## *Global Geometry and Analysis on Locally Pseudo-Riemannian
Homogeneous Spaces*.
Japan-Netherlands Seminar. Nagoya University, Japan, 26-30 August
2013.

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 of general signature, surprising little is known about global
properties of the geometry even if we impose a locally homogeneous
structure.
Taking anti-de Sitter manifolds, which are locally modelled on AdS^n as
an example, I plan to explain two programs:

1. (global shape) Exisitence problem of compact locally homogeneous
spaces, and defomation theory.

2. (spectral analysis) Construction of the spectrum of the Laplacian,
and its stability under the deformation of the geometric structure.

[

program ]

© Toshiyuki Kobayashi