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Lie Groups and Representation Theory
Seminar information archive ～12/28｜Next seminar｜Future seminars 12/29～
| Date, time & place | Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.) |
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2025/07/15
14:30-15:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Kazuki Kannaka (Kanazawa University)
Zariski-dense deformations of standard discontinuous groups for pseudo-Riemannian homogeneous spaces
Kazuki Kannaka (Kanazawa University)
Zariski-dense deformations of standard discontinuous groups for pseudo-Riemannian homogeneous spaces
[ Abstract ]
In higher-dimensional Riemannian compact locally symmetric spaces, rigidity theory has been developed by Selberg, Weil, Mostow, Margulis, and so on. On the other hand, since the late 1980s, Toshiyuki Kobayashi initiated the study of deformation theory for locally symmetric spaces beyond the Riemannian setting. In particular, a family of pseudo-Riemannian compact locally symmetric spaces of arbitrarily high dimension without local rigidity were discovered. In this talk, we focus on a class of pseudo-Riemannian compact locally symmetric spaces known as standard ones. We explore questions such as the following: (1) Do they possess local rigidity? (2) Can they be continuously deformed into non-standard ones? For example, we show that compact space forms of constant negative curvature with signature (4, 3) in dimension 7 admit continuous deformations, analogous to hyperbolic compact Riemann surfaces. These deformations are constructed using the bending construction, originally introduced by Thurston. This talk is based on joint work (arXiv:2507.03476) with Toshiyuki Kobayashi.
In higher-dimensional Riemannian compact locally symmetric spaces, rigidity theory has been developed by Selberg, Weil, Mostow, Margulis, and so on. On the other hand, since the late 1980s, Toshiyuki Kobayashi initiated the study of deformation theory for locally symmetric spaces beyond the Riemannian setting. In particular, a family of pseudo-Riemannian compact locally symmetric spaces of arbitrarily high dimension without local rigidity were discovered. In this talk, we focus on a class of pseudo-Riemannian compact locally symmetric spaces known as standard ones. We explore questions such as the following: (1) Do they possess local rigidity? (2) Can they be continuously deformed into non-standard ones? For example, we show that compact space forms of constant negative curvature with signature (4, 3) in dimension 7 admit continuous deformations, analogous to hyperbolic compact Riemann surfaces. These deformations are constructed using the bending construction, originally introduced by Thurston. This talk is based on joint work (arXiv:2507.03476) with Toshiyuki Kobayashi.
