet (Chalmers) will speak in the differential geometry seminar at 2pm on 18 December. **Please note that this talk will be in the Salle Debever** (our usual room is being used for undergraduate project presentations). Rémi’s title is *“Flats in the space of Kähler metrics”* and his abstract is below.

*We investigate the space of positive metrics on an ample line bundle over a complex projective manifold from the point of view of metric geometry. It has been known since the work of Mabuchi, Chen and Sun that it can be endowed with the structure of a negatively curved, geodesic metric space. In spaces of negative curvature, one is naturally interested areas that are isometric to a flat space. Those flat subspaces vastly generalise the notion of geodesics, which are one-dimensional examples. I will explain how one can construct flat subspaces of infinite dimension in the space of positive metrics. This is joint work with David Witt Nyström.*