Title: On the singular spectrum for substitutions.
Abstract: 
We consider symbolic dynamical systems arising from substitutions on a finite alphabet. The classical examples are: "Thue-Morse", "Fibonacci", "Tribonacci", "Rudin-Shapiro". The talk is devoted to the question: which substitution dynamical systems have purely singular spectrum? It turns out that this is related to the properties of a  certain complex matrix cocycle (twisted or "spectral" cocycle),  associated with the substitution. The main part of the talk is based on joint work with A. I. Bufetov from a few years ago, but more recent progress will be discussed as well.