## *Global Geometry and Analysis on Locally pseudo-Riemannian
Symmetric Spaces*.
Sophus Lie Days.
Cornell, USA, 11 October 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.

[ poster ]

© Toshiyuki Kobayashi