Multiple notions of low complexity exist for dynamical systems: low structural complexity, e.g. symbol substitution systems and interval exchange maps; low dynamical complexity, e.g. (partial) rigidity, countable (or finite) ergodic measures, loosely Bernoulli propertt, lack of weak mixing and discrete spectrum; and low word complexity subshifts.

Recent work, by various authors, established that (sub)linear word complexity implies low complexity in a variety of other senses, e.g. being substitutive of finite alphabet rank, having at most countably many ergodic measures, necessarily being partially rigid, and so on.

Two major conjectures relate forms of low complexity: the S-adic conjecture, which asserts that there is an explicit relationship between (sub)linear word complexity and a substitutive structure, and the Pisot conjecture, which asserts that, in the context of substitution systems, discrete spectrum is equivalent, roughly, to a specific form of algebraic substitutive structure (and presumably these are also implied, in some sense, by a word complexity property).

The goal of the workshop is to bring together experts in various different areas of low complexity systems research to survey the recent progress, aiming to enhance cross-subfield collaboration and connect the various research programs, ideally leading to potential progress on the aforementioned and other longstanding conjectures.