Benjamini-Schramm convergence is a recently emerging subject that connects graph theory to ergodic theory, group theory, geometry, percolation theory and algebraic topology. In the course we will learn spectral theory of graphs and groups, covering some active venues of research in group theory.
This is an Inquiry Based Learning course, using a mixture of Moore method and the Hungarian exploration based teaching tradition. I developed this course format at the University of Chicago where I spent 7 years, teaching IBL for both regular classes and their REU. The workload is considerably higher than for a normal course, and it starts slow, but by the end it gets much more effective.
The prerequisites for the course are as follows. If you have seen graphs, groups, measures, linear algebra, basic probability theory and point set topology (compactness), you will be fine. If a few of those are missing, there will be crash course sheets. If more than 3 of the above topics are missing, the course is probably not for you.