“Global Analysis of Locally Symmetric Spaces with Indefinite metric”
Lunedì 3 Giugno 2019, ore 10:30 - Aula 1BC45 - Toshiyuki Kobayashi (Università di Tokyo)
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 is known about global properties of the geometry even if we impose a locally homogeneous structure. In this talk, I plan to discuss two topics. Global geometry: Existence problem of compact manifolds modeled 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.