Winding Numbers and Topology in Aperiodic Tilings

TYPETheor./Math. Physics Seminar
Speaker:Yaroslav Don
Time:14:30 - 15:30
LocationZoom LINK

Abstract Structural and spectral properties of periodic tilings are well understood and related by the Bloch theorem. For quasiperiodic tilings generated by the Cut and Project (C&P) procedure, we show how to relate structure and spectrum by means of topological numbers originated in windings of a certain phase. For general non-C&P tilings, we illustrate how to establish structural features based on cohomology groups, and present an extension of the Bloch theorem based on these groups.