Joint Discrete Maths and Dynamical Systems seminar - Combinatorics of set-valued substitutions

Dates

Wednesday, January 25, 2023 - 14:00 to 15:00

Speaker: Dan Rust (The Open University)

Abstract:
Symbolic dynamics is a subject that benefits from many areas of mathematics, including topology, ergodic theory, operator theory, number theory and combinatorics. There has been a recent explosion in literature on 'set-valued' or 'random' substitutions, which are like substitutions, but instead of mapping a letter to a single word, it is mapped to an element of a finite set of words according to a non-deterministic generating rule. The language generated by a set-valued substitution can be huge. One way to quantify the size of the language is via the entropy of the system. Another way is to count the number of 'periodic blocks' that the language admits. It's therefore important to develop techniques for counting these quantities and establishing growth rates. In this talk, I'll report on the current state of the art for tackling these problems.