Appears in collection : 2024 - T2 - WS3 - Actions of large groups, geometric structures, and the Zimmer program

A priori, the conformal group of a compact Riemannian manifold has no reason to be compact, since it only preserves angles and not distances. A posteriori, however, it turns out that this group is compact, with a single exception: the round sphere! The Lichnerowicz conjecture refers to similar rigidity statements in the cases of pseudo-Riemannian conformal and projective structures.