Tempered Homogeneous Spaces. Symmetry in Geometry and Analysis (organized by M. Pevzner and H. Sekiguchi). Reims University, France, 6-10 June 2022.

We consider the regular representation on the Hilbert space of square integrable functions on a homogeneous space. We address a question about when this unitary representation is tempered.

Surprisingly, this question triggers a new and rich connection of representation theory with some topics from algebra, topology, analysis, and geometry.

We shall explore such features through the new methods introduced in the proof of the temperedness criterion and a classification theory.

The talk will be based on a series of joint papers with Y. Benoist.

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© Toshiyuki Kobayashi