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.