UBC Ergodic Theory Seminar: Jacob Richey

Consider all shifts of finite type constrained by a condition on the forbidden set, e.g. only allowing a single forbidden word of fixed length. Which such shifts have the minimum/maximum possible entropy? Among all binary shifts forbidding a single word with a fixed number of 1s, which shifts have the minimum/maximum possible density of 1s (i.e. parry measure of the cylinder set of 1)? I will present old and new results, and many unanswered questions. Symbolic dynamics, probability, and combinatorics will each play a role. Joint work with Brian Marcus.