We are interested in Laplacians on graphs associated with finitely generated groups: Cayley graphs and, more generally, Schreier graphs corresponding to some natural group actions. The spectrum of such an operator is a compact subset of the closed interval [-1,1], but not much more can be said about it in general. We will discuss various techniques that allow to construct examples with different types of spectra – connected, union of two intervals, totally disconnected – and with various types of spectral measure. The problem of spectral rigidity will also be addressed.
This video is part of the New York Group Theory Cooperative‘s group theory seminar series.
