Members’ Seminar

Sofic groups are the groups whose Cayley graph that can be approximated by finite graphs. This class of groups contains many known classes, e.g. profinite and amenable groups. Quite a few conjectures are known to hold for sofic groups. The most famous one is Connes' embedding conjecture shown for sofic groups by Elek and Szabo. The question if every group is sofic is open. The metric on graphs in the above definition of sofic groups is the so-called Benjamini-Schramm metric. This plays a basic role in the study of sparse graphs, especially in questions about testability and the newly emerging area of graph metrics and limits. We discuss the above notions, connections and a few open problems. The talk will be addressed to a general audience.