Finite Rank for Infinite Words and Subshifts by Prof. Cesar Silva, Williams College

Finite Rank for Infinite Words and Subshifts by Prof. Cesar Silva, Williams College, Friday April 11, 1:00 – 1:50pm, North Science Building 015, Wachenheim, Faculty Seminar

Abstract: We will discuss a notion of rank for infinite words and subshifts that we call spacer-rank, extending the notion of rank one for symbolic shifts of Gao and Hill. We construct infinite words of each finite spacer-rank and of unbounded spacer-rank. Finite spacer-rank subshifts have topological entropy zero.  We also study shift dynamical systems associated with infinite words, including those associated to Sturmian sequences, which we show are spacer-rank two systems.