Lie Groups and Representation Theory

Seminar information archive ~07/21Next seminarFuture seminars 07/22~

Date, time & place Tuesday 16:30 - 18:00 126Room #126 (Graduate School of Math. Sci. Bldg.)

2021/06/08

17:00-18:00   Room #Online (Graduate School of Math. Sci. Bldg.)
Kazuki KANNAKA (RIKEN iTHEMS)
The multiplicities of stable eigenvalues on compact anti-de Sitter 3-manifolds (Japanese)
[ Abstract ]
A \textit{pseudo-Riemannian locally symmetric space} is the quotient manifold $\Gamma\backslash G/H$ of a semisimple symmetric space $G/H$ by a discontinuous group $\Gamma$.
Toshiyuki Kobayashi initiated the study of spectral analysis of \textit{intrinsic differential operators} (such as the Laplacian) of a pseudo-Rimannian locally symmetric space. Unlike the classical Riemannian setting,
the Laplacian of a pseudo-Rimannian locally symmetric space is no longer an elliptic differential operator.
In its spectral analysis, new phenomena different from those in the Riemannian setting have been discovered in recent years, following pioneering works by Kassel-Kobayashi.
For instance, they studied the behavior of eigenvalues of intrinsic differential operators of $\Gamma\backslash G/H$ when deforming a discontinuous group $\Gamma$. As a special case, they found infinitely many \textit{stable
eigenvalues} of the (hyperbolic) Laplacian of a compact anti-de Sitter $3$-manifold $\Gamma\backslash
\mathrm{SO}(2,2)/\mathrm{SO}(2,1)$ ([Adv.\ Math.\ 2016]).
In this talk, I would like to explain recent results about the \textit{multiplicities} of stable eigenvalues in the anti-de Sitter setting.