# Abstract

A Riemannian orbifold is a metric space locally modelled on quotients of Riemannian manifolds by finite groups of isometries.

The orbit space of an isometric action of a compact Lie group on a Riemannian manifold has a natural structure of metric space, simply by declaring the distance between two points in the orbit space to be the distance between the corresponding orbits in the manifold.

In this talk, we will discuss the geometry of the examples obtained in our recent classification of representations of compact connected Lie groups whose induced action on the unit sphere has an orbit space isometric to a Riemannian orbifold. This work is part of the larger program of investigating how much of a representation can be recovered from the metric structure of the orbit space. (Joint work with A. Lytchak (Cologne).)

Tea at 15:30 h in room 4A-09.