Marcel Schmidt - Benjamini-Schramm convergent graph sequences and Iharas' Zeta function, 3rd November 2014

In this lecture series we give an introduction to the theory of Benjamini-Schramm convergent graph sequences. We lay the main focus on the convergence of associated spectral quantities such as the eigenvalue counting function and the (normalized) Ihara Zeta function. In particular, we will discuss a class of limit objects of finite graph sequences which are called graphings and show how the limits of the studied spectral quantities relate to quantities on the limit graphing. This discussion yields a glimpse on the definition and on properties of the Ihara Zeta function on infinite graphs.