This is an announcement for the paper Isometric actions on Lp-spaces: dependence on the value of p” by Amine Marrakchi<https://arxiv.org/search/math?searchtype=author&query=Marrakchi%2C+A>, Mikael de la Salle<https://arxiv.org/search/math?searchtype=author&query=de+la+Salle%2C+M>. Abstract: We prove that, for every topological group $G$, the following two sets are intervals: the set of real numbers $p > 0$ such that every continuous action of $G$ by isometries on an $L_p$ space has bounded orbits, and the set of $p > 0$ such that $G$ admits a metrically proper continuous action by isometries on an $L_p$ space. This answers a question by Chatterji--Drutu--Haglund. https://arxiv.org/abs/2001.02490