Dirk Frettlöh: Aperiodic Tilings with infinitely many prototiles

Abstract: The study of aperiodic tilings started in the 70s, inspired by works of Dekking, Penrose, Ammann, Hao Wang and others.
Today a lot is known about aperiodic tilings with respect to their spectral, dynamical, topological, combinatorial and algebraic properties. All these results require the tilings to consist of finitely many building blocks ('prototiles') only.
Only recently Manibo, Rust and Walton developed a theory that allows the study of aperiodic tilings with infinitely many prototiles. This talk explores sone of the new phenomena that occur in this context.