"Geometry and Analysis on Groups" Research Seminar

Title: Poincaré profile of connected Lie groups.
Speaker: Romain Tessera (Université Paris-Sud)
Abstract: We introduce a new family of geometric invariants for infinite graphs, and more generally metric measure spaces. Its main strength is that it is monotonous under coarse embedding. For every \(n\) , the \(L^p\) -Poincaré profile is \(n\) times the maximum Cheeger constant of a subgraph of size \(n\) . We compute it for all unimodular connected Lie groups, showing that it is either polynomial or grows like \(n/\log n\). The computation is especially interesting for rank 1 simple Lie groups. We deduce various new non-embeddability results.