David Damanik: Return to Wonderland

Barry Simon's Wonderland Theorem exhibited the genericity and ubiquity of singular continuous spectrum in the study of Schrödinger operators. In this talk we revisit this issue and in particular the following question: "What is the generic spectral type of a Schrödinger operator with a bounded potential?" Based on recent work of Gorodetski and Kleptsyn, a surprising answer can be given. We will explain this answer, why it is surprising, and how it arises. This is joint work with Artur Avila.