Events for 07/23/2018 from all calendars
Workshop in Analysis and Probability Seminar
Time: 3:00PM - 3:50PM
Location: BLOC 220
Speaker: Beata Randrianantoanina, Miami University
Title: Bilipschitz embeddings of Cayley graphs of lamplighter groups
Abstract: We prove that the sequence of Cayley graphs of finite lamplighter groups $\{\mathbb{Z}_2\wr\mathbb{Z}_n\}_{n\ge 2}$ with a standard set of generators embeds bilipschitzly with uniformly bounded distortions into any non-superreflexive Banach space, and that this sequence is a is a set of test-spaces for superreflexivity in the sense of Ostrovskii. Our proof is inspired by the well known identification of Cayley graphs of infinite lamplighter groups with the horocyclic product of trees. We cover $\mathbb{Z}_2\wr\mathbb{Z}_n$ by three sets with a structure similar to a horocyclic product of trees, which enables us to construct well-controlled embeddings. Using known results, we also observe that, for any $q$, the Cayley graph of the infinite lamplighter group $\mathbb{Z}_q\wr\mathbb{Z}$ with respect to any finite generating set is a test space for superreflexivity. Joint work with Mikhail Ostrovskii.