Séminaire Géométrie et groupes discrets

On the Inverse Problem for Isometry Groups of Norms

by Prof. Emmanuel Breuillard (University of Oxford)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

We study the problem of determining when a compact group can be realized as the group of isometries of a norm on a finite-dimensional real vector space. This problem turns out to be difficult to solve in full generality, but we manage to understand the connected groups that arise as connected components of isometry groups. The classification we obtain is related to transitive actions on spheres (Borel, Montgomery-Samelson) on the one hand and to prehomogeneous spaces (Vinberg, Sato-Kimura) on the other. Joint work with Martin Liebeck, Assaf Naor and Aluna Rizzoli.

Organized by

Fanny Kassel