## *Global Geometry and Analysis on Locally Symmetric Spaces with Indefinite-metric*.
“Geometric Quantization and Applications” in honour of M. Vergne.
Luminy, France, 8-12 October 2018.

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 preudo-Riemannian geometry, familiar to us as the spacetime 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.
I plan to explain two projects:

**Global geometry** : Existence problem of compact locally homogeneous spaces, and deformation
theory.

**Spectral analysis** : Construction of periodic eigenfunctions for the Laplacian for indefinitemetric, and discuss the stability of eigenvalued under deformation of geometric structure.

[ program(pdf) |
titles & abstracts(pdf) ]

© Toshiyuki Kobayashi