## *Global Geometry and Analysis on Locally Symmetric
Spaces—Beyond the Riemannian case*.
colloquium. Yale University, USA, 25 March 2009.

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, as well as in various other kinds of geometry (symplectic,
complex geometry, ... ), surprising little is known about global properties
of the geometry even if we impose a locally homogeneous structure.

In this talk, I plan to give an exposition on the recent developments on
the question about the global natures of locally non-Riemannian
homogeneous spaces, with emphasis on the existence problem of compact
forms, rigidity and deformation.

[

announcement ]

© Toshiyuki Kobayashi