Mathematics Colloquium - Yotam Smilansky (The Hebrew University of Jerusalem)
Yotam Smilansky (The Hebrew University of Jerusalem), Multiscale substitution schemes and Kakutani sequences of partitions.
Substitution schemes provide a classical method for constructing tilings of Euclidean space. Allowing multiple scales in the scheme, we introduce a rich family of sequences of tile partitions generated by the substitution rule, which include the sequence of partitions of the unit interval considered by Kakutani as a special case. In this talk we will use new path counting results for directed weighted graphs to show that such sequences of partitions are uniformly distributed, thus extending Kakutani's original 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.
November 8, 2018
12:30 PM — 1:30 PM
The City College of New York
160 Convent Ave
North Academic Center