Global Geometry and Analysis on Locally Symmetric Spaces with Indefinite-metric. “Geometric Quantization and Applications” in honour of M. Vergne. Luminy, France, 8-12 October 2018.

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 preudo-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.

I plan to explain two projects:

Global geometry : Existence problem of compact locally homogeneous spaces, and deformation theory.

Spectral analysis : Construction of periodic eigenfunctions for the Laplacian for indefinitemetric, and discuss the stability of eigenvalued under deformation of geometric structure.

[ program(pdf) | titles & abstracts(pdf) ]

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© Toshiyuki Kobayashi