## *Global Geometry and Analysis on Locally Homogeneous Spaces*.
IPMU Colloquium. IPMU, the University of Tokyo, Japan, 14 December
2011.

The local to global study of geometries was a major trend of 20th
century geometry, with remarkable developments achieved particularly in
Riemannian geometry.
In contrast, in areas such as Lorentz geometry, familiar to us as the
space-time of relativity theory, and more generally in pseudo-Riemannian
geometry, surprising little is known about global properties of the geometry even
if we impose a locally homogeneous structure. Further, almost nothing
is known on global analysis on such spaces.
Taking anti-de Sitter manifolds, which are locally modelled on AdS^n
as an example, I plan to explain two programs:

1. (global shape) Is a locally homogeneous space closed?

2. (spectral analysis) Does spectrum of the Laplacian vary when we
deform the geometric structure?

[ announcement ]

© Toshiyuki Kobayashi