Colloquium

Seminar information archive ~03/28Next seminarFuture seminars 03/29~

Organizer(s) ABE Noriyuki, IWAKI Kohei, KAWAZUMI Nariya (chair), KOIKE Yuta
URL https://www.ms.u-tokyo.ac.jp/seminar/colloquium/index_e.html

2014/07/11

16:30-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Toshiyuki Kobayashi (Graduate School of Mathematical Sciences, University of Tokyo)
Global Geometry and Analysis on Locally Symmetric Spaces with
Indefinite-metric (JAPANESE)
[ Abstract ]
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.

I plan to explain two programs:

1. (global shape) Existence problem of compact locally homogeneous spaces,
and deformation theory.

2. (spectral analysis) Construction of the spectrum of the Laplacian,
and its stability under the deformation of the geometric structure.

by taking anti-de Sitter manifolds as a typical example.