Colloquium: Tuesday, May 7, 2019. Speaker: Yotam Smilansky (Hebrew University). Title: “Multiscale substitution schemes and Kakutani sequences of partitions”.
Place: Room 614 in the Education & Sciences Building
Substitution schemes provide a classical method for constructing tilings of Euclidean space. Allowing multiple scales to appear in the substitution rule we define “multiscale substitution schemes” and study interesting new geometric objects which are generated by such multiscale schemes. In the talk we will focus on Kakutani sequences of partitions, in which every element is defined by the substitution of all tiles of maximal measure in the previous partition, and include the sequences of partitions of the unit interval considered by Kakutani as a special case. Applying new path counting results for directed weighted graphs, we will show that such sequences of partitions are uniformly distributed, thus extending Kakutani’s result. Furthermore, we will describe certain limiting frequencies associated with sequences of partitions, which relate to the distribution of tiles of a given type and the volume they occupy.
Tea will be served before the talk (at 13:50).