Title: Thresholds in Complexity
Abstract: The growth rate of the complexity function of a symbolic dynamical system gives rise to combinatorial invariants that allow for a finer classification of zero entropy systems and can be an obstruction for realizing certain dynamic properties. For instance, a celebrated result of Morse and Hedlund in 1938 established a link between the complexity function associated with a subshift and its periodicity; another result by Boshernitzan showed that bounds on the complexity function were related to the number of ergodic measures supported on the subshift.
In this talk, we will review/introduce symbolic dynamical systems, consider some basic results and examples, and then explore the relationship between complexity and a property called loosely Bernoulli. If time permits, we’ll culminate with a recent result done jointly with Van Cyr, Bryna Kra, and Ayse Sahin.