Séminaires : Séminaire des Thésards

Le séminaire des thésards est l'occasion pour les doctorants de présenter des résultats et des problématiques dignes d'intérêt devant un public de non-spécialistes. L'ambiance y est informelle ; poser des questions naïves est encouragé, et les questions moins naïves sont bienvenues dans la mesure où elles n'entravent pas le bon déroulement de l'exposé.

Un jeudi sur deux à 18h00, en alternance entre Jussieu et Sophie Germain.

I will start by introducing the notion of p-center of mass and circumcenter, for uniformly convex metric spaces. As examples of such spaces we have non positively curved riemannian manifolds, trees, buildings, CAT(0) cube complexes as well as Lp-spaces. A nice easy consequence of this construction is the fact that any isometric action of a group on a uniformly convex metric space that has a bounded orbit will have a fixed point, namely the center of mass of such a bounded orbit. Inspired by this, I will introduce the property FLp for a locally compact group G, this being the property that for any continuous isometric action of G on any Lp-space this action has to have a fixed point. Another rephrasing of this property is the fact that all 1-cocycles have to be bounded. Inspired by the work of Lafforgue, we will explore the growth of such cocycles in case our group doesn't have property FLp, extending his result from the case p=2. This is based on joint work with Antonio López Neumann. No prior notions of riemannian geometry will be assumed for most of the talk.