Speaker: **Masato Mimura** (Tohoku Univ.)

Title: Group approximation in Cayley topology and coarse geometry, part I: coarse embeddings of amenable groups

Time/Date: 4:30-6:00, Wed. May 21, 2014

Room: 122

Abstract: This is part I of a project with Hiroki Sako (Tokai University). Objective of this project is to study metric geometric properties of coarse disjoint union of finite Cayley graphs. Our main strategy is to employ the Cayley topology (and "the space of marked groups"), which are introduced by Grigorchuk. The topology allows us to regard a group as a point in a compact metrizable space. In this talk, we obtain the characterization of a sequence of finite groups to have property A of Yu. As a byproduct, we have explicit examples of finite special linear groups of unbounded rank, which, respectively, have interesting coarse geometric properties.