*Is the Universe Closed? - Existence Problem of Compact Locally Symmetric
Spaces*,

colloquium, Technische Universität Darmstadt, Germany, 12 July 2006.

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 will give a survey 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 models of locally symmetric spaces.

[ poster ]

© Toshiyuki Kobayashi