Existence Problem of Compact Locally Symmetric Spaces, Tuesday Seminar on Topology, University of Tokyo, Japan, 17 April 2007.

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 Lorentz geometry, familiar to us as the space-time of relativity theory, and more generally in pseudo-Riemannian geometry, as well as in various other kinds of geometry (symplectic, complex geometry, ...), surprising little is known about global properties of the geometry even if we impose a locally homogeneous structure.

In this talk, I will give a survey on the recent developments on the question about how the local geometric structure affects the global nature of non-Riemannian manifolds with emphasis on the existence problem of compact models of locally symmetric spaces.

「閉じた局所対称空間の存在問題について」, トポロジー火曜セミナー, 東京大学, 2007年4月17日.

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