Global Analysis of Locally Symmetric Spaces with Indefinite-metric. Colloquium. Yale University, USA, 17 April 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.

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© Toshiyuki Kobayashi