Uniformity of cocycles

18.05.2022, 13:30  –  Haus 9, Raum 0.17 und Zoom
Forschungsseminar Diskrete Spektraltheorie

Prof. Daniel Lenz (Universität Jena)

Abstract: Uniformity of continuous SL(2,R) valued cocycles over uniquely dynamical systems has featured in various contexts. Walters asked in '86 whether every uniquely ergodic system admits a non-uniform cocycle.  On the other hand in the last two decades uniformity of Schroedinger cocycles has become a main tool in establishing Cantor spectrum of Lebesgue measure zero for quasicrystal operators. Recently, this circle of ideas has lead to  spectral results on graph Laplacians associated to certain self-similar groups. In the talk we will provide some overview on the topic.