## *Global Analysis of Locally Symmetric Spaces with
Indefinite-metric*.
Seminar. University of Padova, Italy, 3 June 2019.

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
pseudo-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.
In this colloquim, I plan to discuss two topics.

Global geometry: Existence problem of compact manifolds modelled
locally on homogeneous spaces, and their deformation theory.

Spectral analysis: Construction of periodic eigenfunctions for
the (indefinite) Laplacian, and stability question of eigenvalues
under deformation of geometric structure.

© Toshiyuki Kobayashi