Global Analysis of Locally Symmetric Spaces with Indefinite- metric. Zariski Dense Subgroups, Number Theory and Geometric Applications. ICTS, Bangalore, India, 6-17 April 2020.
* Conference was cancelled. Re-rescheduled, April 17-28, 2023.

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 space-time of relativity theory, and more generally in pseudo-Riemannian geometry of general signature, surprising little wa known about global properties of the geometry even if we impose a locally homogeneous structure. This theme has been developed rapidly in the last three decades.

In the series of lectures, I plan to discuss two topics by the general theory and some typical examples.

1. Global geometry: Properness criterion for the action of discrete groups of isometries on reductive homogeneous spaces, existence problem of compact manifolds modeled on homogeneous spaces, and their deformation theory.

2. Spectral analysis: Construction of periodic $L^2$ eigenfunctions for the (indefinite) Laplacian, stability question of eigenvalues under deformation of geometric structure, and spectral decomposition.

References for the first topic include:

References for the second topic include:

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© Toshiyuki Kobayashi