## Graduate Student Organization Seminar

**Date:** September 11, 2019

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 628

**Speaker:** Konrad Wrobel

**Title:** *Random Rooted Graphs*

**Abstract:** Random rooted graphs are connected to many different areas of mathematics, including percolation theory, sofic groups, locally compact groups, and ergodic theory. They arise naturally when one attempts to define a notion of convergence for sequences of finite graphs. We'll introduce Benjamini-Schramm convergence and discuss some open problems and applications related to it. We'll then switch gears and discuss the Mass Transport Principal and unimodular graphs. If time permits, I will mention some applications to percolation theory.