Speaker: Oriol Sole Pi (MIT)

Title: Graph structure and soficity

Abstract:

A random rooted graph is said to be sofic if it is the Benjamini-Schramm limit of a sequence of finite graphs. Sofic graphs are known to possess a certain property known as unimodularity. In a recent breakthrough, Bowen, Chapman, Lubotzky and Vidick have shown that not all unimodular graphs are sofic. In this talk, I will give an overview of what is known in the other direction: Which additional conditions on the graph are known to imply soficity? Then, I will discuss a novel result in this direction: For any finite graph H, every one-ended, unimodular graph which does not have H as a minor must be sofic.