## *Existence Problem of Compact Locally Symmetric Spaces*.

colloquium. Harvard University, USA, 17 March 2008.

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.
I plan to give an exposition on the recent developments on the question
about how the local geometric structure affects the global nature of
non-Riemannian manifolds, with emphasis on the existence problem of compact forms, rigidity and
deformation.

[ lecture slides ]

© Toshiyuki Kobayashi