Artem Dudko: On spectra of self-similar groups and graphs

Studying spectra of self-similar groups and related questions lead to many important discoveries. Self-similar groups contain examples of groups solving various important open questions, including the Grigorchuk group (the first example of finitely generated groups of intermediate growth), the Basilica group (first example of amenable but not subexponentially amenable groups), and the Lamplighter group (a counterexample to a strong Atiyah conjecture). In this talk I will give an introduction to self-similar groups, discuss methods of studying their spectral properties and spectral properties of associated graphs, and present some results on this topic joint with Rostislav Gigorchuk.